├── requirements.txt ├── src ├── constrained_diffusion.egg-info │ ├── dependency_links.txt │ ├── requires.txt │ ├── top_level.txt │ ├── SOURCES.txt │ └── PKG-INFO ├── __init__.py └── constrained_diffusion.py ├── .gitignore ├── images ├── notebook_image_1.png ├── notebook_image_2.png ├── notebook_image_3.png ├── notebook_image_4.png ├── notebook_image_5.png ├── notebook_image_6.png └── notebook_image_7.png ├── examples └── example_files │ ├── example_1_0.png │ ├── example_3_0.png │ ├── example_3_1.png │ ├── example_3_2.png │ ├── example_3_3.png │ ├── example_3_4.png │ └── example_3_5.png ├── pyproject.toml ├── tests ├── extract_ipynb.py ├── test_lin_log.py └── test_decomposition.py ├── README.md └── LICENSE /requirements.txt: -------------------------------------------------------------------------------- 1 | numpy>=1.0.0 2 | scipy>=1.0.0 3 | -------------------------------------------------------------------------------- /src/constrained_diffusion.egg-info/dependency_links.txt: -------------------------------------------------------------------------------- 1 | 2 | -------------------------------------------------------------------------------- /src/constrained_diffusion.egg-info/requires.txt: -------------------------------------------------------------------------------- 1 | numpy>=1.00 2 | scipy>=1.0 3 | -------------------------------------------------------------------------------- /src/constrained_diffusion.egg-info/top_level.txt: -------------------------------------------------------------------------------- 1 | __init__ 2 | constrained_diffusion 3 | -------------------------------------------------------------------------------- /.gitignore: -------------------------------------------------------------------------------- 1 | .gitignore 2 | /dist 3 | run.sh 4 | src/__pycache__/ 5 | bk 6 | .DS_Store 7 | : 8 | -------------------------------------------------------------------------------- /src/__init__.py: -------------------------------------------------------------------------------- 1 | # Package initialization for src 2 | from .constrained_diffusion import constrained_diffusion_decomposition 3 | -------------------------------------------------------------------------------- /images/notebook_image_1.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/gxli/Constrained-Diffusion-Decomposition/HEAD/images/notebook_image_1.png -------------------------------------------------------------------------------- /images/notebook_image_2.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/gxli/Constrained-Diffusion-Decomposition/HEAD/images/notebook_image_2.png -------------------------------------------------------------------------------- /images/notebook_image_3.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/gxli/Constrained-Diffusion-Decomposition/HEAD/images/notebook_image_3.png -------------------------------------------------------------------------------- /images/notebook_image_4.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/gxli/Constrained-Diffusion-Decomposition/HEAD/images/notebook_image_4.png -------------------------------------------------------------------------------- /images/notebook_image_5.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/gxli/Constrained-Diffusion-Decomposition/HEAD/images/notebook_image_5.png -------------------------------------------------------------------------------- /images/notebook_image_6.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/gxli/Constrained-Diffusion-Decomposition/HEAD/images/notebook_image_6.png -------------------------------------------------------------------------------- /images/notebook_image_7.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/gxli/Constrained-Diffusion-Decomposition/HEAD/images/notebook_image_7.png -------------------------------------------------------------------------------- /examples/example_files/example_1_0.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/gxli/Constrained-Diffusion-Decomposition/HEAD/examples/example_files/example_1_0.png -------------------------------------------------------------------------------- /examples/example_files/example_3_0.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/gxli/Constrained-Diffusion-Decomposition/HEAD/examples/example_files/example_3_0.png -------------------------------------------------------------------------------- /examples/example_files/example_3_1.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/gxli/Constrained-Diffusion-Decomposition/HEAD/examples/example_files/example_3_1.png -------------------------------------------------------------------------------- /examples/example_files/example_3_2.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/gxli/Constrained-Diffusion-Decomposition/HEAD/examples/example_files/example_3_2.png -------------------------------------------------------------------------------- /examples/example_files/example_3_3.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/gxli/Constrained-Diffusion-Decomposition/HEAD/examples/example_files/example_3_3.png -------------------------------------------------------------------------------- /examples/example_files/example_3_4.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/gxli/Constrained-Diffusion-Decomposition/HEAD/examples/example_files/example_3_4.png -------------------------------------------------------------------------------- /examples/example_files/example_3_5.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/gxli/Constrained-Diffusion-Decomposition/HEAD/examples/example_files/example_3_5.png -------------------------------------------------------------------------------- /src/constrained_diffusion.egg-info/SOURCES.txt: -------------------------------------------------------------------------------- 1 | LICENSE 2 | README.md 3 | pyproject.toml 4 | src/__init__.py 5 | src/constrained_diffusion.py 6 | src/constrained_diffusion.egg-info/PKG-INFO 7 | src/constrained_diffusion.egg-info/SOURCES.txt 8 | src/constrained_diffusion.egg-info/dependency_links.txt 9 | src/constrained_diffusion.egg-info/requires.txt 10 | src/constrained_diffusion.egg-info/top_level.txt 11 | tests/test_decomposition.py 12 | tests/test_lin_log.py -------------------------------------------------------------------------------- /pyproject.toml: -------------------------------------------------------------------------------- 1 | 2 | [project] 3 | name = "constrained_diffusion" 4 | version = "1.2.4" 5 | description = "Constrained diffusion decomposition: Diffusion-based Multi-Scale Analysis of Complex Iages" 6 | readme = "README.md" 7 | requires-python = ">=3.0" 8 | license = { file = "LICENSE" } 9 | authors = [ 10 | { name = "Guang-Xing Li", email = "ligx.ngc7293@gmail.com" } 11 | ] 12 | classifiers = [ 13 | "Programming Language :: Python :: 3", 14 | "Operating System :: OS Independent", 15 | ] 16 | dependencies = [ 17 | "numpy>=1.00", 18 | "scipy>=1.0", 19 | ] 20 | 21 | 22 | 23 | [build-system] 24 | requires = ["setuptools>=61.0", "wheel"] 25 | build-backend = "setuptools.build_meta" 26 | 27 | 28 | [project.urls] 29 | Homepage = "https://gxli.github.io/Constrained-Diffusion-Decomposition/" 30 | 31 | 32 | 33 | -------------------------------------------------------------------------------- /tests/extract_ipynb.py: -------------------------------------------------------------------------------- 1 | #!/usr/bin/env python3 2 | import json 3 | import base64 4 | import os 5 | from pathlib import Path 6 | 7 | def extract_images_from_ipynb(ipynb_path): 8 | """ 9 | Extract images from a Jupyter Notebook file and save them in the current directory. 10 | 11 | Args: 12 | ipynb_path (str): Path to the .ipynb file 13 | """ 14 | # Check if file exists and is a .ipynb file 15 | if not os.path.exists(ipynb_path) or not ipynb_path.endswith('.ipynb'): 16 | print(f"Error: {ipynb_path} is not a valid .ipynb file") 17 | return 18 | 19 | try: 20 | # Read the notebook 21 | with open(ipynb_path, 'r', encoding='utf-8') as f: 22 | notebook = json.load(f) 23 | 24 | # Counter for naming images 25 | image_count = 1 26 | 27 | # Create output directory if it doesn't exist 28 | output_dir = Path.cwd() 29 | 30 | # Iterate through all cells 31 | for cell in notebook.get('cells', []): 32 | # Check for outputs in code cells 33 | if cell.get('cell_type') == 'code': 34 | for output in cell.get('outputs', []): 35 | # Look for image outputs 36 | if 'data' in output: 37 | for mime_type, data in output['data'].items(): 38 | if mime_type.startswith('image/'): 39 | # Get the image format (e.g., png, jpeg) 40 | image_format = mime_type.split('/')[-1] 41 | 42 | # Decode base64 image data 43 | try: 44 | image_data = base64.b64decode(data) 45 | 46 | # Generate output filename 47 | output_filename = f"notebook_image_{image_count}.{image_format}" 48 | output_path = output_dir / output_filename 49 | 50 | # Save the image 51 | with open(output_path, 'wb') as img_file: 52 | img_file.write(image_data) 53 | 54 | print(f"Saved image: {output_path}") 55 | image_count += 1 56 | 57 | except Exception as e: 58 | print(f"Error decoding image {image_count}: {str(e)}") 59 | 60 | # Check for markdown cells with embedded images 61 | elif cell.get('cell_type') == 'markdown': 62 | source = ''.join(cell.get('source', [])) 63 | # Simple check for base64 encoded images in markdown 64 | if 'data:image' in source: 65 | print(f"Warning: Found potential embedded image in markdown cell. " 66 | f"Manual extraction may be needed for cell: {source[:50]}...") 67 | 68 | except Exception as e: 69 | print(f"Error processing notebook: {str(e)}") 70 | 71 | if __name__ == "__main__": 72 | import sys 73 | if len(sys.argv) != 2: 74 | print("Usage: python extract_ipynb_images.py ") 75 | sys.exit(1) 76 | 77 | ipynb_file = sys.argv[1] 78 | extract_images_from_ipynb(ipynb_file) -------------------------------------------------------------------------------- /tests/test_lin_log.py: -------------------------------------------------------------------------------- 1 | """ 2 | test_decomposition.py 3 | 4 | A testing program to demonstrate and compare the 'log' and 'lin' modes of the 5 | constrained_diffusion_decomposition function. 6 | 7 | The script generates a complex 1D signal with overlapping positive and negative 8 | features at different scales and visualizes the output for both modes. 9 | """ 10 | import numpy as np 11 | import matplotlib.pyplot as plt 12 | import sys 13 | import os 14 | 15 | # ============================================================================= 16 | # DYNAMIC IMPORT BLOCK 17 | # ============================================================================= 18 | try: 19 | # Assuming the function is in a file named `constrained_diffusion.py` in a 'src' folder 20 | from src.constrained_diffusion import constrained_diffusion_decomposition 21 | except ModuleNotFoundError: 22 | # If the script is in an 'examples' folder, go up one level and into 'src' 23 | current_dir = os.path.dirname(os.path.abspath(__file__)) 24 | # Corrected path joining for robustness 25 | src_path = os.path.join(current_dir, '../src/') 26 | sys.path.append(os.path.normpath(src_path)) 27 | print(f"Added to path: {src_path}") 28 | from constrained_diffusion import constrained_diffusion_decomposition 29 | 30 | # ============================================================================= 31 | # Helper Functions 32 | # ============================================================================= 33 | 34 | def gaussian(x, mu, sig): 35 | """Generates a Gaussian function.""" 36 | return np.exp(-np.power(x - mu, 2.) / (2 * np.power(sig, 2.))) 37 | 38 | def plot_decomposition_1d(original, results, residual, scales, title): 39 | """ 40 | Helper function to plot the 1D decomposition results. 41 | Each channel is plotted below the previous one for clarity. 42 | """ 43 | fig, ax = plt.subplots(figsize=(14, 10)) 44 | fig.suptitle(title, fontsize=18, weight='bold') 45 | 46 | # Plot original signal at the top 47 | ax.plot(original, 'k-', label='Original Signal', linewidth=2.5) 48 | 49 | # Calculate a vertical shift to separate the channels visually 50 | v_shift = (np.max(original) - np.min(original)) * 1.1 51 | colors = plt.cm.viridis(np.linspace(0, 1, len(results))) 52 | 53 | # Plot each decomposition channel 54 | for i, (channel, scale) in enumerate(zip(results, scales)): 55 | y_pos = -(i + 1) * v_shift 56 | ax.plot(channel + y_pos, color=colors[i], linewidth=2, 57 | label=f'Channel {i}') 58 | # Add a text label for the representative scale 59 | ax.text(5, y_pos, f'Scale ≈ {scale:.2f}', verticalalignment='bottom', 60 | fontsize=10, bbox=dict(facecolor='white', alpha=0.5, pad=2)) 61 | 62 | # Plot the residual at the bottom 63 | y_pos_resid = -(len(results) + 1) * v_shift 64 | ax.plot(residual + y_pos_resid, color='firebrick', linestyle='--', 65 | label='Residual', linewidth=2) 66 | ax.text(5, y_pos_resid, 'Residual', verticalalignment='bottom', 67 | fontsize=10, bbox=dict(facecolor='white', alpha=0.5, pad=2)) 68 | 69 | ax.grid(True, linestyle=':', alpha=0.6) 70 | ax.set_title('Decomposition Channels (Vertically Shifted for Clarity)') 71 | ax.set_xlabel('Signal Index') 72 | ax.set_yticks([]) # Hide y-axis ticks as amplitudes are relative 73 | ax.set_ylabel('Component Amplitude -->') 74 | ax.legend(loc='upper right') 75 | plt.tight_layout(rect=[0, 0.03, 1, 0.95]) 76 | plt.show() 77 | 78 | # ============================================================================= 79 | # 1. Generate Complex Test Signal 80 | # ============================================================================= 81 | print("--- Generating test signal with overlapping features ---") 82 | x = np.linspace(0, 1000, 1000) 83 | 84 | # A composite signal with features at different scales and signs 85 | # - Small, sharp positive peak (sigma=8) 86 | # - Medium, broader negative peak (sigma=25) 87 | # - Large, very broad positive peak (sigma=80) 88 | signal = ( 89 | 1.0 * gaussian(x, 200, 8) + 90 | -0.8 * gaussian(x, 350, 25) + 91 | 0.9 * gaussian(x, 650, 80) 92 | ) 93 | print("Signal generated.\n") 94 | 95 | 96 | # ============================================================================= 97 | # 2. Test Case: Logarithmic Decomposition 98 | # ============================================================================= 99 | print("--- Running Test Case 1: Logarithmic Decomposition ---") 100 | log_results, log_residual, log_scales = constrained_diffusion_decomposition( 101 | data=signal, 102 | min_scale=5, 103 | max_scale=100, 104 | mode='log', 105 | log_scale_base=2.0, 106 | constrained=True, 107 | return_scales=True 108 | ) 109 | 110 | print(f"\n--> Returned Representative Log Scales: {np.round(log_scales, 2)}") 111 | plot_decomposition_1d( 112 | signal, 113 | log_results, 114 | log_residual, 115 | log_scales, 116 | "Test Case 1: Logarithmic Decomposition (log_scale_base=2.0)" 117 | ) 118 | 119 | 120 | # ============================================================================= 121 | # 3. Test Case: Linear Decomposition 122 | # ============================================================================= 123 | print("\n--- Running Test Case 2: Linear Decomposition ---") 124 | lin_results, lin_residual, lin_scales = constrained_diffusion_decomposition( 125 | data=signal, 126 | min_scale=5, 127 | max_scale=100, 128 | mode='lin', 129 | linear_scale_step=20, # Create channels of width 20 pixels 130 | constrained=True, 131 | return_scales=True 132 | ) 133 | 134 | print(f"\n--> Returned Representative Linear Scales: {np.round(lin_scales, 2)}") 135 | plot_decomposition_1d( 136 | signal, 137 | lin_results, 138 | lin_residual, 139 | lin_scales, 140 | "Test Case 2: Linear Decomposition (linear_scale_step=20)" 141 | ) -------------------------------------------------------------------------------- /README.md: -------------------------------------------------------------------------------- 1 | # Constrained Diffusion Decomposition: A PDE-based Image Decomposition Method 2 | 3 | ## General Design 4 | A natural image often contains components of different scales. This project provides a powerful tool to decompose N-dimensional `numpy.ndarray` data into its constituent scale components. 5 | 6 | The decomposition is highly flexible, allowing for **logarithmically** or **linearly** spaced scales that can be **automatically determined** from the data's shape or specified manually by the user. 7 | 8 | The code is based on the principles described in 9 | Li 2022, Multi-Scale Decomposition of Astronomical Maps -- Constrained Diffusion Method. 10 | 11 | Assuming an input of I(x, y), the decomposition is achieved by solving the equation: 12 | 13 | ```math 14 | \frac{\partial I_t }{\partial t} ={\rm sgn}(I_t) \mathcal{H}({- \rm sgn}(I_t) \nabla^2 I_t) \nabla^2 I_t 15 | ``` 16 | where the diffusion time `t` is related to the characteristic scale `l` by `t = l²/2`. 17 | 18 | ## Key Features 19 | 20 | * **Automatic Parameter Detection**: For ease of use, the decomposition scales (`min_scale`, `max_scale`) and the number of channels (`num_channels`) are automatically inferred from the input data's shape if not provided. 21 | * **Hybrid Upsampling Strategy**: For maximum accuracy and efficiency, the default (`up_sample=True`) mode uses a hybrid approach: 22 | 1. It performs a high-resolution (4x upsampled) decomposition for small scales (<= 5 pixels) to accurately capture fine details. 23 | 2. It then performs a standard decomposition on the residual for all larger scales. 24 | * **Constrained vs. Unconstrained Modes**: 25 | * The default (`constrained=True`) uses a sign-based constrained algorithm that is guaranteed to be artifact-free and will not create new peaks or valleys. 26 | * An optional `constrained=False` mode provides a standard linear diffusion decomposition, which is faster but may introduce "ringing" artifacts (negative halos around positive peaks). 27 | * **Inverted Decomposition**: A special `inverted=True` mode allows the algorithm to decompose negative features ("holes" or depressions) within a positive background, rather than the standard behavior of decomposing positive peaks. 28 | * **Fine-Grained Scale Control**: Advanced users can specify the `log_scale_base` or `linear_scale_step` to precisely control the spacing and number of decomposition channels. 29 | 30 | ## Installation 31 | 32 | 1. **From source via git clone:** 33 | ```bash 34 | git clone https://github.com/gxli/Constrained-Diffusion-Decomposition.git 35 | cd Constrained-Diffusion-Decomposition 36 | pip install . 37 | ``` 38 | 39 | 2. **Via `pip`:** 40 | ```bash 41 | pip install constrained-diffusion 42 | ``` 43 | 3. **Via `pip`:** 44 | ```bash 45 | pip install -i https://test.pypi.org/simple/ constrained-diffusion==1.2.4 46 | ``` 47 | ## Usage 48 | 49 | The main entry point is the highly automated `constrained_diffusion_decomposition` function. 50 | 51 | ### Function Signature 52 | ```python 53 | constrained_diffusion_decomposition( 54 | data, 55 | num_channels=None, 56 | max_scale=None, 57 | min_scale=1, 58 | mode='log', 59 | log_scale_base=2.0, 60 | linear_scale_step=None, 61 | up_sample=True, 62 | constrained=True, 63 | inverted=False, 64 | return_scales=False 65 | ) 66 | ``` 67 | 68 | ### Key Parameters 69 | 70 | | Parameter | Description | Default | 71 | | :--- | :--- | :--- | 72 | | `data` | The input N-dimensional NumPy array. | (Required) | 73 | | `mode` | Scale spacing: `'log'` (powers of 2) or `'lin'` (linear). | `'log'` | 74 | | `up_sample` | If `True`, uses the efficient hybrid upsampling strategy. | `True` | 75 | | `constrained`| If `True`, uses the artifact-free constrained algorithm. | `True` | 76 | | `inverted` | If `True`, decomposes depressions ("holes") instead of peaks. | `False` | 77 | | `num_channels`| Number of channels. If `None`, calculated automatically. Ignored in linear mode if `linear_scale_step` is set. | `None` | 78 | | `max_scale` | The largest scale to analyze. If `None`, set to `max(data.shape)/2`. | `None` | 79 | | `min_scale` | The smallest scale to analyze. | `1` | 80 | | `log_scale_base` | The base for logarithmic scale generation. Smaller values create finer scales. | `2.0` | 81 | | `linear_scale_step`| If set, defines a fixed step size for linear mode, overriding `num_channels`.| `None` | 82 | | `return_scales`| If `True`, returns the list of scales used for decomposition. | `False` | 83 | 84 | 85 | ### Input: 86 | 87 | - A `numpy.ndarray` of any shape, e.g., `(nx, ny, nz)`. 88 | 89 | ### Output: 90 | 91 | - By default, a tuple `(results, residual)`. 92 | - If `return_scales=True`, a tuple `(results, residual, scales)`. 93 | 94 | Where: 95 | - **`results`**: A `list` of NumPy arrays. `results[i]` contains structures corresponding to `scales[i]`. 96 | - **`residual`**: A NumPy array containing structures larger than the largest scale. 97 | - **`scales`**: (Optional) The list of scale values used for the decomposition. 98 | 99 | The original data can be perfectly recovered via: `data = np.sum(results, axis=0) + residual`. 100 | 101 | ### Quickstart 102 | 103 | ```python 104 | import constrained_diffusion as cdd 105 | import numpy as np 106 | 107 | # Create some sample data 108 | data = np.random.rand(128, 128) 109 | 110 | # Perform decomposition with default automatic settings 111 | results, residual = cdd.constrained_diffusion_decomposition(data) 112 | 113 | print(f"Decomposed into {len(results)} channels.") 114 | ``` 115 | 116 | ## Example 117 | 118 | This example decomposes an image containing two Gaussian structures of different sizes using the recommended default settings. 119 | 120 | ```python 121 | import matplotlib.pyplot as plt 122 | import numpy as np 123 | from mpl_toolkits.axes_grid1.inset_locator import inset_axes 124 | 125 | # Assuming 'result' is a list of 2D arrays 126 | # Example: result = [np.random.rand(10, 10) for _ in range(6)] # Dummy data for testing 127 | n_images = len(result) 128 | cols = 3 # Fixed number of columns 129 | rows = int(np.ceil(n_images / cols)) # Calculate required rows 130 | 131 | # Determine the global min and max for the shared color scale 132 | vmin = min(np.min(img) for img in result) 133 | vmax = max(np.max(img) for img in result) 134 | 135 | # Create a figure with a grid of subplots 136 | fig, axes = plt.subplots(rows, cols, figsize=(4 * cols, 4 * rows), squeeze=False) 137 | axes = axes.flatten() # Flatten for easier iteration 138 | 139 | # Plot each image in the grid 140 | for idx, img in enumerate(result): 141 | ax = axes[idx] 142 | im = ax.imshow(img, cmap='viridis', vmin=vmin, vmax=vmax) # Use shared color scale 143 | ax.set_title(f'Image {idx + 1}') # Add title for clarity 144 | ax.axis('on') # Show axes (can be turned off with ax.axis('off') if desired) 145 | 146 | # Add colorbar only to the first subplot (top-left) 147 | if idx == 0: 148 | # Create an inset axes for the colorbar inside the first subplot 149 | cax = inset_axes(ax, width="5%", height="50%", loc='lower right', 150 | bbox_to_anchor=(0, 0, 1, 1), bbox_transform=ax.transAxes) 151 | fig.colorbar(im, cax=cax) # Add colorbar to inset axes 152 | 153 | # Hide empty subplots if any 154 | for idx in range(len(result), len(axes)): 155 | axes[idx].set_visible(False) 156 | 157 | # Adjust layout to prevent overlap 158 | plt.tight_layout() 159 | plt.show() 160 | ``` 161 | 162 | The output cleanly separates the small, sharp feature into the early channels, 163 | while the large, smooth structure is captured in the later channels and the 164 | residual. 165 | 166 | 167 | 168 | 169 | 170 | 171 | 172 | 173 | 174 | This 1D example shows the constrained diffusion decomposition can separate 175 | the signal made of a few Gaussians, without introducing negative ripples. 176 | 177 | 178 | 179 | 180 | This 1D example shows the option inverted=True leads to a diffusion which fills 181 | the gaps in the signal. This feature can be used to detect holes or absorption 182 | dips. 183 | 184 | 185 | 186 | 187 | This examples shows the option up_sample=True leads to improved accuracy for the 188 | first channels. 189 | 190 | 191 | 192 | Below is a comparison between standard diffusion and constrained diffusion 193 | decomposition, where the constrained version leads to a better localization 194 | behavior, and a cleaner separation of the two Gaussian blobs. 195 | 196 | 197 | 198 | 199 | ## 200 | Reference: Li 2022, Multi-Scale Decomposition of Astronomical Maps -- Constrained Diffusion Method. 201 | 202 | ## License 203 | See the [LICENSE](LICENSE) file for details. 204 | -------------------------------------------------------------------------------- /tests/test_decomposition.py: -------------------------------------------------------------------------------- 1 | """ 2 | This script provides a comprehensive set of examples for the 3 | `constrained_diffusion_decomposition` function. 4 | 5 | The examples are ordered to highlight key features: 6 | 1. Constrained vs. Unconstrained (1D): Shows how the constraint removes artifacts. 7 | 2. Inverted vs. Standard (1D): Shows how to extract negative features ("holes"). 8 | 3. Upsampled vs. Fixed-Grid (1D): Shows how upsampling improves detail resolution. 9 | 4. Unconstrained (2D): Visualizes the ringing artifacts in 2D. 10 | 5. Constrained (2D): Shows the clean, recommended 2D decomposition result. 11 | """ 12 | import numpy as np 13 | import matplotlib.pyplot as plt 14 | from mpl_toolkits.axes_grid1.inset_locator import inset_axes 15 | import sys 16 | import os 17 | 18 | # ============================================================================= 19 | # DYNAMIC IMPORT BLOCK 20 | # ============================================================================= 21 | try: 22 | # Assuming the function is in a file named `constrained_diffusion.py` 23 | from constrained_diffusion import constrained_diffusion_decomposition 24 | except ModuleNotFoundError: 25 | # If the script is in an 'examples' folder, go up one level and into 'src' 26 | current_dir = os.path.dirname(os.path.abspath(__file__)) 27 | src_path = os.path.join(current_dir, '../src/') 28 | sys.path.append(src_path) 29 | print(f"Added to path: {src_path}") 30 | from constrained_diffusion import constrained_diffusion_decomposition 31 | 32 | # ============================================================================= 33 | # Helper Functions for Plotting 34 | # ============================================================================= 35 | 36 | def plot_comparison_1d(original, res1, res2, resid1, resid2, title, label1, label2): 37 | """ 38 | Generic 1D comparison plotter. Result 1 is SOLID, Result 2 is DASHED. 39 | (This function does not use the scales array for plotting). 40 | """ 41 | fig, ax = plt.subplots(figsize=(12, 9)) 42 | fig.suptitle(title, fontsize=16) 43 | ax.plot(original, 'k-', label='Original Signal', linewidth=2.5, zorder=10) 44 | colors = plt.cm.viridis(np.linspace(0, 1, len(res1) + 1)) 45 | shift_amount = np.max(np.abs(original)) * 1.0 46 | 47 | for i in range(len(res1)): 48 | shift = (i + 1) * shift_amount 49 | color = colors[i] 50 | ax.plot(res1[i] - shift, color=color, linestyle='-', label=f'Ch {i} ({label1})', linewidth=1.5) 51 | ax.plot(res2[i] - shift, color=color, linestyle='--', label=f'Ch {i} ({label2})', linewidth=1.5) 52 | 53 | resid_shift = (len(res1) + 1) * shift_amount 54 | ax.plot(resid1 - resid_shift, color='blue', linestyle='-', label=f'Residual ({label1})') 55 | ax.plot(resid2 - resid_shift, color='blue', linestyle='--', label=f'Residual ({label2})') 56 | 57 | handles, labels = ax.get_legend_handles_labels() 58 | unique_labels = dict(zip(labels, handles)) 59 | ax.legend(unique_labels.values(), unique_labels.keys(), loc='upper right') 60 | 61 | ax.grid(True, linestyle='--', alpha=0.6) 62 | ax.set_title('Decomposition Channels (Vertically Shifted for Clarity)') 63 | ax.set_xlabel('Signal Index') 64 | ax.set_yticks([]) 65 | ax.set_ylabel('Component Amplitude (Shifted)') 66 | plt.tight_layout(rect=[0, 0.03, 1, 0.95]) 67 | plt.show() 68 | 69 | def plot_decomposition_2d(original, results, residual, scales, title): 70 | """ 71 | Plots a single 2D decomposition result using the 'seismic' colormap 72 | and the representative scale for each channel in the titles. 73 | """ 74 | all_components = [original] + results + [residual] 75 | v_abs = max(abs(arr.min()) for arr in all_components if arr.size > 0) 76 | v_abs = max(v_abs, max(abs(arr.max()) for arr in all_components if arr.size > 0)) 77 | vmin, vmax = -v_abs, v_abs 78 | 79 | num_plots = len(results) + 2 80 | cols = int(np.ceil(np.sqrt(num_plots))) 81 | rows = int(np.ceil(num_plots / cols)) 82 | 83 | fig, axes = plt.subplots(rows, cols, figsize=(cols * 4.5, rows * 4)) 84 | axes = axes.flatten() 85 | fig.suptitle(title, fontsize=16) 86 | 87 | # --- Create plot info with new, more descriptive titles --- 88 | plot_info = [('Original Image', original)] 89 | 90 | # CHANGED: The `scales` variable now contains the representative scale for each channel. 91 | # The title should reflect this directly. 92 | for i, channel in enumerate(results): 93 | if i < len(scales): 94 | scale_val = scales[i] 95 | channel_title = f'Channel {i} (Scale ≈ {scale_val:.2f})' 96 | plot_info.append((channel_title, channel)) 97 | else: 98 | # Fallback title if scales array doesn't match results 99 | plot_info.append((f'Channel {i}', channel)) 100 | 101 | plot_info.append(('Residual', residual)) 102 | 103 | # --- Plotting loop --- 104 | im = None 105 | for i, (plot_title, data) in enumerate(plot_info): 106 | im = axes[i].imshow(data, cmap='seismic', vmin=vmin, vmax=vmax) 107 | axes[i].set_title(plot_title) 108 | axes[i].set_xticks([]); axes[i].set_yticks([]) 109 | 110 | # Add a colorbar, attaching it to a specific axes to avoid layout issues 111 | if im and num_plots > 0: 112 | fig.colorbar(im, ax=axes[:num_plots].tolist(), shrink=0.8, location='right', pad=0.05) 113 | 114 | # Hide unused axes 115 | for i in range(num_plots, len(axes)): 116 | axes[i].axis('off') 117 | 118 | plt.tight_layout(rect=[0, 0, 1, 0.95]) 119 | plt.show() 120 | 121 | # ============================================================================= 122 | # Signal and Image Generation 123 | # ============================================================================= 124 | def gaussian(x, mu, sig): 125 | return np.exp(-np.power(x - mu, 2.) / (2 * np.power(sig, 2.))) 126 | 127 | x_1d = np.linspace(0, 500, 500) 128 | signal_1d = (gaussian(x_1d, 100, 5) + gaussian(x_1d, 250, 15) + gaussian(x_1d, 400, 30)) 129 | signal_inverted = gaussian(x_1d, 250, 40) - 0.7 * gaussian(x_1d, 250, 8) 130 | y_2d, x_2d = np.mgrid[0:128, 0:128] 131 | image_2d = (gaussian(np.sqrt((x_2d-40)**2 + (y_2d-40)**2), 0, 3) + 132 | gaussian(np.sqrt((x_2d-90)**2 + (y_2d-90)**2), 0, 20)) 133 | 134 | # ============================================================================= 135 | # TEST CASES 136 | # ============================================================================= 137 | 138 | # --- Test Case 1: Constrained vs. Unconstrained Decomposition (1D) --- 139 | print("--- Running Test Case 1: Constrained vs. Unconstrained (1D Log) ---") 140 | res_con, resid_con, sc = constrained_diffusion_decomposition( 141 | data=signal_1d, max_scale=40, mode='log', constrained=True, up_sample=True, return_scales=True) 142 | # NEW: Print the returned scales 143 | print(f"--> Representative Scales: {np.round(sc, 2)}") 144 | res_uncon, resid_uncon, _ = constrained_diffusion_decomposition( 145 | data=signal_1d, max_scale=40, mode='log', constrained=False, up_sample=True, return_scales=True) 146 | plot_comparison_1d(signal_1d, res_con, res_uncon, resid_con, resid_uncon, 147 | 'Constrained vs. Unconstrained (1D Log)', 'Constrained', 'Unconstrained') 148 | 149 | # --- Test Case 2: Inverted vs. Standard Decomposition --- 150 | print("\n--- Running Test Case 2: Inverted vs. Standard (1D Log) ---") 151 | res_std, resid_std, sc = constrained_diffusion_decomposition( 152 | data=signal_inverted, max_scale=50, mode='log', inverted=False, up_sample=True, return_scales=True) 153 | # NEW: Print the returned scales 154 | print(f"--> Representative Scales: {np.round(sc, 2)}") 155 | res_inv, resid_inv, _ = constrained_diffusion_decomposition( 156 | data=signal_inverted, max_scale=50, mode='log', inverted=True, up_sample=True, return_scales=True) 157 | plot_comparison_1d(signal_inverted, res_inv, res_std, resid_inv, resid_std, 158 | 'Inverted vs. Standard (1D Log)', 'Inverted', 'Standard') 159 | 160 | # --- Test Case 3: Upsampled vs. Fixed-Grid Decomposition --- 161 | print("\n--- Running Test Case 3: Upsampled vs. Fixed-Grid (1D Log) ---") 162 | res_up, resid_up, sc = constrained_diffusion_decomposition( 163 | data=signal_1d, max_scale=40, mode='log', up_sample=True, return_scales=True) 164 | # NEW: Print the returned scales 165 | print(f"--> Representative Scales: {np.round(sc, 2)}") 166 | res_noup, resid_noup, _ = constrained_diffusion_decomposition( 167 | data=signal_1d, max_scale=40, mode='log', up_sample=False, return_scales=True) 168 | plot_comparison_1d(signal_1d, res_up, res_noup, resid_up, resid_noup, 169 | 'Upsampled vs. Fixed-Grid (1D Log)', 'Upsampled', 'Fixed Grid') 170 | 171 | # --- Test Case 4: 2D Unconstrained Decomposition --- 172 | print("\n--- Running Test Case 4: 2D Unconstrained Decomposition ---") 173 | res, resid, sc = constrained_diffusion_decomposition( 174 | data=image_2d, max_scale=32, mode='log', constrained=False, up_sample=True, return_scales=True) 175 | # NEW: Print the returned scales 176 | print(f"--> Representative Scales: {np.round(sc, 2)}") 177 | plot_decomposition_2d(image_2d, res, resid, sc, '2D Decomposition (Unconstrained)') 178 | 179 | # --- Test Case 5: 2D Constrained Decomposition --- 180 | print("\n--- Running Test Case 5: 2D Constrained Decomposition ---") 181 | res, resid, sc = constrained_diffusion_decomposition( 182 | data=image_2d, max_scale=32, mode='log', constrained=True, up_sample=True, return_scales=True) 183 | # NEW: Print the returned scales 184 | print(f"--> Representative Scales: {np.round(sc, 2)}") 185 | plot_decomposition_2d(image_2d, res, resid, sc, '2D Decomposition (Constrained)') -------------------------------------------------------------------------------- /src/constrained_diffusion.py: -------------------------------------------------------------------------------- 1 | import numpy as np 2 | from scipy import ndimage 3 | from math import log 4 | 5 | 6 | 7 | # ============================================================================= 8 | # CORE ENGINE 9 | # ============================================================================= 10 | def constrained_multiscale_decomposition(data, scales, e_rel=3e-2, sm_mode='reflect', constrained=True, inverted=False, verbose=True): 11 | """ 12 | (Core Engine) Perform diffusion decomposition on n-dimensional data. 13 | 14 | This function iteratively decomposes an input array into a series of "channels", 15 | each representing structures within a specific range of scales. It uses a 16 | diffusion-like process, where each step involves smoothing the data and 17 | calculating the difference. 18 | 19 | Args: 20 | data (np.ndarray): The n-dimensional input array to decompose. 21 | scales (list or np.ndarray): A sorted list of scale boundaries defining the upper 22 | edge of each decomposition channel. 23 | e_rel (float): The relative error tolerance used to determine the number of 24 | iterations for each scale channel. A smaller value leads to 25 | more iterations and higher accuracy. Defaults to 3e-2. 26 | sm_mode (str): The mode parameter for `ndimage.gaussian_filter`, specifying 27 | how to handle array boundaries. Defaults to 'reflect'. 28 | constrained (bool): If True (default), uses a sign-preserving constraint where 29 | the decomposition at a pixel cannot overshoot the original 30 | data value. If False, performs standard linear diffusion. 31 | inverted (bool): If True and `constrained` is also True, the algorithm is 32 | modified to decompose negative structures (depressions or "holes") 33 | instead of positive peaks. Has no effect if `constrained` is False. 34 | Defaults to False. 35 | verbose (bool): If True (default), prints progress information for each channel 36 | to the console. 37 | 38 | Returns: 39 | tuple: A tuple containing: 40 | - result (list of np.ndarray): A list where each element is an array 41 | representing a single scale channel of the decomposition. 42 | - residual (np.ndarray): The final smooth residual left after all 43 | scale channels have been extracted. 44 | """ 45 | if data.size == 0: 46 | raise ValueError("Input data array is empty") 47 | if not np.all(np.diff(scales) > -1e-9): 48 | raise ValueError("The 'scales' array must be sorted in increasing order.") 49 | 50 | ntot = len(scales) 51 | 52 | if verbose: 53 | if constrained: 54 | if inverted: print("Running in CONSTRAINED (inverted) mode.") 55 | else: print("Running in CONSTRAINED (standard) mode.") 56 | else: 57 | print("Running in UNCONSTRAINED (linear diffusion) mode.") 58 | 59 | current_data = data.copy() 60 | result = [] 61 | t_beginning = 0.0 62 | 63 | for i, scale_end in enumerate(scales): 64 | channel_image = np.zeros_like(current_data) 65 | t_end = scale_end**2 / 2 66 | if t_beginning > 0: delta_t_max = t_beginning * e_rel 67 | else: delta_t_max = t_end * e_rel 68 | if delta_t_max <= 0: delta_t_max = (t_end - t_beginning) * 0.1 69 | niter = int((t_end - t_beginning) / delta_t_max + 0.5) 70 | niter = max(1, niter) 71 | delta_t = (t_end - t_beginning) / niter 72 | kernel_size = np.sqrt(2 * delta_t) 73 | if verbose: 74 | print(f"Channel {i}: Scale < {scale_end:.2f} pixels, Iterations: {niter}") 75 | 76 | for _ in range(niter): 77 | smooth_image = ndimage.gaussian_filter(current_data, kernel_size, mode=sm_mode) 78 | diff_image = None 79 | if constrained: 80 | diff_image_pos = current_data - np.minimum(current_data, smooth_image) 81 | diff_image_neg = current_data - np.maximum(current_data, smooth_image) 82 | diff_image = np.zeros_like(current_data) 83 | if not inverted: 84 | pos1 = np.where(np.logical_and(diff_image_pos > 0, current_data > 0)) 85 | pos2 = np.where(np.logical_and(diff_image_neg < 0, current_data < 0)) 86 | diff_image[pos1] = diff_image_pos[pos1]; diff_image[pos2] = diff_image_neg[pos2] 87 | else: 88 | pos1 = np.where(np.logical_and(diff_image_neg < 0, current_data > 0)) 89 | pos2 = np.where(np.logical_and(diff_image_pos > 0, current_data < 0)) 90 | diff_image[pos1] = diff_image_neg[pos1]; diff_image[pos2] = diff_image_pos[pos2] 91 | else: 92 | diff_image = current_data - smooth_image 93 | channel_image += diff_image 94 | current_data -= diff_image 95 | result.append(channel_image) 96 | t_beginning = t_end 97 | residual = current_data 98 | return result, residual 99 | 100 | 101 | def constrained_diffusion_decomposition( 102 | data, 103 | num_channels=None, 104 | max_scale=None, 105 | min_scale=1, 106 | mode='log', 107 | log_scale_base=2.0, 108 | linear_scale_step=None, 109 | e_rel=3e-2, 110 | sm_mode='reflect', 111 | up_sample=True, 112 | constrained=True, 113 | inverted=False, 114 | return_scales=False, 115 | verbose=True 116 | ): 117 | """ 118 | Overall wrapper for diffusion decomposition with a highly automated interface. 119 | 120 | Args: 121 | data (np.ndarray): n-dimensional array. 122 | num_channels (int, optional): The number of channels. If None, calculated automatically. 123 | For 'lin' mode, this argument is ignored. 124 | max_scale (float, optional): The largest scale size. If None, set to max(data.shape) / 2. 125 | min_scale (float, optional): The smallest scale size. Defaults to 1. 126 | mode (str): Scale generation mode: 'log' (default) or 'lin'. 127 | log_scale_base (float): The base for logarithmic scale generation. Defaults to 2.0. 128 | linear_scale_step (float, optional): If mode is 'lin', this defines the step size 129 | between scales. This argument is required for 'lin' mode. 130 | e_rel (float): Relative error for diffusion step size. 131 | sm_mode (str): Mode for array boundary extension in convolution. 132 | up_sample (bool): If True (default), uses the hybrid upsampling strategy. 133 | constrained (bool): If True (default), uses the sign-based constrained algorithm. 134 | inverted (bool): If True, decomposes depressions ("holes") instead of peaks. 135 | return_scales (bool): If True, the array of scale boundaries (upper edge of each channel) 136 | is also returned. Defaults to False. 137 | verbose (bool): If True (default), prints progress and diagnostic information to the console. 138 | 139 | Returns: 140 | tuple: By default, returns a tuple of `(results, residual)`. 141 | If `return_scales=True`, returns `(results, residual, scale_edges)`. 142 | """ 143 | # --- Step 1: Validate inputs and determine scale range --- 144 | if mode == 'log' and log_scale_base <= 1: 145 | raise ValueError("log_scale_base must be greater than 1 for logarithmic mode.") 146 | if mode == 'lin' and linear_scale_step is None: 147 | raise ValueError("`linear_scale_step` must be provided when mode is 'lin'.") 148 | if mode == 'lin' and linear_scale_step is not None and linear_scale_step <= 0: 149 | raise ValueError("linear_scale_step must be a positive number.") 150 | 151 | effective_min_scale = float(min_scale) 152 | if max_scale is None: 153 | effective_max_scale = float(max(data.shape) / 2) 154 | if verbose: 155 | print(f"Automatically determined max_scale = {effective_max_scale:.2f} (from data shape {data.shape})") 156 | else: 157 | effective_max_scale = float(max_scale) 158 | if effective_max_scale <= effective_min_scale: 159 | raise ValueError(f"max_scale ({effective_max_scale:.2f}) must be greater than min_scale ({effective_min_scale:.2f}).") 160 | 161 | # --- Step 2: Generate Scale Edges --- 162 | scale_edges = None 163 | if mode == 'log': 164 | if num_channels is None: 165 | if verbose: 166 | print("Automatically determining num_channels for log mode.") 167 | if effective_max_scale <= effective_min_scale: effective_num_channels = 0 168 | else: 169 | log_diff = np.log(effective_max_scale * (1 + 1e-9)) - np.log(effective_min_scale) 170 | effective_num_channels = int(log_diff / np.log(log_scale_base)) + 1 171 | if verbose: 172 | print(f"--> Determined num_channels = {effective_num_channels}") 173 | else: 174 | effective_num_channels = int(num_channels) 175 | 176 | if effective_num_channels < 1: 177 | raise ValueError(f"Number of channels must be at least 1. Calculated value was {effective_num_channels}.") 178 | 179 | start_power = np.log(effective_min_scale) / np.log(log_scale_base) 180 | stop_power = start_power + (effective_num_channels - 1) 181 | scale_edges = np.logspace(start_power, stop_power, num=effective_num_channels, base=log_scale_base) 182 | 183 | adjusted_max_scale = scale_edges[-1] 184 | if abs(adjusted_max_scale - effective_max_scale) > 1e-6: 185 | if verbose: 186 | print(f"NOTE: Adjusted max_scale from {effective_max_scale:.2f} to {adjusted_max_scale:.2f} to align with log_scale_base.") 187 | 188 | elif mode == 'lin': 189 | if verbose: 190 | print(f"Generating linear scales with a step of {linear_scale_step}.") 191 | if effective_max_scale <= effective_min_scale: effective_num_channels = 0 192 | else: 193 | scale_range = effective_max_scale - effective_min_scale 194 | effective_num_channels = int(np.floor(scale_range / linear_scale_step)) + 1 195 | if verbose: 196 | print(f"--> Determined num_channels = {effective_num_channels}") 197 | 198 | if effective_num_channels < 1: 199 | raise ValueError(f"Number of channels must be at least 1. Calculated value was {effective_num_channels}.") 200 | 201 | scale_edges = effective_min_scale + np.arange(effective_num_channels) * linear_scale_step 202 | 203 | adjusted_max_scale = scale_edges[-1] 204 | if (effective_max_scale - adjusted_max_scale) > 1e-6: 205 | if verbose: 206 | print(f"NOTE: Adjusted max_scale from {effective_max_scale:.2f} to {adjusted_max_scale:.2f} to align with linear_scale_step.") 207 | 208 | if scale_edges is None or len(scale_edges) == 0: 209 | raise ValueError("Scale generation failed. Check your min/max_scale and step/num_channels parameters.") 210 | 211 | # --- Step 3: Perform decomposition --- 212 | if not constrained and inverted and verbose: 213 | print("Warning: 'inverted=True' has no effect when 'constrained=False'. Ignoring.") 214 | 215 | core_kwargs = {'e_rel': e_rel, 'sm_mode': sm_mode, 'constrained': constrained, 'inverted': inverted if constrained else False, 'verbose': verbose} 216 | 217 | results = [] 218 | residual = data 219 | if up_sample: 220 | switch_scale = 5.0 221 | zoom_factor = 4 222 | scales_small = scale_edges[scale_edges <= switch_scale] 223 | scales_large = scale_edges[scale_edges > switch_scale] 224 | 225 | current_data = data 226 | if len(scales_small) > 0: 227 | if verbose: 228 | print(f"\n--- STAGE 1: Performing high-resolution decomposition for scales <= {switch_scale} ---") 229 | upsampled_data = ndimage.zoom(current_data, zoom_factor, order=1) 230 | upsampled_scales = scales_small * zoom_factor 231 | upsampled_scales = np.maximum(upsampled_scales, zoom_factor) 232 | upsampled_scales = np.unique(upsampled_scales) 233 | results_small_up, residual_up = constrained_multiscale_decomposition(upsampled_data, upsampled_scales, **core_kwargs) 234 | if verbose: 235 | print('Downsampling small-scale results...') 236 | results_small = [ndimage.zoom(res, 1/zoom_factor, order=1) for res in results_small_up] 237 | results.extend(results_small) 238 | current_data = ndimage.zoom(residual_up, 1/zoom_factor, order=1) 239 | 240 | if len(scales_large) > 0: 241 | if verbose: 242 | print(f"\n--- STAGE 2: Performing fixed-grid decomposition on residual for scales > {switch_scale} ---") 243 | results_large, residual_large = constrained_multiscale_decomposition(current_data, scales_large, **core_kwargs) 244 | results.extend(results_large) 245 | residual = residual_large 246 | else: 247 | residual = current_data 248 | else: 249 | if verbose: 250 | print(f'\n--- Performing standard fixed-grid decomposition for all scales ---') 251 | results, residual = constrained_multiscale_decomposition(data, scale_edges, **core_kwargs) 252 | 253 | # --- Step 4: Return the results --- 254 | if return_scales: 255 | return results, residual, scale_edges 256 | else: 257 | return results, residual -------------------------------------------------------------------------------- /LICENSE: -------------------------------------------------------------------------------- 1 | GNU GENERAL PUBLIC LICENSE 2 | Version 3, 29 June 2007 3 | 4 | Copyright (C) 2007 Free Software Foundation, Inc. 5 | Everyone is permitted to copy and distribute verbatim copies 6 | of this license document, but changing it is not allowed. 7 | 8 | Preamble 9 | 10 | The GNU General Public License is a free, copyleft license for 11 | software and other kinds of works. 12 | 13 | The licenses for most software and other practical works are designed 14 | to take away your freedom to share and change the works. By contrast, 15 | the GNU General Public License is intended to guarantee your freedom to 16 | share and change all versions of a program--to make sure it remains free 17 | software for all its users. We, the Free Software Foundation, use the 18 | GNU General Public License for most of our software; it applies also to 19 | any other work released this way by its authors. You can apply it to 20 | your programs, too. 21 | 22 | When we speak of free software, we are referring to freedom, not 23 | price. Our General Public Licenses are designed to make sure that you 24 | have the freedom to distribute copies of free software (and charge for 25 | them if you wish), that you receive source code or can get it if you 26 | want it, that you can change the software or use pieces of it in new 27 | free programs, and that you know you can do these things. 28 | 29 | To protect your rights, we need to prevent others from denying you 30 | these rights or asking you to surrender the rights. Therefore, you have 31 | certain responsibilities if you distribute copies of the software, or if 32 | you modify it: responsibilities to respect the freedom of others. 33 | 34 | For example, if you distribute copies of such a program, whether 35 | gratis or for a fee, you must pass on to the recipients the same 36 | freedoms that you received. You must make sure that they, too, receive 37 | or can get the source code. And you must show them these terms so they 38 | know their rights. 39 | 40 | Developers that use the GNU GPL protect your rights with two steps: 41 | (1) assert copyright on the software, and (2) offer you this License 42 | giving you legal permission to copy, distribute and/or modify it. 43 | 44 | For the developers' and authors' protection, the GPL clearly explains 45 | that there is no warranty for this free software. For both users' and 46 | authors' sake, the GPL requires that modified versions be marked as 47 | changed, so that their problems will not be attributed erroneously to 48 | authors of previous versions. 49 | 50 | Some devices are designed to deny users access to install or run 51 | modified versions of the software inside them, although the manufacturer 52 | can do so. This is fundamentally incompatible with the aim of 53 | protecting users' freedom to change the software. The systematic 54 | pattern of such abuse occurs in the area of products for individuals to 55 | use, which is precisely where it is most unacceptable. Therefore, we 56 | have designed this version of the GPL to prohibit the practice for those 57 | products. If such problems arise substantially in other domains, we 58 | stand ready to extend this provision to those domains in future versions 59 | of the GPL, as needed to protect the freedom of users. 60 | 61 | Finally, every program is threatened constantly by software patents. 62 | States should not allow patents to restrict development and use of 63 | software on general-purpose computers, but in those that do, we wish to 64 | avoid the special danger that patents applied to a free program could 65 | make it effectively proprietary. To prevent this, the GPL assures that 66 | patents cannot be used to render the program non-free. 67 | 68 | The precise terms and conditions for copying, distribution and 69 | modification follow. 70 | 71 | TERMS AND CONDITIONS 72 | 73 | 0. Definitions. 74 | 75 | "This License" refers to version 3 of the GNU General Public License. 76 | 77 | "Copyright" also means copyright-like laws that apply to other kinds of 78 | works, such as semiconductor masks. 79 | 80 | "The Program" refers to any copyrightable work licensed under this 81 | License. Each licensee is addressed as "you". "Licensees" and 82 | "recipients" may be individuals or organizations. 83 | 84 | To "modify" a work means to copy from or adapt all or part of the work 85 | in a fashion requiring copyright permission, other than the making of an 86 | exact copy. The resulting work is called a "modified version" of the 87 | earlier work or a work "based on" the earlier work. 88 | 89 | A "covered work" means either the unmodified Program or a work based 90 | on the Program. 91 | 92 | To "propagate" a work means to do anything with it that, without 93 | permission, would make you directly or secondarily liable for 94 | infringement under applicable copyright law, except executing it on a 95 | computer or modifying a private copy. Propagation includes copying, 96 | distribution (with or without modification), making available to the 97 | public, and in some countries other activities as well. 98 | 99 | To "convey" a work means any kind of propagation that enables other 100 | parties to make or receive copies. Mere interaction with a user through 101 | a computer network, with no transfer of a copy, is not conveying. 102 | 103 | An interactive user interface displays "Appropriate Legal Notices" 104 | to the extent that it includes a convenient and prominently visible 105 | feature that (1) displays an appropriate copyright notice, and (2) 106 | tells the user that there is no warranty for the work (except to the 107 | extent that warranties are provided), that licensees may convey the 108 | work under this License, and how to view a copy of this License. If 109 | the interface presents a list of user commands or options, such as a 110 | menu, a prominent item in the list meets this criterion. 111 | 112 | 1. Source Code. 113 | 114 | The "source code" for a work means the preferred form of the work 115 | for making modifications to it. "Object code" means any non-source 116 | form of a work. 117 | 118 | A "Standard Interface" means an interface that either is an official 119 | standard defined by a recognized standards body, or, in the case of 120 | interfaces specified for a particular programming language, one that 121 | is widely used among developers working in that language. 122 | 123 | The "System Libraries" of an executable work include anything, other 124 | than the work as a whole, that (a) is included in the normal form of 125 | packaging a Major Component, but which is not part of that Major 126 | Component, and (b) serves only to enable use of the work with that 127 | Major Component, or to implement a Standard Interface for which an 128 | implementation is available to the public in source code form. A 129 | "Major Component", in this context, means a major essential component 130 | (kernel, window system, and so on) of the specific operating system 131 | (if any) on which the executable work runs, or a compiler used to 132 | produce the work, or an object code interpreter used to run it. 133 | 134 | The "Corresponding Source" for a work in object code form means all 135 | the source code needed to generate, install, and (for an executable 136 | work) run the object code and to modify the work, including scripts to 137 | control those activities. However, it does not include the work's 138 | System Libraries, or general-purpose tools or generally available free 139 | programs which are used unmodified in performing those activities but 140 | which are not part of the work. For example, Corresponding Source 141 | includes interface definition files associated with source files for 142 | the work, and the source code for shared libraries and dynamically 143 | linked subprograms that the work is specifically designed to require, 144 | such as by intimate data communication or control flow between those 145 | subprograms and other parts of the work. 146 | 147 | The Corresponding Source need not include anything that users 148 | can regenerate automatically from other parts of the Corresponding 149 | Source. 150 | 151 | The Corresponding Source for a work in source code form is that 152 | same work. 153 | 154 | 2. Basic Permissions. 155 | 156 | All rights granted under this License are granted for the term of 157 | copyright on the Program, and are irrevocable provided the stated 158 | conditions are met. This License explicitly affirms your unlimited 159 | permission to run the unmodified Program. The output from running a 160 | covered work is covered by this License only if the output, given its 161 | content, constitutes a covered work. This License acknowledges your 162 | rights of fair use or other equivalent, as provided by copyright law. 163 | 164 | You may make, run and propagate covered works that you do not 165 | convey, without conditions so long as your license otherwise remains 166 | in force. You may convey covered works to others for the sole purpose 167 | of having them make modifications exclusively for you, or provide you 168 | with facilities for running those works, provided that you comply with 169 | the terms of this License in conveying all material for which you do 170 | not control copyright. Those thus making or running the covered works 171 | for you must do so exclusively on your behalf, under your direction 172 | and control, on terms that prohibit them from making any copies of 173 | your copyrighted material outside their relationship with you. 174 | 175 | Conveying under any other circumstances is permitted solely under 176 | the conditions stated below. Sublicensing is not allowed; section 10 177 | makes it unnecessary. 178 | 179 | 3. Protecting Users' Legal Rights From Anti-Circumvention Law. 180 | 181 | No covered work shall be deemed part of an effective technological 182 | measure under any applicable law fulfilling obligations under article 183 | 11 of the WIPO copyright treaty adopted on 20 December 1996, or 184 | similar laws prohibiting or restricting circumvention of such 185 | measures. 186 | 187 | When you convey a covered work, you waive any legal power to forbid 188 | circumvention of technological measures to the extent such circumvention 189 | is effected by exercising rights under this License with respect to 190 | the covered work, and you disclaim any intention to limit operation or 191 | modification of the work as a means of enforcing, against the work's 192 | users, your or third parties' legal rights to forbid circumvention of 193 | technological measures. 194 | 195 | 4. Conveying Verbatim Copies. 196 | 197 | You may convey verbatim copies of the Program's source code as you 198 | receive it, in any medium, provided that you conspicuously and 199 | appropriately publish on each copy an appropriate copyright notice; 200 | keep intact all notices stating that this License and any 201 | non-permissive terms added in accord with section 7 apply to the code; 202 | keep intact all notices of the absence of any warranty; and give all 203 | recipients a copy of this License along with the Program. 204 | 205 | You may charge any price or no price for each copy that you convey, 206 | and you may offer support or warranty protection for a fee. 207 | 208 | 5. Conveying Modified Source Versions. 209 | 210 | You may convey a work based on the Program, or the modifications to 211 | produce it from the Program, in the form of source code under the 212 | terms of section 4, provided that you also meet all of these conditions: 213 | 214 | a) The work must carry prominent notices stating that you modified 215 | it, and giving a relevant date. 216 | 217 | b) The work must carry prominent notices stating that it is 218 | released under this License and any conditions added under section 219 | 7. This requirement modifies the requirement in section 4 to 220 | "keep intact all notices". 221 | 222 | c) You must license the entire work, as a whole, under this 223 | License to anyone who comes into possession of a copy. This 224 | License will therefore apply, along with any applicable section 7 225 | additional terms, to the whole of the work, and all its parts, 226 | regardless of how they are packaged. This License gives no 227 | permission to license the work in any other way, but it does not 228 | invalidate such permission if you have separately received it. 229 | 230 | d) If the work has interactive user interfaces, each must display 231 | Appropriate Legal Notices; however, if the Program has interactive 232 | interfaces that do not display Appropriate Legal Notices, your 233 | work need not make them do so. 234 | 235 | A compilation of a covered work with other separate and independent 236 | works, which are not by their nature extensions of the covered work, 237 | and which are not combined with it such as to form a larger program, 238 | in or on a volume of a storage or distribution medium, is called an 239 | "aggregate" if the compilation and its resulting copyright are not 240 | used to limit the access or legal rights of the compilation's users 241 | beyond what the individual works permit. Inclusion of a covered work 242 | in an aggregate does not cause this License to apply to the other 243 | parts of the aggregate. 244 | 245 | 6. Conveying Non-Source Forms. 246 | 247 | You may convey a covered work in object code form under the terms 248 | of sections 4 and 5, provided that you also convey the 249 | machine-readable Corresponding Source under the terms of this License, 250 | in one of these ways: 251 | 252 | a) Convey the object code in, or embodied in, a physical product 253 | (including a physical distribution medium), accompanied by the 254 | Corresponding Source fixed on a durable physical medium 255 | customarily used for software interchange. 256 | 257 | b) Convey the object code in, or embodied in, a physical product 258 | (including a physical distribution medium), accompanied by a 259 | written offer, valid for at least three years and valid for as 260 | long as you offer spare parts or customer support for that product 261 | model, to give anyone who possesses the object code either (1) a 262 | copy of the Corresponding Source for all the software in the 263 | product that is covered by this License, on a durable physical 264 | medium customarily used for software interchange, for a price no 265 | more than your reasonable cost of physically performing this 266 | conveying of source, or (2) access to copy the 267 | Corresponding Source from a network server at no charge. 268 | 269 | c) Convey individual copies of the object code with a copy of the 270 | written offer to provide the Corresponding Source. This 271 | alternative is allowed only occasionally and noncommercially, and 272 | only if you received the object code with such an offer, in accord 273 | with subsection 6b. 274 | 275 | d) Convey the object code by offering access from a designated 276 | place (gratis or for a charge), and offer equivalent access to the 277 | Corresponding Source in the same way through the same place at no 278 | further charge. You need not require recipients to copy the 279 | Corresponding Source along with the object code. If the place to 280 | copy the object code is a network server, the Corresponding Source 281 | may be on a different server (operated by you or a third party) 282 | that supports equivalent copying facilities, provided you maintain 283 | clear directions next to the object code saying where to find the 284 | Corresponding Source. Regardless of what server hosts the 285 | Corresponding Source, you remain obligated to ensure that it is 286 | available for as long as needed to satisfy these requirements. 287 | 288 | e) Convey the object code using peer-to-peer transmission, provided 289 | you inform other peers where the object code and Corresponding 290 | Source of the work are being offered to the general public at no 291 | charge under subsection 6d. 292 | 293 | A separable portion of the object code, whose source code is excluded 294 | from the Corresponding Source as a System Library, need not be 295 | included in conveying the object code work. 296 | 297 | A "User Product" is either (1) a "consumer product", which means any 298 | tangible personal property which is normally used for personal, family, 299 | or household purposes, or (2) anything designed or sold for incorporation 300 | into a dwelling. In determining whether a product is a consumer product, 301 | doubtful cases shall be resolved in favor of coverage. For a particular 302 | product received by a particular user, "normally used" refers to a 303 | typical or common use of that class of product, regardless of the status 304 | of the particular user or of the way in which the particular user 305 | actually uses, or expects or is expected to use, the product. A product 306 | is a consumer product regardless of whether the product has substantial 307 | commercial, industrial or non-consumer uses, unless such uses represent 308 | the only significant mode of use of the product. 309 | 310 | "Installation Information" for a User Product means any methods, 311 | procedures, authorization keys, or other information required to install 312 | and execute modified versions of a covered work in that User Product from 313 | a modified version of its Corresponding Source. The information must 314 | suffice to ensure that the continued functioning of the modified object 315 | code is in no case prevented or interfered with solely because 316 | modification has been made. 317 | 318 | If you convey an object code work under this section in, or with, or 319 | specifically for use in, a User Product, and the conveying occurs as 320 | part of a transaction in which the right of possession and use of the 321 | User Product is transferred to the recipient in perpetuity or for a 322 | fixed term (regardless of how the transaction is characterized), the 323 | Corresponding Source conveyed under this section must be accompanied 324 | by the Installation Information. But this requirement does not apply 325 | if neither you nor any third party retains the ability to install 326 | modified object code on the User Product (for example, the work has 327 | been installed in ROM). 328 | 329 | The requirement to provide Installation Information does not include a 330 | requirement to continue to provide support service, warranty, or updates 331 | for a work that has been modified or installed by the recipient, or for 332 | the User Product in which it has been modified or installed. Access to a 333 | network may be denied when the modification itself materially and 334 | adversely affects the operation of the network or violates the rules and 335 | protocols for communication across the network. 336 | 337 | Corresponding Source conveyed, and Installation Information provided, 338 | in accord with this section must be in a format that is publicly 339 | documented (and with an implementation available to the public in 340 | source code form), and must require no special password or key for 341 | unpacking, reading or copying. 342 | 343 | 7. Additional Terms. 344 | 345 | "Additional permissions" are terms that supplement the terms of this 346 | License by making exceptions from one or more of its conditions. 347 | Additional permissions that are applicable to the entire Program shall 348 | be treated as though they were included in this License, to the extent 349 | that they are valid under applicable law. If additional permissions 350 | apply only to part of the Program, that part may be used separately 351 | under those permissions, but the entire Program remains governed by 352 | this License without regard to the additional permissions. 353 | 354 | When you convey a copy of a covered work, you may at your option 355 | remove any additional permissions from that copy, or from any part of 356 | it. (Additional permissions may be written to require their own 357 | removal in certain cases when you modify the work.) You may place 358 | additional permissions on material, added by you to a covered work, 359 | for which you have or can give appropriate copyright permission. 360 | 361 | Notwithstanding any other provision of this License, for material you 362 | add to a covered work, you may (if authorized by the copyright holders of 363 | that material) supplement the terms of this License with terms: 364 | 365 | a) Disclaiming warranty or limiting liability differently from the 366 | terms of sections 15 and 16 of this License; or 367 | 368 | b) Requiring preservation of specified reasonable legal notices or 369 | author attributions in that material or in the Appropriate Legal 370 | Notices displayed by works containing it; or 371 | 372 | c) Prohibiting misrepresentation of the origin of that material, or 373 | requiring that modified versions of such material be marked in 374 | reasonable ways as different from the original version; or 375 | 376 | d) Limiting the use for publicity purposes of names of licensors or 377 | authors of the material; or 378 | 379 | e) Declining to grant rights under trademark law for use of some 380 | trade names, trademarks, or service marks; or 381 | 382 | f) Requiring indemnification of licensors and authors of that 383 | material by anyone who conveys the material (or modified versions of 384 | it) with contractual assumptions of liability to the recipient, for 385 | any liability that these contractual assumptions directly impose on 386 | those licensors and authors. 387 | 388 | All other non-permissive additional terms are considered "further 389 | restrictions" within the meaning of section 10. If the Program as you 390 | received it, or any part of it, contains a notice stating that it is 391 | governed by this License along with a term that is a further 392 | restriction, you may remove that term. If a license document contains 393 | a further restriction but permits relicensing or conveying under this 394 | License, you may add to a covered work material governed by the terms 395 | of that license document, provided that the further restriction does 396 | not survive such relicensing or conveying. 397 | 398 | If you add terms to a covered work in accord with this section, you 399 | must place, in the relevant source files, a statement of the 400 | additional terms that apply to those files, or a notice indicating 401 | where to find the applicable terms. 402 | 403 | Additional terms, permissive or non-permissive, may be stated in the 404 | form of a separately written license, or stated as exceptions; 405 | the above requirements apply either way. 406 | 407 | 8. Termination. 408 | 409 | You may not propagate or modify a covered work except as expressly 410 | provided under this License. Any attempt otherwise to propagate or 411 | modify it is void, and will automatically terminate your rights under 412 | this License (including any patent licenses granted under the third 413 | paragraph of section 11). 414 | 415 | However, if you cease all violation of this License, then your 416 | license from a particular copyright holder is reinstated (a) 417 | provisionally, unless and until the copyright holder explicitly and 418 | finally terminates your license, and (b) permanently, if the copyright 419 | holder fails to notify you of the violation by some reasonable means 420 | prior to 60 days after the cessation. 421 | 422 | Moreover, your license from a particular copyright holder is 423 | reinstated permanently if the copyright holder notifies you of the 424 | violation by some reasonable means, this is the first time you have 425 | received notice of violation of this License (for any work) from that 426 | copyright holder, and you cure the violation prior to 30 days after 427 | your receipt of the notice. 428 | 429 | Termination of your rights under this section does not terminate the 430 | licenses of parties who have received copies or rights from you under 431 | this License. If your rights have been terminated and not permanently 432 | reinstated, you do not qualify to receive new licenses for the same 433 | material under section 10. 434 | 435 | 9. Acceptance Not Required for Having Copies. 436 | 437 | You are not required to accept this License in order to receive or 438 | run a copy of the Program. Ancillary propagation of a covered work 439 | occurring solely as a consequence of using peer-to-peer transmission 440 | to receive a copy likewise does not require acceptance. However, 441 | nothing other than this License grants you permission to propagate or 442 | modify any covered work. These actions infringe copyright if you do 443 | not accept this License. Therefore, by modifying or propagating a 444 | covered work, you indicate your acceptance of this License to do so. 445 | 446 | 10. Automatic Licensing of Downstream Recipients. 447 | 448 | Each time you convey a covered work, the recipient automatically 449 | receives a license from the original licensors, to run, modify and 450 | propagate that work, subject to this License. You are not responsible 451 | for enforcing compliance by third parties with this License. 452 | 453 | An "entity transaction" is a transaction transferring control of an 454 | organization, or substantially all assets of one, or subdividing an 455 | organization, or merging organizations. If propagation of a covered 456 | work results from an entity transaction, each party to that 457 | transaction who receives a copy of the work also receives whatever 458 | licenses to the work the party's predecessor in interest had or could 459 | give under the previous paragraph, plus a right to possession of the 460 | Corresponding Source of the work from the predecessor in interest, if 461 | the predecessor has it or can get it with reasonable efforts. 462 | 463 | You may not impose any further restrictions on the exercise of the 464 | rights granted or affirmed under this License. For example, you may 465 | not impose a license fee, royalty, or other charge for exercise of 466 | rights granted under this License, and you may not initiate litigation 467 | (including a cross-claim or counterclaim in a lawsuit) alleging that 468 | any patent claim is infringed by making, using, selling, offering for 469 | sale, or importing the Program or any portion of it. 470 | 471 | 11. Patents. 472 | 473 | A "contributor" is a copyright holder who authorizes use under this 474 | License of the Program or a work on which the Program is based. The 475 | work thus licensed is called the contributor's "contributor version". 476 | 477 | A contributor's "essential patent claims" are all patent claims 478 | owned or controlled by the contributor, whether already acquired or 479 | hereafter acquired, that would be infringed by some manner, permitted 480 | by this License, of making, using, or selling its contributor version, 481 | but do not include claims that would be infringed only as a 482 | consequence of further modification of the contributor version. For 483 | purposes of this definition, "control" includes the right to grant 484 | patent sublicenses in a manner consistent with the requirements of 485 | this License. 486 | 487 | Each contributor grants you a non-exclusive, worldwide, royalty-free 488 | patent license under the contributor's essential patent claims, to 489 | make, use, sell, offer for sale, import and otherwise run, modify and 490 | propagate the contents of its contributor version. 491 | 492 | In the following three paragraphs, a "patent license" is any express 493 | agreement or commitment, however denominated, not to enforce a patent 494 | (such as an express permission to practice a patent or covenant not to 495 | sue for patent infringement). To "grant" such a patent license to a 496 | party means to make such an agreement or commitment not to enforce a 497 | patent against the party. 498 | 499 | If you convey a covered work, knowingly relying on a patent license, 500 | and the Corresponding Source of the work is not available for anyone 501 | to copy, free of charge and under the terms of this License, through a 502 | publicly available network server or other readily accessible means, 503 | then you must either (1) cause the Corresponding Source to be so 504 | available, or (2) arrange to deprive yourself of the benefit of the 505 | patent license for this particular work, or (3) arrange, in a manner 506 | consistent with the requirements of this License, to extend the patent 507 | license to downstream recipients. "Knowingly relying" means you have 508 | actual knowledge that, but for the patent license, your conveying the 509 | covered work in a country, or your recipient's use of the covered work 510 | in a country, would infringe one or more identifiable patents in that 511 | country that you have reason to believe are valid. 512 | 513 | If, pursuant to or in connection with a single transaction or 514 | arrangement, you convey, or propagate by procuring conveyance of, a 515 | covered work, and grant a patent license to some of the parties 516 | receiving the covered work authorizing them to use, propagate, modify 517 | or convey a specific copy of the covered work, then the patent license 518 | you grant is automatically extended to all recipients of the covered 519 | work and works based on it. 520 | 521 | A patent license is "discriminatory" if it does not include within 522 | the scope of its coverage, prohibits the exercise of, or is 523 | conditioned on the non-exercise of one or more of the rights that are 524 | specifically granted under this License. You may not convey a covered 525 | work if you are a party to an arrangement with a third party that is 526 | in the business of distributing software, under which you make payment 527 | to the third party based on the extent of your activity of conveying 528 | the work, and under which the third party grants, to any of the 529 | parties who would receive the covered work from you, a discriminatory 530 | patent license (a) in connection with copies of the covered work 531 | conveyed by you (or copies made from those copies), or (b) primarily 532 | for and in connection with specific products or compilations that 533 | contain the covered work, unless you entered into that arrangement, 534 | or that patent license was granted, prior to 28 March 2007. 535 | 536 | Nothing in this License shall be construed as excluding or limiting 537 | any implied license or other defenses to infringement that may 538 | otherwise be available to you under applicable patent law. 539 | 540 | 12. No Surrender of Others' Freedom. 541 | 542 | If conditions are imposed on you (whether by court order, agreement or 543 | otherwise) that contradict the conditions of this License, they do not 544 | excuse you from the conditions of this License. If you cannot convey a 545 | covered work so as to satisfy simultaneously your obligations under this 546 | License and any other pertinent obligations, then as a consequence you may 547 | not convey it at all. For example, if you agree to terms that obligate you 548 | to collect a royalty for further conveying from those to whom you convey 549 | the Program, the only way you could satisfy both those terms and this 550 | License would be to refrain entirely from conveying the Program. 551 | 552 | 13. Use with the GNU Affero General Public License. 553 | 554 | Notwithstanding any other provision of this License, you have 555 | permission to link or combine any covered work with a work licensed 556 | under version 3 of the GNU Affero General Public License into a single 557 | combined work, and to convey the resulting work. The terms of this 558 | License will continue to apply to the part which is the covered work, 559 | but the special requirements of the GNU Affero General Public License, 560 | section 13, concerning interaction through a network will apply to the 561 | combination as such. 562 | 563 | 14. Revised Versions of this License. 564 | 565 | The Free Software Foundation may publish revised and/or new versions of 566 | the GNU General Public License from time to time. Such new versions will 567 | be similar in spirit to the present version, but may differ in detail to 568 | address new problems or concerns. 569 | 570 | Each version is given a distinguishing version number. If the 571 | Program specifies that a certain numbered version of the GNU General 572 | Public License "or any later version" applies to it, you have the 573 | option of following the terms and conditions either of that numbered 574 | version or of any later version published by the Free Software 575 | Foundation. If the Program does not specify a version number of the 576 | GNU General Public License, you may choose any version ever published 577 | by the Free Software Foundation. 578 | 579 | If the Program specifies that a proxy can decide which future 580 | versions of the GNU General Public License can be used, that proxy's 581 | public statement of acceptance of a version permanently authorizes you 582 | to choose that version for the Program. 583 | 584 | Later license versions may give you additional or different 585 | permissions. However, no additional obligations are imposed on any 586 | author or copyright holder as a result of your choosing to follow a 587 | later version. 588 | 589 | 15. Disclaimer of Warranty. 590 | 591 | THERE IS NO WARRANTY FOR THE PROGRAM, TO THE EXTENT PERMITTED BY 592 | APPLICABLE LAW. EXCEPT WHEN OTHERWISE STATED IN WRITING THE COPYRIGHT 593 | HOLDERS AND/OR OTHER PARTIES PROVIDE THE PROGRAM "AS IS" WITHOUT WARRANTY 594 | OF ANY KIND, EITHER EXPRESSED OR IMPLIED, INCLUDING, BUT NOT LIMITED TO, 595 | THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR 596 | PURPOSE. THE ENTIRE RISK AS TO THE QUALITY AND PERFORMANCE OF THE PROGRAM 597 | IS WITH YOU. SHOULD THE PROGRAM PROVE DEFECTIVE, YOU ASSUME THE COST OF 598 | ALL NECESSARY SERVICING, REPAIR OR CORRECTION. 599 | 600 | 16. Limitation of Liability. 601 | 602 | IN NO EVENT UNLESS REQUIRED BY APPLICABLE LAW OR AGREED TO IN WRITING 603 | WILL ANY COPYRIGHT HOLDER, OR ANY OTHER PARTY WHO MODIFIES AND/OR CONVEYS 604 | THE PROGRAM AS PERMITTED ABOVE, BE LIABLE TO YOU FOR DAMAGES, INCLUDING ANY 605 | GENERAL, SPECIAL, INCIDENTAL OR CONSEQUENTIAL DAMAGES ARISING OUT OF THE 606 | USE OR INABILITY TO USE THE PROGRAM (INCLUDING BUT NOT LIMITED TO LOSS OF 607 | DATA OR DATA BEING RENDERED INACCURATE OR LOSSES SUSTAINED BY YOU OR THIRD 608 | PARTIES OR A FAILURE OF THE PROGRAM TO OPERATE WITH ANY OTHER PROGRAMS), 609 | EVEN IF SUCH HOLDER OR OTHER PARTY HAS BEEN ADVISED OF THE POSSIBILITY OF 610 | SUCH DAMAGES. 611 | 612 | 17. Interpretation of Sections 15 and 16. 613 | 614 | If the disclaimer of warranty and limitation of liability provided 615 | above cannot be given local legal effect according to their terms, 616 | reviewing courts shall apply local law that most closely approximates 617 | an absolute waiver of all civil liability in connection with the 618 | Program, unless a warranty or assumption of liability accompanies a 619 | copy of the Program in return for a fee. 620 | 621 | END OF TERMS AND CONDITIONS 622 | 623 | How to Apply These Terms to Your New Programs 624 | 625 | If you develop a new program, and you want it to be of the greatest 626 | possible use to the public, the best way to achieve this is to make it 627 | free software which everyone can redistribute and change under these terms. 628 | 629 | To do so, attach the following notices to the program. It is safest 630 | to attach them to the start of each source file to most effectively 631 | state the exclusion of warranty; and each file should have at least 632 | the "copyright" line and a pointer to where the full notice is found. 633 | 634 | 635 | Copyright (C) 636 | 637 | This program is free software: you can redistribute it and/or modify 638 | it under the terms of the GNU General Public License as published by 639 | the Free Software Foundation, either version 3 of the License, or 640 | (at your option) any later version. 641 | 642 | This program is distributed in the hope that it will be useful, 643 | but WITHOUT ANY WARRANTY; without even the implied warranty of 644 | MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 645 | GNU General Public License for more details. 646 | 647 | You should have received a copy of the GNU General Public License 648 | along with this program. If not, see . 649 | 650 | Also add information on how to contact you by electronic and paper mail. 651 | 652 | If the program does terminal interaction, make it output a short 653 | notice like this when it starts in an interactive mode: 654 | 655 | Copyright (C) 656 | This program comes with ABSOLUTELY NO WARRANTY; for details type `show w'. 657 | This is free software, and you are welcome to redistribute it 658 | under certain conditions; type `show c' for details. 659 | 660 | The hypothetical commands `show w' and `show c' should show the appropriate 661 | parts of the General Public License. Of course, your program's commands 662 | might be different; for a GUI interface, you would use an "about box". 663 | 664 | You should also get your employer (if you work as a programmer) or school, 665 | if any, to sign a "copyright disclaimer" for the program, if necessary. 666 | For more information on this, and how to apply and follow the GNU GPL, see 667 | . 668 | 669 | The GNU General Public License does not permit incorporating your program 670 | into proprietary programs. If your program is a subroutine library, you 671 | may consider it more useful to permit linking proprietary applications with 672 | the library. If this is what you want to do, use the GNU Lesser General 673 | Public License instead of this License. But first, please read 674 | -------------------------------------------------------------------------------- /src/constrained_diffusion.egg-info/PKG-INFO: -------------------------------------------------------------------------------- 1 | Metadata-Version: 2.4 2 | Name: constrained_diffusion 3 | Version: 1.2.4 4 | Summary: Constrained diffusion decomposition: Diffusion-based Multi-Scale Analysis of Complex Iages 5 | Author-email: Guang-Xing Li 6 | License: GNU GENERAL PUBLIC LICENSE 7 | Version 3, 29 June 2007 8 | 9 | Copyright (C) 2007 Free Software Foundation, Inc. 10 | Everyone is permitted to copy and distribute verbatim copies 11 | of this license document, but changing it is not allowed. 12 | 13 | Preamble 14 | 15 | The GNU General Public License is a free, copyleft license for 16 | software and other kinds of works. 17 | 18 | The licenses for most software and other practical works are designed 19 | to take away your freedom to share and change the works. By contrast, 20 | the GNU General Public License is intended to guarantee your freedom to 21 | share and change all versions of a program--to make sure it remains free 22 | software for all its users. We, the Free Software Foundation, use the 23 | GNU General Public License for most of our software; it applies also to 24 | any other work released this way by its authors. You can apply it to 25 | your programs, too. 26 | 27 | When we speak of free software, we are referring to freedom, not 28 | price. Our General Public Licenses are designed to make sure that you 29 | have the freedom to distribute copies of free software (and charge for 30 | them if you wish), that you receive source code or can get it if you 31 | want it, that you can change the software or use pieces of it in new 32 | free programs, and that you know you can do these things. 33 | 34 | To protect your rights, we need to prevent others from denying you 35 | these rights or asking you to surrender the rights. Therefore, you have 36 | certain responsibilities if you distribute copies of the software, or if 37 | you modify it: responsibilities to respect the freedom of others. 38 | 39 | For example, if you distribute copies of such a program, whether 40 | gratis or for a fee, you must pass on to the recipients the same 41 | freedoms that you received. You must make sure that they, too, receive 42 | or can get the source code. And you must show them these terms so they 43 | know their rights. 44 | 45 | Developers that use the GNU GPL protect your rights with two steps: 46 | (1) assert copyright on the software, and (2) offer you this License 47 | giving you legal permission to copy, distribute and/or modify it. 48 | 49 | For the developers' and authors' protection, the GPL clearly explains 50 | that there is no warranty for this free software. For both users' and 51 | authors' sake, the GPL requires that modified versions be marked as 52 | changed, so that their problems will not be attributed erroneously to 53 | authors of previous versions. 54 | 55 | Some devices are designed to deny users access to install or run 56 | modified versions of the software inside them, although the manufacturer 57 | can do so. This is fundamentally incompatible with the aim of 58 | protecting users' freedom to change the software. The systematic 59 | pattern of such abuse occurs in the area of products for individuals to 60 | use, which is precisely where it is most unacceptable. Therefore, we 61 | have designed this version of the GPL to prohibit the practice for those 62 | products. If such problems arise substantially in other domains, we 63 | stand ready to extend this provision to those domains in future versions 64 | of the GPL, as needed to protect the freedom of users. 65 | 66 | Finally, every program is threatened constantly by software patents. 67 | States should not allow patents to restrict development and use of 68 | software on general-purpose computers, but in those that do, we wish to 69 | avoid the special danger that patents applied to a free program could 70 | make it effectively proprietary. To prevent this, the GPL assures that 71 | patents cannot be used to render the program non-free. 72 | 73 | The precise terms and conditions for copying, distribution and 74 | modification follow. 75 | 76 | TERMS AND CONDITIONS 77 | 78 | 0. Definitions. 79 | 80 | "This License" refers to version 3 of the GNU General Public License. 81 | 82 | "Copyright" also means copyright-like laws that apply to other kinds of 83 | works, such as semiconductor masks. 84 | 85 | "The Program" refers to any copyrightable work licensed under this 86 | License. Each licensee is addressed as "you". "Licensees" and 87 | "recipients" may be individuals or organizations. 88 | 89 | To "modify" a work means to copy from or adapt all or part of the work 90 | in a fashion requiring copyright permission, other than the making of an 91 | exact copy. The resulting work is called a "modified version" of the 92 | earlier work or a work "based on" the earlier work. 93 | 94 | A "covered work" means either the unmodified Program or a work based 95 | on the Program. 96 | 97 | To "propagate" a work means to do anything with it that, without 98 | permission, would make you directly or secondarily liable for 99 | infringement under applicable copyright law, except executing it on a 100 | computer or modifying a private copy. Propagation includes copying, 101 | distribution (with or without modification), making available to the 102 | public, and in some countries other activities as well. 103 | 104 | To "convey" a work means any kind of propagation that enables other 105 | parties to make or receive copies. Mere interaction with a user through 106 | a computer network, with no transfer of a copy, is not conveying. 107 | 108 | An interactive user interface displays "Appropriate Legal Notices" 109 | to the extent that it includes a convenient and prominently visible 110 | feature that (1) displays an appropriate copyright notice, and (2) 111 | tells the user that there is no warranty for the work (except to the 112 | extent that warranties are provided), that licensees may convey the 113 | work under this License, and how to view a copy of this License. If 114 | the interface presents a list of user commands or options, such as a 115 | menu, a prominent item in the list meets this criterion. 116 | 117 | 1. Source Code. 118 | 119 | The "source code" for a work means the preferred form of the work 120 | for making modifications to it. "Object code" means any non-source 121 | form of a work. 122 | 123 | A "Standard Interface" means an interface that either is an official 124 | standard defined by a recognized standards body, or, in the case of 125 | interfaces specified for a particular programming language, one that 126 | is widely used among developers working in that language. 127 | 128 | The "System Libraries" of an executable work include anything, other 129 | than the work as a whole, that (a) is included in the normal form of 130 | packaging a Major Component, but which is not part of that Major 131 | Component, and (b) serves only to enable use of the work with that 132 | Major Component, or to implement a Standard Interface for which an 133 | implementation is available to the public in source code form. A 134 | "Major Component", in this context, means a major essential component 135 | (kernel, window system, and so on) of the specific operating system 136 | (if any) on which the executable work runs, or a compiler used to 137 | produce the work, or an object code interpreter used to run it. 138 | 139 | The "Corresponding Source" for a work in object code form means all 140 | the source code needed to generate, install, and (for an executable 141 | work) run the object code and to modify the work, including scripts to 142 | control those activities. However, it does not include the work's 143 | System Libraries, or general-purpose tools or generally available free 144 | programs which are used unmodified in performing those activities but 145 | which are not part of the work. For example, Corresponding Source 146 | includes interface definition files associated with source files for 147 | the work, and the source code for shared libraries and dynamically 148 | linked subprograms that the work is specifically designed to require, 149 | such as by intimate data communication or control flow between those 150 | subprograms and other parts of the work. 151 | 152 | The Corresponding Source need not include anything that users 153 | can regenerate automatically from other parts of the Corresponding 154 | Source. 155 | 156 | The Corresponding Source for a work in source code form is that 157 | same work. 158 | 159 | 2. Basic Permissions. 160 | 161 | All rights granted under this License are granted for the term of 162 | copyright on the Program, and are irrevocable provided the stated 163 | conditions are met. This License explicitly affirms your unlimited 164 | permission to run the unmodified Program. The output from running a 165 | covered work is covered by this License only if the output, given its 166 | content, constitutes a covered work. This License acknowledges your 167 | rights of fair use or other equivalent, as provided by copyright law. 168 | 169 | You may make, run and propagate covered works that you do not 170 | convey, without conditions so long as your license otherwise remains 171 | in force. You may convey covered works to others for the sole purpose 172 | of having them make modifications exclusively for you, or provide you 173 | with facilities for running those works, provided that you comply with 174 | the terms of this License in conveying all material for which you do 175 | not control copyright. Those thus making or running the covered works 176 | for you must do so exclusively on your behalf, under your direction 177 | and control, on terms that prohibit them from making any copies of 178 | your copyrighted material outside their relationship with you. 179 | 180 | Conveying under any other circumstances is permitted solely under 181 | the conditions stated below. Sublicensing is not allowed; section 10 182 | makes it unnecessary. 183 | 184 | 3. Protecting Users' Legal Rights From Anti-Circumvention Law. 185 | 186 | No covered work shall be deemed part of an effective technological 187 | measure under any applicable law fulfilling obligations under article 188 | 11 of the WIPO copyright treaty adopted on 20 December 1996, or 189 | similar laws prohibiting or restricting circumvention of such 190 | measures. 191 | 192 | When you convey a covered work, you waive any legal power to forbid 193 | circumvention of technological measures to the extent such circumvention 194 | is effected by exercising rights under this License with respect to 195 | the covered work, and you disclaim any intention to limit operation or 196 | modification of the work as a means of enforcing, against the work's 197 | users, your or third parties' legal rights to forbid circumvention of 198 | technological measures. 199 | 200 | 4. Conveying Verbatim Copies. 201 | 202 | You may convey verbatim copies of the Program's source code as you 203 | receive it, in any medium, provided that you conspicuously and 204 | appropriately publish on each copy an appropriate copyright notice; 205 | keep intact all notices stating that this License and any 206 | non-permissive terms added in accord with section 7 apply to the code; 207 | keep intact all notices of the absence of any warranty; and give all 208 | recipients a copy of this License along with the Program. 209 | 210 | You may charge any price or no price for each copy that you convey, 211 | and you may offer support or warranty protection for a fee. 212 | 213 | 5. Conveying Modified Source Versions. 214 | 215 | You may convey a work based on the Program, or the modifications to 216 | produce it from the Program, in the form of source code under the 217 | terms of section 4, provided that you also meet all of these conditions: 218 | 219 | a) The work must carry prominent notices stating that you modified 220 | it, and giving a relevant date. 221 | 222 | b) The work must carry prominent notices stating that it is 223 | released under this License and any conditions added under section 224 | 7. This requirement modifies the requirement in section 4 to 225 | "keep intact all notices". 226 | 227 | c) You must license the entire work, as a whole, under this 228 | License to anyone who comes into possession of a copy. This 229 | License will therefore apply, along with any applicable section 7 230 | additional terms, to the whole of the work, and all its parts, 231 | regardless of how they are packaged. This License gives no 232 | permission to license the work in any other way, but it does not 233 | invalidate such permission if you have separately received it. 234 | 235 | d) If the work has interactive user interfaces, each must display 236 | Appropriate Legal Notices; however, if the Program has interactive 237 | interfaces that do not display Appropriate Legal Notices, your 238 | work need not make them do so. 239 | 240 | A compilation of a covered work with other separate and independent 241 | works, which are not by their nature extensions of the covered work, 242 | and which are not combined with it such as to form a larger program, 243 | in or on a volume of a storage or distribution medium, is called an 244 | "aggregate" if the compilation and its resulting copyright are not 245 | used to limit the access or legal rights of the compilation's users 246 | beyond what the individual works permit. Inclusion of a covered work 247 | in an aggregate does not cause this License to apply to the other 248 | parts of the aggregate. 249 | 250 | 6. Conveying Non-Source Forms. 251 | 252 | You may convey a covered work in object code form under the terms 253 | of sections 4 and 5, provided that you also convey the 254 | machine-readable Corresponding Source under the terms of this License, 255 | in one of these ways: 256 | 257 | a) Convey the object code in, or embodied in, a physical product 258 | (including a physical distribution medium), accompanied by the 259 | Corresponding Source fixed on a durable physical medium 260 | customarily used for software interchange. 261 | 262 | b) Convey the object code in, or embodied in, a physical product 263 | (including a physical distribution medium), accompanied by a 264 | written offer, valid for at least three years and valid for as 265 | long as you offer spare parts or customer support for that product 266 | model, to give anyone who possesses the object code either (1) a 267 | copy of the Corresponding Source for all the software in the 268 | product that is covered by this License, on a durable physical 269 | medium customarily used for software interchange, for a price no 270 | more than your reasonable cost of physically performing this 271 | conveying of source, or (2) access to copy the 272 | Corresponding Source from a network server at no charge. 273 | 274 | c) Convey individual copies of the object code with a copy of the 275 | written offer to provide the Corresponding Source. This 276 | alternative is allowed only occasionally and noncommercially, and 277 | only if you received the object code with such an offer, in accord 278 | with subsection 6b. 279 | 280 | d) Convey the object code by offering access from a designated 281 | place (gratis or for a charge), and offer equivalent access to the 282 | Corresponding Source in the same way through the same place at no 283 | further charge. You need not require recipients to copy the 284 | Corresponding Source along with the object code. If the place to 285 | copy the object code is a network server, the Corresponding Source 286 | may be on a different server (operated by you or a third party) 287 | that supports equivalent copying facilities, provided you maintain 288 | clear directions next to the object code saying where to find the 289 | Corresponding Source. Regardless of what server hosts the 290 | Corresponding Source, you remain obligated to ensure that it is 291 | available for as long as needed to satisfy these requirements. 292 | 293 | e) Convey the object code using peer-to-peer transmission, provided 294 | you inform other peers where the object code and Corresponding 295 | Source of the work are being offered to the general public at no 296 | charge under subsection 6d. 297 | 298 | A separable portion of the object code, whose source code is excluded 299 | from the Corresponding Source as a System Library, need not be 300 | included in conveying the object code work. 301 | 302 | A "User Product" is either (1) a "consumer product", which means any 303 | tangible personal property which is normally used for personal, family, 304 | or household purposes, or (2) anything designed or sold for incorporation 305 | into a dwelling. In determining whether a product is a consumer product, 306 | doubtful cases shall be resolved in favor of coverage. For a particular 307 | product received by a particular user, "normally used" refers to a 308 | typical or common use of that class of product, regardless of the status 309 | of the particular user or of the way in which the particular user 310 | actually uses, or expects or is expected to use, the product. A product 311 | is a consumer product regardless of whether the product has substantial 312 | commercial, industrial or non-consumer uses, unless such uses represent 313 | the only significant mode of use of the product. 314 | 315 | "Installation Information" for a User Product means any methods, 316 | procedures, authorization keys, or other information required to install 317 | and execute modified versions of a covered work in that User Product from 318 | a modified version of its Corresponding Source. The information must 319 | suffice to ensure that the continued functioning of the modified object 320 | code is in no case prevented or interfered with solely because 321 | modification has been made. 322 | 323 | If you convey an object code work under this section in, or with, or 324 | specifically for use in, a User Product, and the conveying occurs as 325 | part of a transaction in which the right of possession and use of the 326 | User Product is transferred to the recipient in perpetuity or for a 327 | fixed term (regardless of how the transaction is characterized), the 328 | Corresponding Source conveyed under this section must be accompanied 329 | by the Installation Information. But this requirement does not apply 330 | if neither you nor any third party retains the ability to install 331 | modified object code on the User Product (for example, the work has 332 | been installed in ROM). 333 | 334 | The requirement to provide Installation Information does not include a 335 | requirement to continue to provide support service, warranty, or updates 336 | for a work that has been modified or installed by the recipient, or for 337 | the User Product in which it has been modified or installed. Access to a 338 | network may be denied when the modification itself materially and 339 | adversely affects the operation of the network or violates the rules and 340 | protocols for communication across the network. 341 | 342 | Corresponding Source conveyed, and Installation Information provided, 343 | in accord with this section must be in a format that is publicly 344 | documented (and with an implementation available to the public in 345 | source code form), and must require no special password or key for 346 | unpacking, reading or copying. 347 | 348 | 7. Additional Terms. 349 | 350 | "Additional permissions" are terms that supplement the terms of this 351 | License by making exceptions from one or more of its conditions. 352 | Additional permissions that are applicable to the entire Program shall 353 | be treated as though they were included in this License, to the extent 354 | that they are valid under applicable law. If additional permissions 355 | apply only to part of the Program, that part may be used separately 356 | under those permissions, but the entire Program remains governed by 357 | this License without regard to the additional permissions. 358 | 359 | When you convey a copy of a covered work, you may at your option 360 | remove any additional permissions from that copy, or from any part of 361 | it. (Additional permissions may be written to require their own 362 | removal in certain cases when you modify the work.) You may place 363 | additional permissions on material, added by you to a covered work, 364 | for which you have or can give appropriate copyright permission. 365 | 366 | Notwithstanding any other provision of this License, for material you 367 | add to a covered work, you may (if authorized by the copyright holders of 368 | that material) supplement the terms of this License with terms: 369 | 370 | a) Disclaiming warranty or limiting liability differently from the 371 | terms of sections 15 and 16 of this License; or 372 | 373 | b) Requiring preservation of specified reasonable legal notices or 374 | author attributions in that material or in the Appropriate Legal 375 | Notices displayed by works containing it; or 376 | 377 | c) Prohibiting misrepresentation of the origin of that material, or 378 | requiring that modified versions of such material be marked in 379 | reasonable ways as different from the original version; or 380 | 381 | d) Limiting the use for publicity purposes of names of licensors or 382 | authors of the material; or 383 | 384 | e) Declining to grant rights under trademark law for use of some 385 | trade names, trademarks, or service marks; or 386 | 387 | f) Requiring indemnification of licensors and authors of that 388 | material by anyone who conveys the material (or modified versions of 389 | it) with contractual assumptions of liability to the recipient, for 390 | any liability that these contractual assumptions directly impose on 391 | those licensors and authors. 392 | 393 | All other non-permissive additional terms are considered "further 394 | restrictions" within the meaning of section 10. If the Program as you 395 | received it, or any part of it, contains a notice stating that it is 396 | governed by this License along with a term that is a further 397 | restriction, you may remove that term. If a license document contains 398 | a further restriction but permits relicensing or conveying under this 399 | License, you may add to a covered work material governed by the terms 400 | of that license document, provided that the further restriction does 401 | not survive such relicensing or conveying. 402 | 403 | If you add terms to a covered work in accord with this section, you 404 | must place, in the relevant source files, a statement of the 405 | additional terms that apply to those files, or a notice indicating 406 | where to find the applicable terms. 407 | 408 | Additional terms, permissive or non-permissive, may be stated in the 409 | form of a separately written license, or stated as exceptions; 410 | the above requirements apply either way. 411 | 412 | 8. Termination. 413 | 414 | You may not propagate or modify a covered work except as expressly 415 | provided under this License. Any attempt otherwise to propagate or 416 | modify it is void, and will automatically terminate your rights under 417 | this License (including any patent licenses granted under the third 418 | paragraph of section 11). 419 | 420 | However, if you cease all violation of this License, then your 421 | license from a particular copyright holder is reinstated (a) 422 | provisionally, unless and until the copyright holder explicitly and 423 | finally terminates your license, and (b) permanently, if the copyright 424 | holder fails to notify you of the violation by some reasonable means 425 | prior to 60 days after the cessation. 426 | 427 | Moreover, your license from a particular copyright holder is 428 | reinstated permanently if the copyright holder notifies you of the 429 | violation by some reasonable means, this is the first time you have 430 | received notice of violation of this License (for any work) from that 431 | copyright holder, and you cure the violation prior to 30 days after 432 | your receipt of the notice. 433 | 434 | Termination of your rights under this section does not terminate the 435 | licenses of parties who have received copies or rights from you under 436 | this License. If your rights have been terminated and not permanently 437 | reinstated, you do not qualify to receive new licenses for the same 438 | material under section 10. 439 | 440 | 9. Acceptance Not Required for Having Copies. 441 | 442 | You are not required to accept this License in order to receive or 443 | run a copy of the Program. Ancillary propagation of a covered work 444 | occurring solely as a consequence of using peer-to-peer transmission 445 | to receive a copy likewise does not require acceptance. However, 446 | nothing other than this License grants you permission to propagate or 447 | modify any covered work. These actions infringe copyright if you do 448 | not accept this License. Therefore, by modifying or propagating a 449 | covered work, you indicate your acceptance of this License to do so. 450 | 451 | 10. Automatic Licensing of Downstream Recipients. 452 | 453 | Each time you convey a covered work, the recipient automatically 454 | receives a license from the original licensors, to run, modify and 455 | propagate that work, subject to this License. You are not responsible 456 | for enforcing compliance by third parties with this License. 457 | 458 | An "entity transaction" is a transaction transferring control of an 459 | organization, or substantially all assets of one, or subdividing an 460 | organization, or merging organizations. If propagation of a covered 461 | work results from an entity transaction, each party to that 462 | transaction who receives a copy of the work also receives whatever 463 | licenses to the work the party's predecessor in interest had or could 464 | give under the previous paragraph, plus a right to possession of the 465 | Corresponding Source of the work from the predecessor in interest, if 466 | the predecessor has it or can get it with reasonable efforts. 467 | 468 | You may not impose any further restrictions on the exercise of the 469 | rights granted or affirmed under this License. For example, you may 470 | not impose a license fee, royalty, or other charge for exercise of 471 | rights granted under this License, and you may not initiate litigation 472 | (including a cross-claim or counterclaim in a lawsuit) alleging that 473 | any patent claim is infringed by making, using, selling, offering for 474 | sale, or importing the Program or any portion of it. 475 | 476 | 11. Patents. 477 | 478 | A "contributor" is a copyright holder who authorizes use under this 479 | License of the Program or a work on which the Program is based. The 480 | work thus licensed is called the contributor's "contributor version". 481 | 482 | A contributor's "essential patent claims" are all patent claims 483 | owned or controlled by the contributor, whether already acquired or 484 | hereafter acquired, that would be infringed by some manner, permitted 485 | by this License, of making, using, or selling its contributor version, 486 | but do not include claims that would be infringed only as a 487 | consequence of further modification of the contributor version. For 488 | purposes of this definition, "control" includes the right to grant 489 | patent sublicenses in a manner consistent with the requirements of 490 | this License. 491 | 492 | Each contributor grants you a non-exclusive, worldwide, royalty-free 493 | patent license under the contributor's essential patent claims, to 494 | make, use, sell, offer for sale, import and otherwise run, modify and 495 | propagate the contents of its contributor version. 496 | 497 | In the following three paragraphs, a "patent license" is any express 498 | agreement or commitment, however denominated, not to enforce a patent 499 | (such as an express permission to practice a patent or covenant not to 500 | sue for patent infringement). To "grant" such a patent license to a 501 | party means to make such an agreement or commitment not to enforce a 502 | patent against the party. 503 | 504 | If you convey a covered work, knowingly relying on a patent license, 505 | and the Corresponding Source of the work is not available for anyone 506 | to copy, free of charge and under the terms of this License, through a 507 | publicly available network server or other readily accessible means, 508 | then you must either (1) cause the Corresponding Source to be so 509 | available, or (2) arrange to deprive yourself of the benefit of the 510 | patent license for this particular work, or (3) arrange, in a manner 511 | consistent with the requirements of this License, to extend the patent 512 | license to downstream recipients. "Knowingly relying" means you have 513 | actual knowledge that, but for the patent license, your conveying the 514 | covered work in a country, or your recipient's use of the covered work 515 | in a country, would infringe one or more identifiable patents in that 516 | country that you have reason to believe are valid. 517 | 518 | If, pursuant to or in connection with a single transaction or 519 | arrangement, you convey, or propagate by procuring conveyance of, a 520 | covered work, and grant a patent license to some of the parties 521 | receiving the covered work authorizing them to use, propagate, modify 522 | or convey a specific copy of the covered work, then the patent license 523 | you grant is automatically extended to all recipients of the covered 524 | work and works based on it. 525 | 526 | A patent license is "discriminatory" if it does not include within 527 | the scope of its coverage, prohibits the exercise of, or is 528 | conditioned on the non-exercise of one or more of the rights that are 529 | specifically granted under this License. You may not convey a covered 530 | work if you are a party to an arrangement with a third party that is 531 | in the business of distributing software, under which you make payment 532 | to the third party based on the extent of your activity of conveying 533 | the work, and under which the third party grants, to any of the 534 | parties who would receive the covered work from you, a discriminatory 535 | patent license (a) in connection with copies of the covered work 536 | conveyed by you (or copies made from those copies), or (b) primarily 537 | for and in connection with specific products or compilations that 538 | contain the covered work, unless you entered into that arrangement, 539 | or that patent license was granted, prior to 28 March 2007. 540 | 541 | Nothing in this License shall be construed as excluding or limiting 542 | any implied license or other defenses to infringement that may 543 | otherwise be available to you under applicable patent law. 544 | 545 | 12. No Surrender of Others' Freedom. 546 | 547 | If conditions are imposed on you (whether by court order, agreement or 548 | otherwise) that contradict the conditions of this License, they do not 549 | excuse you from the conditions of this License. If you cannot convey a 550 | covered work so as to satisfy simultaneously your obligations under this 551 | License and any other pertinent obligations, then as a consequence you may 552 | not convey it at all. For example, if you agree to terms that obligate you 553 | to collect a royalty for further conveying from those to whom you convey 554 | the Program, the only way you could satisfy both those terms and this 555 | License would be to refrain entirely from conveying the Program. 556 | 557 | 13. Use with the GNU Affero General Public License. 558 | 559 | Notwithstanding any other provision of this License, you have 560 | permission to link or combine any covered work with a work licensed 561 | under version 3 of the GNU Affero General Public License into a single 562 | combined work, and to convey the resulting work. The terms of this 563 | License will continue to apply to the part which is the covered work, 564 | but the special requirements of the GNU Affero General Public License, 565 | section 13, concerning interaction through a network will apply to the 566 | combination as such. 567 | 568 | 14. Revised Versions of this License. 569 | 570 | The Free Software Foundation may publish revised and/or new versions of 571 | the GNU General Public License from time to time. Such new versions will 572 | be similar in spirit to the present version, but may differ in detail to 573 | address new problems or concerns. 574 | 575 | Each version is given a distinguishing version number. If the 576 | Program specifies that a certain numbered version of the GNU General 577 | Public License "or any later version" applies to it, you have the 578 | option of following the terms and conditions either of that numbered 579 | version or of any later version published by the Free Software 580 | Foundation. If the Program does not specify a version number of the 581 | GNU General Public License, you may choose any version ever published 582 | by the Free Software Foundation. 583 | 584 | If the Program specifies that a proxy can decide which future 585 | versions of the GNU General Public License can be used, that proxy's 586 | public statement of acceptance of a version permanently authorizes you 587 | to choose that version for the Program. 588 | 589 | Later license versions may give you additional or different 590 | permissions. However, no additional obligations are imposed on any 591 | author or copyright holder as a result of your choosing to follow a 592 | later version. 593 | 594 | 15. Disclaimer of Warranty. 595 | 596 | THERE IS NO WARRANTY FOR THE PROGRAM, TO THE EXTENT PERMITTED BY 597 | APPLICABLE LAW. EXCEPT WHEN OTHERWISE STATED IN WRITING THE COPYRIGHT 598 | HOLDERS AND/OR OTHER PARTIES PROVIDE THE PROGRAM "AS IS" WITHOUT WARRANTY 599 | OF ANY KIND, EITHER EXPRESSED OR IMPLIED, INCLUDING, BUT NOT LIMITED TO, 600 | THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR 601 | PURPOSE. THE ENTIRE RISK AS TO THE QUALITY AND PERFORMANCE OF THE PROGRAM 602 | IS WITH YOU. SHOULD THE PROGRAM PROVE DEFECTIVE, YOU ASSUME THE COST OF 603 | ALL NECESSARY SERVICING, REPAIR OR CORRECTION. 604 | 605 | 16. Limitation of Liability. 606 | 607 | IN NO EVENT UNLESS REQUIRED BY APPLICABLE LAW OR AGREED TO IN WRITING 608 | WILL ANY COPYRIGHT HOLDER, OR ANY OTHER PARTY WHO MODIFIES AND/OR CONVEYS 609 | THE PROGRAM AS PERMITTED ABOVE, BE LIABLE TO YOU FOR DAMAGES, INCLUDING ANY 610 | GENERAL, SPECIAL, INCIDENTAL OR CONSEQUENTIAL DAMAGES ARISING OUT OF THE 611 | USE OR INABILITY TO USE THE PROGRAM (INCLUDING BUT NOT LIMITED TO LOSS OF 612 | DATA OR DATA BEING RENDERED INACCURATE OR LOSSES SUSTAINED BY YOU OR THIRD 613 | PARTIES OR A FAILURE OF THE PROGRAM TO OPERATE WITH ANY OTHER PROGRAMS), 614 | EVEN IF SUCH HOLDER OR OTHER PARTY HAS BEEN ADVISED OF THE POSSIBILITY OF 615 | SUCH DAMAGES. 616 | 617 | 17. Interpretation of Sections 15 and 16. 618 | 619 | If the disclaimer of warranty and limitation of liability provided 620 | above cannot be given local legal effect according to their terms, 621 | reviewing courts shall apply local law that most closely approximates 622 | an absolute waiver of all civil liability in connection with the 623 | Program, unless a warranty or assumption of liability accompanies a 624 | copy of the Program in return for a fee. 625 | 626 | END OF TERMS AND CONDITIONS 627 | 628 | How to Apply These Terms to Your New Programs 629 | 630 | If you develop a new program, and you want it to be of the greatest 631 | possible use to the public, the best way to achieve this is to make it 632 | free software which everyone can redistribute and change under these terms. 633 | 634 | To do so, attach the following notices to the program. It is safest 635 | to attach them to the start of each source file to most effectively 636 | state the exclusion of warranty; and each file should have at least 637 | the "copyright" line and a pointer to where the full notice is found. 638 | 639 | 640 | Copyright (C) 641 | 642 | This program is free software: you can redistribute it and/or modify 643 | it under the terms of the GNU General Public License as published by 644 | the Free Software Foundation, either version 3 of the License, or 645 | (at your option) any later version. 646 | 647 | This program is distributed in the hope that it will be useful, 648 | but WITHOUT ANY WARRANTY; without even the implied warranty of 649 | MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 650 | GNU General Public License for more details. 651 | 652 | You should have received a copy of the GNU General Public License 653 | along with this program. If not, see . 654 | 655 | Also add information on how to contact you by electronic and paper mail. 656 | 657 | If the program does terminal interaction, make it output a short 658 | notice like this when it starts in an interactive mode: 659 | 660 | Copyright (C) 661 | This program comes with ABSOLUTELY NO WARRANTY; for details type `show w'. 662 | This is free software, and you are welcome to redistribute it 663 | under certain conditions; type `show c' for details. 664 | 665 | The hypothetical commands `show w' and `show c' should show the appropriate 666 | parts of the General Public License. Of course, your program's commands 667 | might be different; for a GUI interface, you would use an "about box". 668 | 669 | You should also get your employer (if you work as a programmer) or school, 670 | if any, to sign a "copyright disclaimer" for the program, if necessary. 671 | For more information on this, and how to apply and follow the GNU GPL, see 672 | . 673 | 674 | The GNU General Public License does not permit incorporating your program 675 | into proprietary programs. If your program is a subroutine library, you 676 | may consider it more useful to permit linking proprietary applications with 677 | the library. If this is what you want to do, use the GNU Lesser General 678 | Public License instead of this License. But first, please read 679 | 680 | Project-URL: Homepage, https://gxli.github.io/Constrained-Diffusion-Decomposition/ 681 | Classifier: Programming Language :: Python :: 3 682 | Classifier: Operating System :: OS Independent 683 | Requires-Python: >=3.0 684 | Description-Content-Type: text/markdown 685 | License-File: LICENSE 686 | Requires-Dist: numpy>=1.00 687 | Requires-Dist: scipy>=1.0 688 | Dynamic: license-file 689 | 690 | # Constrained Diffusion Decomposition: A PDE-based Image Decomposition Method 691 | 692 | ## General Design 693 | A natural image often contains components of different scales. This project provides a powerful tool to decompose N-dimensional `numpy.ndarray` data into its constituent scale components. 694 | 695 | The decomposition is highly flexible, allowing for **logarithmically** or **linearly** spaced scales that can be **automatically determined** from the data's shape or specified manually by the user. 696 | 697 | The code is based on the principles described in 698 | Li 2022, Multi-Scale Decomposition of Astronomical Maps -- Constrained Diffusion Method. 699 | 700 | Assuming an input of I(x, y), the decomposition is achieved by solving the equation: 701 | 702 | ```math 703 | \frac{\partial I_t }{\partial t} ={\rm sgn}(I_t) \mathcal{H}({- \rm sgn}(I_t) \nabla^2 I_t) \nabla^2 I_t 704 | ``` 705 | where the diffusion time `t` is related to the characteristic scale `l` by `t = l²/2`. 706 | 707 | ## Key Features 708 | 709 | * **Automatic Parameter Detection**: For ease of use, the decomposition scales (`min_scale`, `max_scale`) and the number of channels (`num_channels`) are automatically inferred from the input data's shape if not provided. 710 | * **Hybrid Upsampling Strategy**: For maximum accuracy and efficiency, the default (`up_sample=True`) mode uses a hybrid approach: 711 | 1. It performs a high-resolution (4x upsampled) decomposition for small scales (<= 5 pixels) to accurately capture fine details. 712 | 2. It then performs a standard decomposition on the residual for all larger scales. 713 | * **Constrained vs. Unconstrained Modes**: 714 | * The default (`constrained=True`) uses a sign-based constrained algorithm that is guaranteed to be artifact-free and will not create new peaks or valleys. 715 | * An optional `constrained=False` mode provides a standard linear diffusion decomposition, which is faster but may introduce "ringing" artifacts (negative halos around positive peaks). 716 | * **Inverted Decomposition**: A special `inverted=True` mode allows the algorithm to decompose negative features ("holes" or depressions) within a positive background, rather than the standard behavior of decomposing positive peaks. 717 | * **Fine-Grained Scale Control**: Advanced users can specify the `log_scale_base` or `linear_scale_step` to precisely control the spacing and number of decomposition channels. 718 | 719 | ## Installation 720 | 721 | 1. **From source via git clone:** 722 | ```bash 723 | git clone https://github.com/gxli/Constrained-Diffusion-Decomposition.git 724 | cd Constrained-Diffusion-Decomposition 725 | pip install . 726 | ``` 727 | 728 | 2. **Via `pip`:** 729 | ```bash 730 | pip install constrained-diffusion 731 | ``` 732 | 3. **Via `pip`:** 733 | ```bash 734 | pip install -i https://test.pypi.org/simple/ constrained-diffusion==1.2.3 735 | ``` 736 | ## Usage 737 | 738 | The main entry point is the highly automated `constrained_diffusion_decomposition` function. 739 | 740 | ### Function Signature 741 | ```python 742 | constrained_diffusion_decomposition( 743 | data, 744 | num_channels=None, 745 | max_scale=None, 746 | min_scale=1, 747 | mode='log', 748 | log_scale_base=2.0, 749 | linear_scale_step=None, 750 | up_sample=True, 751 | constrained=True, 752 | inverted=False, 753 | return_scales=False 754 | ) 755 | ``` 756 | 757 | ### Key Parameters 758 | 759 | | Parameter | Description | Default | 760 | | :--- | :--- | :--- | 761 | | `data` | The input N-dimensional NumPy array. | (Required) | 762 | | `mode` | Scale spacing: `'log'` (powers of 2) or `'lin'` (linear). | `'log'` | 763 | | `up_sample` | If `True`, uses the efficient hybrid upsampling strategy. | `True` | 764 | | `constrained`| If `True`, uses the artifact-free constrained algorithm. | `True` | 765 | | `inverted` | If `True`, decomposes depressions ("holes") instead of peaks. | `False` | 766 | | `num_channels`| Number of channels. If `None`, calculated automatically. Ignored in linear mode if `linear_scale_step` is set. | `None` | 767 | | `max_scale` | The largest scale to analyze. If `None`, set to `max(data.shape)/2`. | `None` | 768 | | `min_scale` | The smallest scale to analyze. | `1` | 769 | | `log_scale_base` | The base for logarithmic scale generation. Smaller values create finer scales. | `2.0` | 770 | | `linear_scale_step`| If set, defines a fixed step size for linear mode, overriding `num_channels`.| `None` | 771 | | `return_scales`| If `True`, returns the list of scales used for decomposition. | `False` | 772 | 773 | 774 | ### Input: 775 | 776 | - A `numpy.ndarray` of any shape, e.g., `(nx, ny, nz)`. 777 | 778 | ### Output: 779 | 780 | - By default, a tuple `(results, residual)`. 781 | - If `return_scales=True`, a tuple `(results, residual, scales)`. 782 | 783 | Where: 784 | - **`results`**: A `list` of NumPy arrays. `results[i]` contains structures corresponding to `scales[i]`. 785 | - **`residual`**: A NumPy array containing structures larger than the largest scale. 786 | - **`scales`**: (Optional) The list of scale values used for the decomposition. 787 | 788 | The original data can be perfectly recovered via: `data = np.sum(results, axis=0) + residual`. 789 | 790 | ### Quickstart 791 | 792 | ```python 793 | import constrained_diffusion as cdd 794 | import numpy as np 795 | 796 | # Create some sample data 797 | data = np.random.rand(128, 128) 798 | 799 | # Perform decomposition with default automatic settings 800 | results, residual = cdd.constrained_diffusion_decomposition(data) 801 | 802 | print(f"Decomposed into {len(results)} channels.") 803 | ``` 804 | 805 | ## Example 806 | 807 | This example decomposes an image containing two Gaussian structures of different sizes using the recommended default settings. 808 | 809 | ```python 810 | import matplotlib.pyplot as plt 811 | import numpy as np 812 | from mpl_toolkits.axes_grid1.inset_locator import inset_axes 813 | 814 | # Assuming 'result' is a list of 2D arrays 815 | # Example: result = [np.random.rand(10, 10) for _ in range(6)] # Dummy data for testing 816 | n_images = len(result) 817 | cols = 3 # Fixed number of columns 818 | rows = int(np.ceil(n_images / cols)) # Calculate required rows 819 | 820 | # Determine the global min and max for the shared color scale 821 | vmin = min(np.min(img) for img in result) 822 | vmax = max(np.max(img) for img in result) 823 | 824 | # Create a figure with a grid of subplots 825 | fig, axes = plt.subplots(rows, cols, figsize=(4 * cols, 4 * rows), squeeze=False) 826 | axes = axes.flatten() # Flatten for easier iteration 827 | 828 | # Plot each image in the grid 829 | for idx, img in enumerate(result): 830 | ax = axes[idx] 831 | im = ax.imshow(img, cmap='viridis', vmin=vmin, vmax=vmax) # Use shared color scale 832 | ax.set_title(f'Image {idx + 1}') # Add title for clarity 833 | ax.axis('on') # Show axes (can be turned off with ax.axis('off') if desired) 834 | 835 | # Add colorbar only to the first subplot (top-left) 836 | if idx == 0: 837 | # Create an inset axes for the colorbar inside the first subplot 838 | cax = inset_axes(ax, width="5%", height="50%", loc='lower right', 839 | bbox_to_anchor=(0, 0, 1, 1), bbox_transform=ax.transAxes) 840 | fig.colorbar(im, cax=cax) # Add colorbar to inset axes 841 | 842 | # Hide empty subplots if any 843 | for idx in range(len(result), len(axes)): 844 | axes[idx].set_visible(False) 845 | 846 | # Adjust layout to prevent overlap 847 | plt.tight_layout() 848 | plt.show() 849 | ``` 850 | 851 | The output cleanly separates the small, sharp feature into the early channels, 852 | while the large, smooth structure is captured in the later channels and the 853 | residual. 854 | 855 | 856 | 857 | 858 | 859 | 860 | 861 | 862 | 863 | This 1D example shows the constrained diffusion decomposition can separate 864 | the signal made of a few Gaussians, without introducing negative ripples. 865 | 866 | 867 | 868 | 869 | This 1D example shows the option inverted=True leads to a diffusion which fills 870 | the gaps in the signal. This feature can be used to detect holes or absorption 871 | dips. 872 | 873 | 874 | 875 | 876 | This examples shows the option up_sample=True leads to improved accuracy for the 877 | first channels. 878 | 879 | 880 | 881 | Below is a comparison between standard diffusion and constrained diffusion 882 | decomposition, where the constrained version leads to a better localization 883 | behavior, and a cleaner separation of the two Gaussian blobs. 884 | 885 | 886 | 887 | 888 | ## 889 | Reference: Li 2022, Multi-Scale Decomposition of Astronomical Maps -- Constrained Diffusion Method. 890 | 891 | ## License 892 | See the [LICENSE](LICENSE) file for details. 893 | --------------------------------------------------------------------------------