├── .python-version ├── LICENSE ├── README.md ├── __pycache__ └── curve_extraction.cpython-313.pyc ├── assets ├── 2020-11-10-11-16-57.png ├── 2020-11-10-11-17-08.png ├── 2020-11-10-11-17-15.png └── image.png ├── curve_extraction.py ├── main.py ├── pyproject.toml ├── uv.lock └── visualization.py /.python-version: -------------------------------------------------------------------------------- 1 | 3.13 2 | -------------------------------------------------------------------------------- /LICENSE: -------------------------------------------------------------------------------- 1 | MIT License 2 | 3 | Copyright (c) 2021-PRESENT aliadnani 4 | 5 | Permission is hereby granted, free of charge, to any person obtaining a copy 6 | of this software and associated documentation files (the "Software"), to deal 7 | in the Software without restriction, including without limitation the rights 8 | to use, copy, modify, merge, publish, distribute, sublicense, and/or sell 9 | copies of the Software, and to permit persons to whom the Software is 10 | furnished to do so, subject to the following conditions: 11 | 12 | The above copyright notice and this permission notice shall be included in all 13 | copies or substantial portions of the Software. 14 | 15 | THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR 16 | IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, 17 | FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE 18 | AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER 19 | LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, 20 | OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE 21 | SOFTWARE. -------------------------------------------------------------------------------- /README.md: -------------------------------------------------------------------------------- 1 | # 3D Point Cloud Curve Extraction 2 | 3 | Extracts smooth curves from noisy 3D point clouds using PCA-based thinning and directional sorting. 4 | 5 | Heavily based on "Curve Reconstruction from Unorganized Points" by In-Kwon Lee 6 | 7 | 8 | ## Usage 9 | 10 | ```python 11 | from curve_extraction import thin_line, sort_points 12 | import numpy as np 13 | 14 | # Your Nx3 array of points in [x,y,z] form 15 | points = np.array([[x1, y1, z1], [x2, y2, z2], ...]) 16 | 17 | # 1. Thin the point cloud 18 | thinned_points, regression_lines = thin_line(points) 19 | 20 | # 2. Sort points into a curve 21 | sorted_points = sort_points(thinned_points, regression_lines) 22 | ``` 23 | 24 | 25 | This is not currently published as a library so for now just copy `curve_extraction.py` into your project and use as follows. If you do, I suggest removing the timing and print statements. 26 | 27 | 28 | ## Demo 29 | 30 | Run the demo to see it work on a noisy spiral: 31 | 32 | ```bash 33 | uv run visualization.py 34 | ``` 35 | 36 | ![](assets/image.png) 37 | 38 | ## Parameters 39 | 40 | **thin_line** 41 | - `point_cloud_thickness` - radius for selecting points during PCA (default: 0.53) 42 | 43 | **sort_points** 44 | - `sorted_point_distance` - radius for finding adjacent points when ordering (default: 0.2) 45 | 46 | ## Files 47 | 48 | - `curve_extraction.py` - core algorithm 49 | - `visualization.py` - demo and plotting functions -------------------------------------------------------------------------------- /__pycache__/curve_extraction.cpython-313.pyc: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/aliadnani/curves/63249071d0085c0b6266585f25460c384b5fc704/__pycache__/curve_extraction.cpython-313.pyc -------------------------------------------------------------------------------- /assets/2020-11-10-11-16-57.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/aliadnani/curves/63249071d0085c0b6266585f25460c384b5fc704/assets/2020-11-10-11-16-57.png -------------------------------------------------------------------------------- /assets/2020-11-10-11-17-08.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/aliadnani/curves/63249071d0085c0b6266585f25460c384b5fc704/assets/2020-11-10-11-17-08.png -------------------------------------------------------------------------------- /assets/2020-11-10-11-17-15.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/aliadnani/curves/63249071d0085c0b6266585f25460c384b5fc704/assets/2020-11-10-11-17-15.png -------------------------------------------------------------------------------- /assets/image.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/aliadnani/curves/63249071d0085c0b6266585f25460c384b5fc704/assets/image.png -------------------------------------------------------------------------------- /curve_extraction.py: -------------------------------------------------------------------------------- 1 | import time 2 | from typing import List, Tuple 3 | 4 | import numpy as np 5 | import numpy.typing as npt 6 | import scipy.spatial as spatial 7 | import vg 8 | 9 | 10 | # == FUNCTIONS ======================================================================================================== 11 | 12 | 13 | def thin_line( 14 | points: npt.NDArray[np.float64], 15 | point_cloud_thickness: float = 0.53, 16 | iterations: int = 1, 17 | sample_points: int = 0 18 | ) -> Tuple[npt.NDArray[np.float64], List[List[List[float]]]]: 19 | """Takes points in [[x1, y1, z1], [x2, y2, z2]...] Numpy Array format.""" 20 | total_start_time = time.perf_counter() 21 | if sample_points: 22 | points = points[:sample_points] 23 | 24 | # Sort points into KDTree for nearest neighbors computation later 25 | point_tree = spatial.cKDTree(points) 26 | 27 | # Empty arrays for transformed points and regression lines 28 | new_points: List[List[float]] = [] 29 | regression_lines: List[List[List[float]]] = [] 30 | 31 | # Timing variables 32 | nearest_neighbor_time = regression_line_time = projection_time = 0.0 33 | 34 | for point in point_tree.data: 35 | # Get list of points within specified radius {point_cloud_thickness} 36 | start_time = time.perf_counter() 37 | points_in_radius: npt.NDArray[np.float64] = point_tree.data[ 38 | point_tree.query_ball_point(point, point_cloud_thickness) 39 | ] 40 | nearest_neighbor_time += time.perf_counter() - start_time 41 | 42 | # Get mean of points within radius 43 | start_time = time.perf_counter() 44 | data_mean: npt.NDArray[np.float64] = points_in_radius.mean(axis=0) 45 | 46 | # Calculate 3D regression line/principal component in point form with 2 coordinates 47 | _, _, principal_components = np.linalg.svd(points_in_radius - data_mean) 48 | line_points: npt.NDArray[np.float64] = principal_components[0] * np.mgrid[-1:1:2j][:, np.newaxis] 49 | line_points += data_mean 50 | regression_lines.append(line_points.tolist()) 51 | regression_line_time += time.perf_counter() - start_time 52 | 53 | # Project original point onto 3D regression line 54 | start_time = time.perf_counter() 55 | point_to_line_start: npt.NDArray[np.float64] = point - line_points[0] 56 | line_direction: npt.NDArray[np.float64] = line_points[1] - line_points[0] 57 | point_moved: npt.NDArray[np.float64] = ( 58 | line_points[0] + np.dot(point_to_line_start, line_direction) / np.dot(line_direction, line_direction) * line_direction 59 | ) 60 | projection_time += time.perf_counter() - start_time 61 | 62 | new_points.append(point_moved.tolist()) 63 | 64 | elapsed_time = time.perf_counter() - total_start_time 65 | print(f"--- {elapsed_time:.6f} seconds to thin points ---") 66 | print(f"Finding nearest neighbors for calculating regression lines: {nearest_neighbor_time:.6f}") 67 | print(f"Calculating regression lines: {regression_line_time:.6f}") 68 | print(f"Projecting original points on regression lines: {projection_time:.6f}\n") 69 | 70 | return np.array(new_points), regression_lines 71 | 72 | 73 | def sort_points( 74 | points: npt.NDArray[np.float64], 75 | regression_lines: List[List[List[float]]], 76 | sorted_point_distance: float = 0.2 77 | ) -> npt.NDArray[np.float64]: 78 | """Sorts points output from thin_line().""" 79 | sort_points_time = time.perf_counter() 80 | 81 | # Sort points into KDTree for nearest neighbors computation later 82 | point_tree = spatial.cKDTree(points) 83 | 84 | def traverse_direction(start_index: int, direction: int = 1) -> List[npt.NDArray[np.float64]]: 85 | """Traverse points in one direction from start index.""" 86 | result: List[npt.NDArray[np.float64]] = [] 87 | current_index = start_index 88 | previous_regression_vector: npt.NDArray[np.float64] = ( 89 | np.array(regression_lines[current_index][1]) - np.array(regression_lines[current_index][0]) 90 | ) 91 | 92 | while True: 93 | # Calculate regression line vector; ensure similar direction as previous 94 | current_regression_vector: npt.NDArray[np.float64] = ( 95 | np.array(regression_lines[current_index][1]) - np.array(regression_lines[current_index][0]) 96 | ) 97 | cos_angle: np.float64 = np.dot(previous_regression_vector, current_regression_vector) / ( 98 | np.linalg.norm(previous_regression_vector) * np.linalg.norm(current_regression_vector) 99 | ) 100 | if cos_angle < 0: 101 | current_regression_vector = -current_regression_vector 102 | previous_regression_vector = current_regression_vector 103 | 104 | # Find point on regression line at specified distance 105 | target_point: npt.NDArray[np.float64] = ( 106 | points[current_index] + direction * (current_regression_vector / np.linalg.norm(current_regression_vector)) * sorted_point_distance 107 | ) 108 | 109 | # Search nearest neighbors 110 | points_in_radius: npt.NDArray[np.float64] = point_tree.data[ 111 | point_tree.query_ball_point(target_point, sorted_point_distance / 3) 112 | ] 113 | if len(points_in_radius) < 1: 114 | break 115 | 116 | # Find neighbor with smallest angle to regression line vector 117 | # CAN BE OPTIMIZED 118 | target_point_vector: npt.NDArray[np.float64] = target_point - points[current_index] 119 | nearest_point: npt.NDArray[np.float64] = min( 120 | points_in_radius, 121 | key=lambda x: vg.angle(target_point_vector, x - points[current_index]) 122 | ) 123 | 124 | current_index = np.where(np.all(points == nearest_point, axis=1))[0][0] 125 | result.append(nearest_point) 126 | 127 | return result 128 | 129 | # Start from first point and traverse both directions 130 | start_index = 0 131 | sort_points_left: List[npt.NDArray[np.float64]] = ( 132 | [points[start_index]] + traverse_direction(start_index, direction=1) 133 | ) 134 | sort_points_right: List[npt.NDArray[np.float64]] = traverse_direction(start_index, direction=-1) 135 | 136 | # Combine both directions: right (reversed) + left 137 | sorted_points_list: List[npt.NDArray[np.float64]] = sort_points_right[::-1] + sort_points_left 138 | 139 | elapsed_time = time.perf_counter() - sort_points_time 140 | print(f"--- {elapsed_time:.6f} seconds to sort points ---") 141 | 142 | return np.array(sorted_points_list) 143 | -------------------------------------------------------------------------------- /main.py: -------------------------------------------------------------------------------- 1 | def main(): 2 | print("Hello from curves!") 3 | 4 | 5 | if __name__ == "__main__": 6 | main() 7 | -------------------------------------------------------------------------------- /pyproject.toml: 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20 | figsize: tuple[int, int] = (10, 8), 21 | show_thinned: bool = False 22 | ) -> Figure: 23 | """Plot the curve reconstruction results in 3D. 24 | 25 | Args: 26 | original_points: Original noisy point cloud as (x, y, z) arrays 27 | sorted_points: Sorted points after reconstruction 28 | thinned_points: Optional thinned points to display 29 | figsize: Figure size as (width, height) 30 | show_thinned: Whether to show thinned points 31 | 32 | Returns: 33 | The matplotlib Figure object 34 | """ 35 | # Plotting 36 | fig: Figure = plt.figure(figsize=figsize) 37 | ax3d = fig.add_subplot(111, projection="3d") 38 | 39 | # Plot unordered point cloud 40 | ax3d.plot( 41 | original_points[:, 0], 42 | original_points[:, 1], 43 | original_points[:, 2], 44 | "m*", 45 | label="Original noisy points" 46 | ) 47 | 48 | # Plot sorted points 49 | ax3d.plot( 50 | sorted_points.T[0], sorted_points.T[1], sorted_points.T[2], 51 | "bo", label="Sorted points" 52 | ) 53 | 54 | # Plot line going through sorted points 55 | ax3d.plot( 56 | sorted_points.T[0], sorted_points.T[1], sorted_points.T[2], 57 | "-b", linewidth=2, label="Reconstructed curve" 58 | ) 59 | 60 | # Plot thinned points (optional) 61 | if show_thinned and thinned_points is not None: 62 | ax3d.plot( 63 | thinned_points.T[0], thinned_points.T[1], thinned_points.T[2], 64 | 'go', label="Thinned points" 65 | ) 66 | 67 | ax3d.legend() 68 | ax3d.set_xlabel("X") 69 | ax3d.set_ylabel("Y") 70 | ax3d.set_zlabel("Z") 71 | ax3d.set_title("3D Curve Reconstruction from Point Cloud") 72 | 73 | return fig 74 | 75 | 76 | def show_plot() -> None: 77 | """Display all matplotlib plots.""" 78 | plt.show() 79 | 80 | 81 | # == DEMO FUNCTIONS ==================================================================================================== 82 | 83 | 84 | def generate_spiral_points( 85 | total_rad: float = 10, 86 | z_factor: float = 3, 87 | noise: float = 0.10, 88 | num_sample_pts: int = 3000 89 | ) -> Tuple[npt.NDArray[np.float64], npt.NDArray[np.float64], npt.NDArray[np.float64], npt.NDArray[np.float64]]: 90 | """Generate noisy spiral points for testing.""" 91 | s_sample: npt.NDArray[np.float64] = np.linspace(0, total_rad, num_sample_pts) 92 | x_sample: npt.NDArray[np.float64] = np.cos(s_sample) + noise * np.random.randn(num_sample_pts) 93 | y_sample: npt.NDArray[np.float64] = np.sin(s_sample) + noise * np.random.randn(num_sample_pts) 94 | z_sample: npt.NDArray[np.float64] = s_sample / z_factor + noise * np.random.randn(num_sample_pts) 95 | 96 | # Make a [(x1, y1, z1), (x2, y2, z2)...] Numpy Array 97 | points: npt.NDArray[np.float64] = np.vstack((x_sample, y_sample, z_sample)).T 98 | 99 | return points, x_sample, y_sample, z_sample 100 | 101 | 102 | # == RUN SCRIPT ======================================================================================================== 103 | 104 | 105 | def main() -> None: 106 | """Main execution function.""" 107 | start_time = time.perf_counter() 108 | 109 | # Generate spiral points with noise 110 | points, x_sample, y_sample, z_sample = generate_spiral_points() 111 | 112 | # Shuffle points 113 | np.random.shuffle(points) 114 | 115 | generate_points_time = time.perf_counter() 116 | elapsed: float = generate_points_time - start_time 117 | print(f"\nFor {len(x_sample)} points:") 118 | print(f"\n--- {elapsed:.6f} seconds to generate sample points ---\n") 119 | 120 | # Thin & sort points 121 | thinned_points, regression_lines = thin_line(points) 122 | sorted_points = sort_points(thinned_points, regression_lines) 123 | 124 | # Create visualization 125 | original_points: npt.NDArray[np.float64] = np.vstack((x_sample, y_sample, z_sample)).T 126 | plot_curve_reconstruction( 127 | original_points=original_points, 128 | sorted_points=sorted_points, 129 | thinned_points=thinned_points, 130 | show_thinned=False 131 | ) 132 | 133 | show_plot() 134 | 135 | 136 | if __name__ == "__main__": 137 | main() 138 | 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