├── .gitignore ├── .ipynb_checkpoints └── example-checkpoint.ipynb ├── LICENSE ├── README.md ├── examples ├── example.ipynb └── 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 ├── requirements.txt └── src ├── __init__.py ├── __pycache__ └── __init__.cpython-39.pyc ├── constrained_diffusion.egg-info ├── PKG-INFO ├── SOURCES.txt ├── dependency_links.txt ├── requires.txt └── top_level.txt ├── constrained_diffusion.py └── tests ├── __init__.py └── test_constrained_diffusion_decomposition.py /.gitignore: -------------------------------------------------------------------------------- 1 | .gitignore 2 | /dist 3 | run.sh 4 | : 5 | -------------------------------------------------------------------------------- /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. 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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 | -------------------------------------------------------------------------------- /README.md: -------------------------------------------------------------------------------- 1 | 2 | 3 | # Constrained diffusion decomposition: A new PDE-based image decomposition method 4 | 5 | 6 | # General Design 7 | A natural image often contains components of different scales. 8 | 9 | This project decomposition to numpy.ndarray data, decomposing it into scale components, or scales, 1, 2, 4, 8, 16, ... pixels, enabling multi-scale analysis. 10 | 11 | The code is based on 12 | Li 2022, Multi-Scale Decomposition of Astronomical Maps -- Constrained Diffusion Method . 13 | 14 | 15 | Assuuming an input of I(x, y), the decomposition is achieved by solving the equation 16 | 17 | ```math 18 | \frac{\partial I_t }{\partial t} ={\rm sgn}(I_t) \mathcal{H}({- \rm sgn}(I_t) \nabla^2 I_t) \nabla^2 I_t ;, 19 | ``` 20 | where t is related to the scale l by t = l**2. 21 | 22 | 23 | 24 | 25 | # Installation 26 | 27 | 28 | 1. Use git clone 29 | ```bash 30 | git clone https://github.com/gxli/Constrained-Diffusion-Decomposition.git 31 | cd constrained_diffusion 32 | pip install . 33 | ``` 34 | 35 | 2. Use pip 36 | 37 | ```bash 38 | pip install --upgrade scipy numpy 39 | pip install -i https://test.pypi.org/simple/ constrained-diffusion==1.0.1 40 | ``` 41 | https://test.pypi.org/project/constrained-diffusion/1.0.1/ 42 | 43 | 44 | # Usage: 45 | 46 | ### Input: 47 | 48 | numpy nd array, of shape e.g. (nx, ny, nz) 49 | 50 | ### Output: 51 | 52 | result: numpy nd array, of shape (m, nx, ny, nz). The mth commponent contain structures of sizes 2$^(m-1)$ to 2$^m$ pixels. residual: numpy nd array, of shape (nx, ny, nz) the input data will be recovered as input = sum_i result[i] + residual 53 | 54 | 55 | 56 | ```python 57 | import constrained_diffusion as cdd 58 | 59 | result, residual = cdd.constrained_diffusion_decomposition(data) 60 | ``` 61 | 62 | 63 | 64 | 65 | # Example 66 | 67 | ```python 68 | import matplotlib.pyplot as plt 69 | from matplotlib import cm 70 | import numpy as np 71 | from astropy.io import fits 72 | from constrained_diffusion import constrained_diffusion_decomposition 73 | 74 | def multivariate_gaussian(pos, mu, Sigma): 75 | """Return the multivariate Gaussian distribution on array pos. 76 | 77 | pos is an array constructed by packing the meshed arrays of variables 78 | x_1, x_2, x_3, ..., x_k into its _last_ dimension. 79 | 80 | """ 81 | 82 | n = mu.shape[0] 83 | Sigma_det = np.linalg.det(Sigma) 84 | Sigma_inv = np.linalg.inv(Sigma) 85 | N = np.sqrt((2*np.pi)**n * Sigma_det) 86 | 87 | fac = np.einsum('...k,kl,...l->...', pos-mu, Sigma_inv, pos-mu) 88 | 89 | return np.exp(-fac / 2) / N 90 | ``` 91 | 92 | 93 | ```python 94 | # Preparing sample input 95 | N_x = 300 96 | N_y = 200 97 | X = np.linspace(0, 300, N_x) 98 | Y = np.linspace(0, 200, N_y) 99 | X, Y = np.meshgrid(X, Y) 100 | 101 | mu = np.array([150., 100.]) 102 | Sigma = np.array([[200, 0], [0, 200]]) 103 | 104 | pos = np.empty(X.shape + (2,)) 105 | pos[:, :, 0] = X 106 | pos[:, :, 1] = Y 107 | 108 | 109 | Z1 = multivariate_gaussian(pos, mu, Sigma) * 100 110 | Z3 = multivariate_gaussian(pos, mu - 10 , Sigma * 0.03) * 3 111 | 112 | Z = Z1 + Z3 113 | 114 | plt.figure() 115 | plt.imshow(Z) 116 | plt.colorbar() 117 | plt.show() 118 | ``` 119 | 120 | 121 | 122 | 123 | 124 | 125 | 126 | 127 | ```python 128 | # performing decomposition 129 | result, residual = constrained_diffusion_decomposition(Z) 130 | ``` 131 | 132 | ntot 6 133 | i = 0 134 | kernel_size 0.31622776601683794 135 | i = 1 136 | kernel_size 0.34641016151377546 137 | i = 2 138 | kernel_size 0.6928203230275509 139 | i = 3 140 | kernel_size 1.3856406460551018 141 | i = 4 142 | kernel_size 2.7712812921102037 143 | i = 5 144 | kernel_size 5.542562584220407 145 | 146 | 147 | 148 | ```python 149 | # visualizing results 150 | from pylab import * 151 | for i in result: 152 | figure() 153 | imshow(i) 154 | colorbar() 155 | ``` 156 | 157 | 158 | 159 | 160 | 161 | 162 | 163 | 164 | 165 | 166 | 167 | 168 | 169 | 170 | 171 | 172 | 173 | 174 | 175 | 176 | 177 | 178 | 179 | 180 | ## License 181 | See the [LICENSE](LICENSE) file for details. 182 | 183 | -------------------------------------------------------------------------------- /examples/example.ipynb: -------------------------------------------------------------------------------- 1 | { 2 | "cells": [ 3 | { 4 | "cell_type": "code", 5 | "execution_count": 1, 6 | "metadata": {}, 7 | "outputs": [], 8 | "source": [ 9 | "import matplotlib.pyplot as plt\n", 10 | "from matplotlib import cm\n", 11 | "import numpy as np\n", 12 | "from astropy.io import fits\n", 13 | "from constrained_diffusion import constrained_diffusion_decomposition\n", 14 | "\n", 15 | "def multivariate_gaussian(pos, mu, Sigma):\n", 16 | " \"\"\"Return the multivariate Gaussian distribution on array pos.\n", 17 | "\n", 18 | " pos is an array constructed by packing the meshed arrays of variables\n", 19 | " x_1, x_2, x_3, ..., x_k into its _last_ dimension.\n", 20 | "\n", 21 | " \"\"\"\n", 22 | "\n", 23 | " n = mu.shape[0]\n", 24 | " Sigma_det = np.linalg.det(Sigma)\n", 25 | " Sigma_inv = np.linalg.inv(Sigma)\n", 26 | " N = np.sqrt((2*np.pi)**n * Sigma_det)\n", 27 | "\n", 28 | " fac = np.einsum('...k,kl,...l->...', pos-mu, Sigma_inv, pos-mu)\n", 29 | "\n", 30 | " return np.exp(-fac / 2) / N" 31 | ] 32 | }, 33 | { 34 | "cell_type": "code", 35 | "execution_count": 2, 36 | "metadata": {}, 37 | "outputs": [ 38 | { 39 | "data": { 40 | "image/png": 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tJMnF7hvlmHQ6LhPsmJpneR6i66rkGdYRZXwMok2MtsHC9CLLIm0VCtF2aagEdUuUQ1aUlJlQLuj2OjWVCVMRIu5UuC0OuqEIQyVjxyRF0XutHmEvBi39Dl7rauw/IAzHTOves6YWORvDuCi7PqQn3KoGyqSz840S7E055aYg2OWmSrSDHWIdesKtnngnd+2JtYFKocLI8gxKsCXIMkPdEGVnUh1Vp4+VcIeZgoqQiqg4erIokDTZJvFoe36w9nZE+ohIZzzDbJGBaVBVT7MaM0SiYNumINrlpix0JnZEuTmj3JyIdi3WSbQ9xB5RCRhkRRDusmNkXQveeNfIMiPLosVNv2BbNYoSUJYFMc5sjL/t0fZC0NLvXxdtp1GUXR+X2iKpj111OtYRd9Yn2MWWjOKoLDxuhrKjvgUMTASFVbINIcqOPf0qoSwgKwwVUfBzkWWGZeE/MAPilFLhEhamdK0jbsuRWZ+/Xdskgy/Xo+05xyNtZ96oBHxwpr7KFklHM1bRdtLpWAv2UTndozMOPz9j6fnQPVqUm2IE3YWsSy3OfYJdESNtlYYKKAuRdWN03g3nhOaFNlYuR1aNnoQgtFl1odh2U88mgV60jWePLAQt/XhdtJ3x9KX7Zf22SO1nR1skj2l8nYxyU45tyig3ZxRHicPHZjx3onjuRGPp+ALbZGhJ5D/I6Dwr8sOg2BfYJ9pGItpCBdEW6Xnh9Al9FO4yRtz1sPcwO6DKrBdtK6ttEizpjMzUP0mVM39UedotxEV70WlijaRednVOpr7RjiHvOnrZUbzLTkaxOWPp6IxDLxDP/guDM37IWS96nGM3HeL//fAYvvfo8Rx+dAudZ0R+SD2fMbVHyt6jimCJWE60RZLXEI8pLQv+t1n4MimJIygteu8W0lTM6n9c1cPoE/HGLZJ5pq0foYu2M5zB4er1UmFZL8qu5gyJUTa5worpffaI6B4tDh8HxSmHec2PPMC/PelOTs6f4h+eewlf3vRy7i1PpmubsTyJtiuMJGsk2Ckhyg4diFm1ok0lvjHTxDrCytDpqDIOwikzrAwWSPUlZPV6kkUt2L1MErdI5hoXbWfuqawR6Pey4zwiliW52DEaLjui2AzF0cbRxz7HTxz7XV579AOclG3mqOxe9h/7Ir57zHE8+2wHLCPrDvnJGuccUQFZLqwbv0MU20FMB6zEvVQ4J1fMCw+jJ1X72VnP265elymMsHQWB7dHnHlgVNbIsg7I6G9bpmiREKLsTNEaiSWP3rOMssx4ptjC48UmMg7zdHkcpWXkeQmdEtssinzg1pWnXUSrIqb29Y2cNAVRLxUH34SovCwVskwKRQFX8LbLuNBvlgXzO+2QHDLPyMipW51Wo5Z+pC7aTmDUhElZtuy41BpJI+56SHqelHh6flg89/QWbn/8JWzJupy06Wm+c+hEvvPMCzl8uBNS/ToW/GaoPW2L0bOVwRpRtxp8Y2Qo9Bcmg25qG6VDEOxkfhOlEXY1crKySNJUggFfu+89crtkPjAFy6yFuGgvMqNmrxvmZw+zRipPu5r8KfraPaEMUbZKIzsksu93uHfLyTx56CiO2XyY57odnnz2aJYOxT/DzKLlkYRAVi0b1hs1U9aKTrBBOiF/W7FkeW+wjlU+e55heZmM5kwK9CwSa+hre2dk+2npx+ei7ayMxBrpRdnEbZJouzfCUQbZEmx6OmMp28LDP8zJtoRI1kphRRWOh1xqZYOiDRTCkpmEzYR1DCtFWYLyKqvEKHMF4c6tF2VX/nfd1tTmKVubs+usARdtZy7pSwnsj8ytztmuIu6QNldHuVmvrycrID8E9gPRLTvY5jzYIVlVQHmJMgtOTZIVEhZczzDKINwllB3CrH6VMNfRdVqCl24aWNasEvLUARnzOp05xUXbmVfqTsh6e3mxGMmmg13qOUXSnOuuyA737ETrUEfXygzlFtL4EtEuJaDELKNawaaySyynlwIYS99Q+LoutHFY+yWF/990dKQz37R4cM2I3qd+JF0l6RFJ30rqTpB0s6Rvx8cXxnpJ+n1J+yXdKemV69V4Z4ZIsk6sFvGkRFTZ1qkdIaJwQ6Yg3lksyizWgfJeVE6cb6Q32RS1550Kd182yLDMGGdhqdNEJ5RZo5FoA58Dzh+ouxS4xczOBm6JzyGsZHN2LBcTlh9zWsDQdL+JJ6knjBlJZ2UvkKlFHJY9ViouWSiJYKfCXe2vOyqTSJrkmlVb+uYwyVT/pVva+biSl+mCP39YwzJjNBJtM/saYen3lO3A1XH7auBtSf3nLXAr8AJJp06hrc4s0VD4Gv0CXUk4kxy77AtgJfcE964XnHmPtIdxSrKs2PeAU+L2acCDyXEHYp0zTzRMdxv8o6+e99WvxFtMjh16rSHPR19rBv8jnSPHAi/si5mZtLLvJEkXE+wTjuJ502iGs0astJXbAHGBAYM4MVPVgZiKqqE6LI7H1T8/Q76zxdQ+K0VJLwg2C2v5hf1Kzhm4FlVkZPV2/dO2tDqlT3HWv5XiIyLnjBm1Ppqwlkj74cr2iI+PxPqDwBnJcafHuj7MbKeZbTOzbZvYsoZmODNBImpBpCGdoS/Mskct5mF+EEWhD0PNrYQyinQZi5WKdWBF/zkqVa9qoziTX9+sgImID7bRceba0x7BLuDCuH0h8BdJ/XtjFslrgCcTG8VpIRZC4GR7ealXTE+i6FS46xJHLVJvC2KxIsMKUZYZZZGHUoY6K7L6OBXquwZl/z3Se/e+LHptHCxWCbuVvW1n7lHZrEy8jnS+pHtixtylQ/ZvkXRd3H+bpDOTfT8l6euS9kn6pqSjJt2vkT0i6Rrg9cBJkg4AHwN+B7he0kXAA8C74uG7gbcA+4Fngfc3uYczo6QiNiBoKi3YBvVCAxYnbqI3cdOgYJdBqLPCoCvKmKpnxMEzlsXRi7087WpEJN0sCrbIugrrRRbqv3ZfsTraVtJOqulaG75OZ06ZwscsKQeuAM4j9N/tkbTLzO5KDrsIeMLMXiZpB/Bx4N2SOsAfA+8xs3+QdCKwNOmejUTbzC4YsevcIcca8MEm13VaSGlhPcWyWvUl+sVm1KumlxbF1cji8mCK6zpmBVg3pNApC6vXVITRjhbT9XqiHSLmGGEvxVIQVmDvxsV+C+I9qjUkLQp5JdgMtNWS1+IivWhMMTPkHGC/md0HIOlaQgZdKtrbgcvi9g3ApxUm9nkjcKeZ/QOAmT3W5IZrsUectjMqogzmcs8qqISt7mQcsEbKMopkGeatLqJwxwg4K8I6kFmXWmSzbpiPJOsSRPhwLEsZdENUHUqo6+1X37lZXBihun4t4PWakhbbFNtYlsstEui9vjKxgcqeLdT4vXPaQ/PskZMk7U3KxclVmmTL1ceYWRd4EjgR+DHAJN0k6Q5Jv96k2T6M3QlYydDpWcsyLCuWHGdx/uo+4StLVGa1UKowsq6FOUG6xPlBrJ5EygQZAkIUbGWcPyQnTpcabtc3n3ZRrREJ2VKMspcqAbco3EYW762+L5AoyMP87EFhHrIye/0eOfND8+/dR81s2zq0oAP8HPAzBCv5Fkm3m9ktk05ynJqhaX9R3GRxwYDEIlFpWFGiLMMqgawEO7M4TWpYvKCawKnK5ytj+p5KKOOMfdaFvqHvSadmEGz1IutKsJdsmXCrmwh3afUvAIoyCnhijUThtjTyHnhPnPljSvZIk2y56pgD0cc+HniMEJV/zcweBZC0G3glYYT5SNwecZozzCJJoleVJeqWtRWRFRYEtRLTSmQPG9lhyA5DfhiyQ5AfCgv75rE+Lfnh3v7sEAPHWBJtR+FessTXjm1Ko+x0e/B1OYvBYFbT6rNH9gBnSzpL0mZgByGDLiXNtHsH8NXY93cT8JOSnhfF/Ofp98KH4pG2MxwLkbRlMeitbBIrl1kkKkosK+Pc1BZEMlNdsiVL5hoJG9WAm2ou7LKkNxvf4GI5Sf511iWxSAx1IV+CfCmK9VLsjFyKYt2NPnu3DFF2US63Rirbo6mf7cwHU/ieNrOupEsIApwDV5nZPkmXA3vNbBdwJfAFSfsJ04HsiOc+IemTBOE3YLeZ/dWke7poLzrWsysqX3uZRVIGQTYzhHqZF0VBPcVpWaKiiJNGgYqMbKmM/nXWv2pZJdZlENiyE7zqdGrVZfZIkjZYRe6VTVILdmWLLJXRHqmi/iJaIbEUZWh72Yu2LY3C06bWvyySeu+EnA+m9DGa2W5CqnNa99Fk+zngnSPO/WNC2l9jXLSd8ZQGeVTQsowiHVTUTEEQJZSVmHrrMGYqKEmXmMx6PzWjCJfVqumF1Svd1KKdUou29ZYU6/Z72PnhINj54TKIdVoqL7voCXYdZQ9kjdSv2Zl7ZnEyqCa4aDujqSLv6FeT58s7JJVEqKWgWwTNlcikemlHgIKMHPqGnmcFlHm18ozRt4ABsGxkZZ2HXWWKVDZJIthL/cJNN4m00xztorJ6eqmN6ehIx5lFXLSdZhZJdVwVbRPXeASkGG3H52QK+dUEwS7pCXdZzRnSCVkjlqUL8cZoe+C2qgftVMJt0d+2vkyRWrCXSrRUQLeyQwrULXpRdlGGlYDrSLscnzXi1sh80tKP0kXbGU/aIZl62yU9m6RU2EeVY13UAl4Lt4X1c1UqjpDMyLpG2YlrSebUq9AMt0esTvtTWaXzgbpliLy7obMxCHcQbBVFiPwrW6QssbLss0VSL9s7IBcIazavyCziou0EJkXbpfVlkliW9WySqkMSoEufYNfCHbM1rMxQR3W2iIqszuFGYHnsGEyyTCCINWnE3S2jvRI6HevUvm7ZL9jdomePFEUsiS0ymDFSvR0eZc8/Lf04XbSdyaSjJWO03WeT5HkYYFMdXwl3PVFTHgSvMNQxyjIjzwzrCCustkQsD5kowR7p/UfVMwgWllglIbqmDLYIMRe79rCLGGEngm11ut+ALZJ2QnqUvRCk09u0DRdtp8e4aHuYTVIUiJw+f7u6Vpfe4ghmyPJ6gqmsPl8xYySKdS566z32R9phKHs1iKc38pI470kl2pVI1x52KthlUaf6WVGMtEU8yl4QWvqRumg7oxlnkwzztyn6hbvazuIw+CwLswN2spg6kqE8inYmrNsT7WTpmvgYBbyaRySZ/KkaOBMEPMnFHhTscT52/ZI9e2QhsDmOtCVdBfw74BEz+4lY99+BXwQOA/cC7zez78fJve8G7omn32pmv7weDXfWiTTaXravZ5PUaYBS8LeLAmLUXUfXWexhzOOSZHlvBCV5nNq1IMxbIoVLj7y3hZzuOr0wfnFUlsegYBdF6HQsrSfYVX52TP/rW/BgnEh7lD2ftPR7uUmk/Tng08Dnk7qbgY/EIZwfBz4C/Oe4714z2zrNRjobyAibhCyJhKuOyaIgXSLdiCIbrZE6Os+DJ64sXkdlzDpJkroHqQR7cC7s6kugFuhk8ExlgVSWSDrvSH3dCbaIM7fMbaRtZl9Ll8eJdV9Ont5KmATFmRcGo+0G/nYt3CXE8Dmcqqx/7pKyJ96orP1sJFTdczA/fMg83vVKNOlMfVGkLWaHVFkiywS7qY9d3dOZT1r60U7D0/6PwHXJ87Mk/T3wFPBfzOxvhp3kq7HPOCNskpHCHc8xhWRrVf2TmWFR9FVdMwp2GP7eE+30fhaFu29ZsMFIe2DWvlqsE0G2Kgoflt43KNjD3gNnPjEWU7Ql/SbQBf4kVj0EvMTMHpP0KuDPJb3CzJ4aPNfMdgI7AY7TCS19++acIdkkYXO5cMNA1A1IFuwSZX3iTRbskJ6AVyse9CJtFUk70ki7eqyEOhXgdHtUdF1db5hge7bIQjG39sgoJL2P0EF5bpwbFjM7BByK27dLupewpM7etTfV2XDGCDeZep2TiXBj2TLxxoRVed+VgMPoTsj6/hYfkoyPcWJdnbNSwXYWg0USbUnnA78O/LyZPZvUnww8bmaFpB8Fzgbum0pLnY1hhL8dNgeEG/rtknHiTRm86zLmZA9b6mxoe5KOxFS4R4h12BwQeSYItkfZC8HcDmOXdA3wesLilgeAjxGyRbYAN8coqUrtex1wuaQlQkLNL5vZ4+vUdudI0VS4ldV53DBBvKGXaVKJOCzvhKwYJrJlGnmPEOv0XBdsp2KePW0zu2BI9ZUjjv0i8MW1NsqZQYYJNyzPKoG+qBsGxLso6tGO1QFKzcXBKf4q0gEwyVSqdduS56sS6/Q6ztyTzv7bNnxEpNOcYRklSTog0Fy8oZ5oqpbKLINijHD2zRFiy+pHiXXYdMF2BmjpR+6i7ayMMcIdNieLN0XR63yEfhFvQiLefaMaJ4n1wL7kIs3u68wVC5c94iwwlciNsEvC09HiDYmAQy3WmpA9YsPEdUQE7WLtTKSlH7+LtrN6RkXdMF68oU/A61OxZh2Rw+5XP20g1lXbncXF5jh7xHHGMizqhpHiHao0XExj9snoew3/Lxs6otHF2plES/8UXLSd6TBqdsAB8Q5V/f8t9bSvDQe4jBx2PukaLthOgnvajjMq6oZ+MR0YSDNWhBvdd4LYu1g7w2jpn4WLtjN9UpGcJOApk0ZFrmSouQu1M4G2RtoNxw47ziqpZuJrdGw5vkz7fs7iYoRBuE3KBCSdL+keSfslXTpk/xZJ18X9tw1OdS3pJZKekfRrTZruou0cGdJpVacpqut1XWeuqRb2bVLGXkfKgSuANwMvBy6Q9PKBwy4CnjCzlwGfAj4+sP+TwP9u2nYXbWdjGBTbJoK7mnMcZxTWsIznHGC/md1nZoeBa4HtA8dsB66O2zcA5yoOSpD0NuCfgX1Nm+2i7cwOw0TZBdpZJ2TWqBAmy9ublIuTy5wGPJg8PxDrGHaMmXWBJ4ETJT2fsEzjf11Ju70j0nGcxWNls/w9ambb1qEVlwGfMrNnJo0GTpkYaUu6StIjkr6V1F0m6aCkb8TylmTfR6Lhfo+kN63wRTiO4xwRpuFpAweBM5Lnp8e6ocdI6gDHA48BrwZ+V9L9wIeA35B0yaQbrnY1dgjfEL+XVkQDfgfwCuDFwFck/ZiZNZwJyHEc58gwpWHse4CzJZ1FEOcdwC8NHLMLuBD4OmER9K/G1b5eW7dFugx4xsw+PemGEyNtM/sa0HQhg+3AtWZ2yMz+GdhPMOodx3Fmiyl0REaP+hLgJuBu4Hoz2yfpcklvjYddSfCw9wO/CixLC1wJa/G0L5H0XsL6jx82sycIhvutyTHDTHnAV2N3HGcDaWZ9NLuU2W5g90DdR5Pt54B3TrjGZU3vt9rskc8ALwW2ElZg/8RKL2BmO81sm5lt28SWVTbDcRxnlUwn5e+Is6pI28werrYlfRb4y/i0iSnvOI6zoVSDa9rIqiJtSacmT98OVJklu4AdcdjmWYTV2P9ubU10HMeZPiqtUZk1Vrsa++slbSX8eLgf+ABANOCvB+4CusAHPXPEcZyZY0atjyZMdTX2ePxvA7+9lkY5juOsN75yjeM4TpuY10jbcRxnHmlrR6SLtuM4i4fR2knIXLQdx1lI3NN2HMdpCW3O03bRdhxn8WjxHO0u2o7jLCQeaTuO47QJF23HcZz24JG24zhOWzCgaKdqu2g7jrOQeKTtOI7TJjx7xHEcpz20NdJe7Wrs1yUrsd8v6Rux/kxJP0z2/Y91bLvjOM7qaLpqzQwK+6pWYzezd1fbkj4BPJkcf6+ZbZ1S+xzHcaaOAM1rR6SZfU3SmcP2SRLwLuAXptwux3GcdUUt9bRXu7BvxWuBh83s20ndWZL+XtL/kfTaUSdKuljSXkl7lzi0xmY4juOsgDm3R8ZxAXBN8vwh4CVm9pikVwF/LukVZvbU4IlmthPYCXCcTpjBt8ZxnPllAecekdQB/j3wqqrOzA5BCJvN7HZJ9wI/BuxdYzsdx3Gmytxmj4zh3wD/aGYHqgpJJ0vK4/aPElZjv29tTXQcx1kHqpn+JpUZo0nK3zXA14Efl3RA0kVx1w76rRGA1wF3xhTAG4BfNrPHp9hex3GctWMhe6RJmYSk8yXdI2m/pEuH7N8S06T3S7qtSuyQdJ6k2yV9Mz42SuhY7WrsmNn7htR9Efhikxs7juNsKFMIoqOzcAVwHnAA2CNpl5ndlRx2EfCEmb1M0g7g48C7gUeBXzSz70r6CeAm4LRJ91xr9ojjOE4rkVmjMoFzgP1mdp+ZHQauBbYPHLMduDpu3wCcK0lm9vdm9t1Yvw84WtKWSTd00XYcZzGZjqd9GvBg8vwAy6Pl+hgz6xIGI544cMx/AO6IyRxj8blHHMdZPAxovrDvSZLSDLidMWV5Kkh6BcEyeWOT4120HcdZOEQj66PiUTPbNmLfQeCM5PnpsW7YMQdiqvTxwGMAkk4HbgTea2b3NmmM2yOO4ywmZdmsjGcPcLaksyRtJmTV7Ro4ZhdwYdx+B/BVMzNJLwD+CrjUzP62abNdtB3HWTwqe6RJGXeZ4FFfQsj8uBu43sz2Sbpc0lvjYVcCJ0raD/wqUKUFXgK8DPhoMjPqiyY13e0Rx3EWkmlNGGVmu4HdA3UfTbafA9455LzfAn5rpfdz0XYcZzGZwdGOTXDRdhxnAZnNIepNcNF2HGfx8NXYHcdx2kVbF0Fw0XYcZzFx0XYcx2kJBpQu2o7jOC3BOyIdx3HahYu24zhOSzCgaD5j1CwxE6L9NE88+hW74QeEScHbwkm0q73gbT4StK290L42/8jaL2FgLtqrxsxOlrR3zExaM0fb2gve5iNB29oL7WzzVHB7xHEcpyV49ojjOE7L8Eh7zUxtJYgjRNvaC97mI0Hb2gvtbPPaaaloy1racMdxnNVy/KYX2b8+adlsqUP50vf+4PZZ8vxnKdJ2HMc5crQ0YHXRdhxnMWmpaG/4cmOSzpd0j6T9ki6dfMbGIOl+Sd+MSwLtjXUnSLpZ0rfj4ws3uI1XSXpE0reSuqFtVOD34/t+p6RXzkh7L5N0MFl+6S3Jvo/E9t4j6U1Hur2xDWdI+mtJd0naJ+lXYv1Mvs9j2jvT7/P6YyF7pEmZMTZUtCXlwBXAm4GXAxdIevlGtmkCbzCzrYm/dSlwi5mdDdxCb+23jeJzwPkDdaPa+Gbg7FguBj5zhNqY8jmWtxfgU/F93hqXciL+XewAXhHP+YP493Ok6QIfNrOXA68BPhjbNqvv86j2wmy/z+uLgVnZqMwaGx1pnwPsN7P7zOwwcC2wfYPbtBK2A1fH7auBt21cU8DMvgY8PlA9qo3bgc9b4FbgBZJOPSINjYxo7yi2A9ea2SEz+2dgP+Hv54hiZg+Z2R1x+2nCYq6nMaPv85j2jmIm3ucjQlE2KzPGRov2acCDyfMDjP+D2kgM+LKk2yVdHOtOMbOH4vb3gFM2pmljGdXGWX7vL4lWwlWJ5TRz7ZV0JvDTwG204H0eaC+05H1eF8ygLJuVGWOjRbtN/JyZvZLwc/eDkl6X7rSQOzl7BlhCG9pIsA9eCmwFHgI+saGtGYGk5wNfBD5kZk+l+2bxfR7S3la8z+uKWbMyY2y0aB8Ezkienx7rZg4zOxgfHwFuJPxkfLj6qRsfH9m4Fo5kVBtn8r03s4fNrLBgJn6W3k/zmWmvpE0EAfwTM/uzWD2z7/Ow9rbhfV5vrCwblVljo0V7D3C2pLMkbSZ0gOza4DYtQ9Ixko6ttoE3At8itPXCeNiFwF9sTAvHMqqNu4D3xuyG1wBPJj/vN4wBv/fthPcZQnt3SNoi6SxCx97fbUD7BFwJ3G1mn0x2zeT7PKq9s/4+rz8No+wZjLQ3NE/bzLqSLgFuAnLgKjPbt5FtGsEpwI3h758O8Kdm9iVJe4DrJV0EPAC8awPbiKRrgNcDJ0k6AHwM+B2Gt3E38BZCR9OzwPtnpL2vl7SVYC/cD3wAwMz2SboeuIuQEfFBMyuOdJuBnwXeA3xT0jdi3W8wu+/zqPZeMOPv8/rS4gmjfBi74zgLx3HZifaaTrMU9JuXrpmpYewbbY84juMceSwugtCkTEATBghGq+m6uP+2mMVT7VvxQCYXbcdxFhIrrVEZR8MBghcBT5jZy4BPAR+P565qIJOLtuM4i8l0Iu0mAwTTgVc3AOfGDuJVDWTyCaMcx1k4nuaJm75iN5zU8PCjFOcbiuw0s2oO8mGDkV49cH59TEy+eBI4MdbfOnDuxIFMLtqO4ywcZjZszptW4PaI4zjO6mkyGKk+RlIHOB54rOG5y3DRdhzHWT1NBgimA6/eAXw1TnWwqoFMbo84juOsklEDBCVdDuw1s12EEalfkLSfMKvljnjuqgYy+eAax3GcFuH2iOM4Totw0XYcx2kRLtqO4zgtwkXbcRynRbhoO47jtAgXbcdxnBbhou04jtMi/j/wlr6gb0ATZwAAAABJRU5ErkJggg==", 41 | "text/plain": [ 42 | "
" 43 | ] 44 | }, 45 | "metadata": { 46 | "needs_background": "light" 47 | }, 48 | "output_type": "display_data" 49 | } 50 | ], 51 | "source": [ 52 | "# Preparing sample input\n", 53 | "N_x = 300\n", 54 | "N_y = 200\n", 55 | "X = np.linspace(0, 300, N_x)\n", 56 | "Y = np.linspace(0, 200, N_y)\n", 57 | "X, Y = np.meshgrid(X, Y)\n", 58 | "\n", 59 | "mu = np.array([150., 100.])\n", 60 | "Sigma = np.array([[200, 0], [0, 200]])\n", 61 | "\n", 62 | "pos = np.empty(X.shape + (2,))\n", 63 | "pos[:, :, 0] = X\n", 64 | "pos[:, :, 1] = Y\n", 65 | "\n", 66 | "\n", 67 | "Z1 = multivariate_gaussian(pos, mu, Sigma) * 100\n", 68 | "Z3 = multivariate_gaussian(pos, mu - 10 , Sigma * 0.03) * 3\n", 69 | "\n", 70 | "Z = Z1 + Z3\n", 71 | "\n", 72 | "plt.figure()\n", 73 | "plt.imshow(Z)\n", 74 | "plt.colorbar()\n", 75 | "plt.show()" 76 | ] 77 | }, 78 | { 79 | "cell_type": "code", 80 | "execution_count": 3, 81 | "metadata": {}, 82 | "outputs": [ 83 | { 84 | "name": "stdout", 85 | "output_type": "stream", 86 | "text": [ 87 | "total number of scales 6\n", 88 | "current channel 0 current scale 1\n", 89 | "current channel 1 current scale 2\n", 90 | "current channel 2 current scale 4\n", 91 | "current channel 3 current scale 8\n", 92 | "current channel 4 current scale 16\n", 93 | "current channel 5 current scale 32\n" 94 | ] 95 | } 96 | ], 97 | "source": [ 98 | "# performing decomposition\n", 99 | "result, residual = constrained_diffusion_decomposition(Z)" 100 | ] 101 | }, 102 | { 103 | "cell_type": "code", 104 | "execution_count": 4, 105 | "metadata": {}, 106 | "outputs": [ 107 | { 108 | "data": { 109 | "image/png": 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", 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FOJlbZ9VrnWvo2IQOk5e6rXed3OvHJHK3ym0m+uxr4mRusyO1zusmdGnSeuWT5HcaapTI3Sq3aXA3i9l0VVvnUyR0qEnqdS9TbZ1PkcjdKrciolwjVYpwMrfZ0Sihw8QGzdFsoGxN4nYit5b02dellXHmZtMTUyTjqGTJeqqSG3fuRG4ta9OkIUmrJL2QVoq9ts7r8yTdk15/UtKyVL9Q0k8kvSXpuzXnnCfp6XTOdzRp8aLJnMxtdsWxCTwqMVEmTRaqKXWPzV/TbBrasdCWpGHgJrLVYs8B1ko6p+awq4GDEXEWcCPw7VT/DvB14D/VufTNwBc5ugJt7aq1kziZ2+yLmJTUs4cxZak9/pjrmHXH+cBoRLwUEe8Cd5OtHJuXX2H2PuAiSYqIX0XET8mS+oS0PMr8iHgizdu5g6Or0jbkZG7dUy+pNyu155nNVPFulkWStubKutxViqwSO3FMRIwBbwALp4js1HSdqa45iW+AWvfVbOrc9BizVk1vNMv+iFjZwWjawi1z6y3VVndtMWu39twALbJK7MQxkkaAE4EDTa55WpNrTuJkbmYDR7Rtp6EtwHJJZ0iaC6whWzk2L7/C7GXAYzHFCnFpldk3JV2QRrFcydFVaRtyN4uZDaY2/MEXEWOS1gMPAcPAxojYIel6YGtEbAJuBe6UNEq2/eaa6vmSXgbmA3MlXQpcHBHPAn9CtvfybwB/l8qUnMzNbPC0cdXEiNhMtvR3vu663ON3gMsbnLusQf1W4EPTiaNpN4ukjZL2SXomV/ffJD0v6SlJD0g6KdUvk/RrSdtT+evpBGNmNmsqBUtJFOkzv43JA9YfBj4UEf8C+Cfgq7nXdkbEilS+3J4wzczaq0195j2jaTKPiMfJ+nnydT9O4yUBnuDYO69mZr2vTdP5e0U7RrP8B47tnD9D0s8l/b2kjzU6SdK66iD8IxxuQxhmZgUVTeQlSuYt3QCV9F+AMeD7qWoP8P6IOCDpPOBvJZ0bEW/WnhsRG4ANAPO1oEQfmZn1gzJ1oRQx45a5pD8G/hD4XHXMZEQcjogD6fE2YCdwdhviNDNrL7fMsyUfgf8M/OuIeDtXvxh4PSLGJX2AbLWvl9oSqZlZGw3c5hSS7gIuJFtsZhfwDbLRK/OAh9Myu0+kkSsfB66XdIRsUM+XI+L1uhc2M+uWkrW6i2iazCNibZ3qWxscez9wf6tBmZl1klLpJ54BamaDadBa5mZm/ajfRrM4mZvZYHIyNzMrueltTlEKTuZmNpjcMjczKz/3mZuZ9QMnczOz8nPL3Mys7IJSbTxRhJO5mQ2c6obO/cTJ3MwGk5O5mVn5KformzuZm9ng6cNVE5tuTiFpo6R9kp7J1X1T0m5J21O5JPfaVyWNSnpB0qc6FbiZWSsGbkNn4DZgVZ36GyNiRSqbASSdA6wBzk3nfE/ScLuCNTNrF1WKlbJomswj4nGg6AYTq4G70/ZxvwBGgfNbiM/MrDP6bNu4Ge8BCqyX9FTqhjk51Z0KvJo7Zleqm0TSOklbJW09wuEWwjAzm6aCXSz91s1Sz83AmcAKYA9ww3QvEBEbImJlRKycw7wZhmFmNkN91jKf0WiWiNhbfSzpFuCH6elu4PTcoaelOjOzntGPk4Zm1DKXtDT39DNAdaTLJmCNpHmSzgCWA//YWohmZu2nShQqZdG0ZS7pLuBCYJGkXcA3gAslrSD7I+Rl4EsAEbFD0r3As8AYcE1EjHckcjOzmSpZF0oRTZN5RKytU33rFMd/C/hWK0GZmXVamYYdFuEZoGY2mAatZW5m1o/67Qaok7mZDZ4AvNCWmVn5uc/czKzk+nGcuZO5mQ2eCHezmJn1g35rmbey0JaZWXm1aW0WSavS/g2jkq6t8/o8Sfek15+UtCz3Wt39HyS9LOnptF/E1iL/HLfMzWwgtaNlnvZruAn4JNkqsVskbYqIZ3OHXQ0cjIizJK0Bvg18tmb/h/cBj0g6Ozdr/hMRsb9oLG6Zm9ngCWA8ipWpnQ+MRsRLEfEucDfZvg55q4Hb0+P7gIskiTbv/+BkbmYDaRrrmS+q7r2QyrrcZYrs4TBxTESMAW8AC5ucG8CPJW2reb+G3M1iZoOp+GiW/RGxspOh1PHRiNgt6RTgYUnPp13fGnLL3MwGUpt2Giqyh8PEMZJGgBOBA1OdGxHVn/uAByjQ/dI0madt4fZJeiZXd0+6y7o93XXdnuqXSfp17rW/bnZ9M7NZV3QkS/NkvgVYLukMSXPJbmhuqjlmE3BVenwZ8FhEBA32f5B0nKQTACQdB1zM0T0jGirSzXIb8F3gjmpFRHy2+ljSDWR9QFU7I2JFgeuamXWFADW/udlURIxJWg88BAwDG9O+DtcDWyNiE9mS4XdKGgVeJ0v4Dfd/kLQEeCC7R8oI8IOI+FGzWIqsZ/54flxkXrojewXwB82uY2bWS9SmGaARsRnYXFN3Xe7xO8DlDc6dtP9DRLwE/O5042i1z/xjwN6IeDFXd4akn0v6e0kfa3SipHXVu8NHONxiGGZm09C+bpae0epolrXAXbnne4D3R8QBSecBfyvp3Ih4s/bEiNgAbACYrwUl+sjMrPy8NsuEdFf23wHnVesi4jBkzeyI2CZpJ3A2UGg6qpnZbPHaLEf9G+D5iNhVrZC0OE1vRdIHyO7OvtRaiGZmHVBdObFZKYkiQxPvAv4B+G1JuyRdnV5aw7FdLAAfB55KQxXvA74cEa+3MV4zs9ZFNpqlSCmLIqNZ1jao/+M6dfcD97celplZh5UnTxfi6fxmNpDaNTSxVziZm9lgcjI3Myu5ALyhs5lZuYlwN4uZWV+o9FfT3MnczAaPu1nMzPqDu1nMzPqBk7mZWdmVa6p+EU7mZjZ4AijRVP0inMzNbCC5z9zMrB84mZuZlVwAFSdzM7OS8w1QM7P+4GRuZlZyAYz31xTQnkjmhzi4/5G471fA/m7HMg2LKFe84JhnQ9nihfLF/FutXyIgnMzbLiIWS9oaESu7HUtRZYsXHPNsKFu8UM6Y28LdLGZmJefRLGZmfcIt847Z0O0Apqls8YJjng1lixfKGXPr+iyZK/rsH2Rm1syJc06Jf7Xo8kLH/ui1720rwz2FXmqZm5nNnj5ryDqZm9lg6rNkPtTtACStkvSCpFFJ13Y7nkYkvSzpaUnbJW1NdQskPSzpxfTz5C7HuFHSPknP5OrqxqjMd9Ln/pSkD/dIvN+UtDt9ztslXZJ77asp3hckfWq2400xnC7pJ5KelbRD0ldSfU9+zlPE29Ofc+dFNpqlSCmJriZzScPATcCngXOAtZLO6WZMTXwiIlbk+s+uBR6NiOXAo+l5N90GrKqpaxTjp4HlqawDbp6lGPNuY3K8ADemz3lFRGwGSN+LNcC56Zzvpe/PbBsD/iwizgEuAK5JsfXq59woXujtz7mzAiIqhUpZdLtlfj4wGhEvRcS7wN3A6i7HNB2rgdvT49uBS7sXCkTE48DrNdWNYlwN3BGZJ4CTJC2dlUCTBvE2shq4OyIOR8QvgFGy78+siog9EfGz9PgQ8BxwKj36OU8RbyM98TnPivFKsVIS3U7mpwKv5p7vYuovWjcF8GNJ2yStS3VLImJPevwasKQ7oU2pUYy9/NmvT10SG3NdVz0Xr6RlwO8BT1KCz7kmXijJ59wREVCpFCsl0e1kXiYfjYgPk/3ZfI2kj+dfjGyMZ093sJUhRrJuiDOBFcAe4IauRtOApOOB+4E/jYg386/14udcJ95SfM4dFVGslES3k/lu4PTc89NSXc+JiN3p5z7gAbI/PfdW/2ROP/d1L8KGGsXYk599ROyNiPHIOitv4eif+D0Tr6Q5ZInx+xHxN6m6Zz/nevGW4XPutKhUCpWy6HYy3wIsl3SGpLlkN142dTmmSSQdJ+mE6mPgYuAZslivSoddBTzYnQin1CjGTcCVabTFBcAbuW6CrqnpT/4M2ecMWbxrJM2TdAbZDcV/7EJ8Am4FnouIv8q91JOfc6N4e/1z7ryCrfIStcy7Os48IsYkrQceAoaBjRGxo5sxNbAEeCD7f8EI8IOI+JGkLcC9kq4GXgGu6GKMSLoLuBBYJGkX8A3gL6gf42bgErIbXG8DX+iReC+UtIKsm+Jl4EsAEbFD0r3As2QjNK6JiPHZjhn4feDzwNOStqe6r9G7n3OjeNf2+OfcWX240Jan85vZwJk/tDAuGCk2hP7hI3eVYjp/t7tZzMxmX6TNKYqUJtRk4mPqsronvf5kGlVUfa3uBK1m16zHydzMBlJUolCZSsGJj1cDByPiLOBG4Nvp3LoTtGY6mdLJ3MwGU3ta5kUmPuYnlN0HXJRuTDeaoDWjyZReaMvMBs4hDj70SNy3qODh71FajynZEBHVNeDrTbL6SM35E8ekQR9vAAtT/RM151YnaDW75iRO5mY2cCKi3ppApeZuFjOzmSsyyWriGEkjwInAgSnOndHELSdzM7OZKzLxMT+h7DLgsbTkQ6MJWjOaTOluFjOzGWo08VHS9cDWiNhENgP3TkmjZKuErknnNpygNZPJlJ40ZGbWB9zNYmbWB5zMzcz6gJO5mVkfcDI3M+sDTuZmZn3AydzMrA84mZuZ9YH/D3WJxuL+PMhKAAAAAElFTkSuQmCC", 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", 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cG3ToFx2qIqfOcyzPYiBvRoyaYu+XkJFVRqhzVAWyqoPaAV2CTN46n3YT9r/eg7lbm6ZVnmWLrfJOQZgpqGcK6pks9lqZFfUMVLMQ5mo62wbs2DbP2XPHOGfmCGd2jrE97zObl+QpmNeW0Q8Fx+oux+oOh6oeBwczHC56HMlrjuZdyswIKlhItIcYyLOmC2OVxYunZUBlwDoFKtN8MHkVc+d4y3yqeZrFORanrE0zH1LEVEvoFosDgnpQz0A9Y4TZQDZbMTtTctbsPOfOHOaFM4d4QXGUM4ujzGUDuqoAGFhBaTlHQ5fD9QzPV7NsKwY8X8zwXD5HlgWOZj36gkDsoB5b5CKrhKrF3i+hm5NVASsLVORpoq8c8hqrM0+1TDF5y9y5uDKQpHTxM8eKPM63UmSETkbdIY7u7EDognUD3V7F9pk+L+gdZWfvMC/sHGJn5xBn5UfYlvXppJZyIGNgOUdDj4P5LNvz+Rjss4oiC2QLuXUYBMWZcaucUMb+51kJ9UBkXZENRCgysiLOzLiQ48/itLyeaplSFntKTRIP5u7UtVcEaoJjHoN56GaEbpxrJXRSX/COoW6g06mZ65Ts6PQ5o5jn7OIw5+SHOSs/wo5snhmlYG5iQMa8ddgRjrEt28aMKjpZTS4jmOIWYo+XshJ1LyMrIQya17Y0slQLszKqSL8gFqbazfBUyxSbsO/wVRZddG4FzUAhKQbHIicUGaFQ2kibYYWhPNDJa3p5xWxesiOfZy7rsyM7xlnZMc7KBpyVVZydVezMS87N+pyTHePc/BDn5gc5tzjIzuIwZxVHeUH3GDu6feZ6AzrdCnUD1g2LXx5Fa+uk7otFhjU5/uMWwvB/AlPLhtxWIekaSY9I2ifpxmWe70m6Mz1/r6SLU/k5kr4h6bCkjy055m/SOR9I2wtXq4e3zN2pa6/dmQLjQp/v1O/bcha6fJOBciPPjEKBQjUd1cxkJTNZyZwq5mRsU0aWWv3BjBmr6aQl45rUy3ynoB8KjhRdjnU6HOt0KDsFZZGnLw7iLIxF7LoY8nQ/i8P9UVPv2DqfsMaZOxUj+J+flsz8OHHCwf3AfZL2mNnDrd2uB54zs0sl7QI+BLwVmAfeC7w4bUu9zcz2DlsXb5a4dZGE5dnCgszNNLbNhsCyOKxeMjLFnHemQI7RJaZOuhIdZcyoYE5d5rIOc1nODhk7VLIjO8YZ+Tw7snm2F322FQNmi9hHPS8CFAErLLbG8zRuKG/qkYJ5U9f24hfZZOVN3ZCaQUPDbCf3MmCfmT1mZgPgDuDaJftcC9yW7t8FXCVJZnbEzP6WGNTXbahgLulWSU9JerBVdrakr0j6x3T7glQuSR9NPym+K+klo6io21qU+mq3l3mzXDF4L/P5bxpBwbKU844fvToN9smAjIyCnI5yCnJmVDCjjG1ZYJtK5tRnLuvTU8VsHi+IdvM0ejQzaH4NHPdFEutEs4KR0kxcSl9A8Y/Z4HfLbUWy4TZgp6S9rW136zQXAD9sPd6fylhuHzOrgOdZMtvsCv4spVjeqyEWVx62Zf4p4JolZTcCXzOzy4CvpccQVx66LG27icvIuQmybGt2pU/SQu5R1EFUllFZTpm2mozadMI0GbkyMmLaJQM6CnRV003pmY5qiiyQZ4Esi8HcMkuDiEiBfPH+Qh2bgO7c8Dnzp83sytZ282mo3dvM7KeBX0jbqlOLDxXMzeybwLNLits/HW4D3tAq/7RF3wLOknT+MK/jxowW0yvLalo3QYRaVHVOWef064L50OFI6HE09OhbzrwZfauoqKktUFsgrDITUtZOeraroOMfW2uB6MWDPaBPu1NomZ/MAeCi1uMLU9my+0gqgDOBZ052UjM7kG4PAZ8lpnNOaj058/Nay8P9CDgv3R/mZ4ebJO1+2gsBfHE+cmphtajqjH5dcKzucLiOgfxI6HHEOhwJGfMWmLeKftpKqykthvQapS1bSM2E4yI2x99vx3mzuDB0W/BLn1NvNDnz+4DLJF2SFrffBexZss8e4B3p/puAr5utPLhBUiFpZ7rfAX6JIZbfHElvFjMz6dTGU6W8026AGeZGUQ13mliIFzSxEOcIh7iIRAqaTSCPqwPFlYHqKqOqcuargsNVjyN1j+frWeayPjPZgI5qchtQh5quAlk8JQOzFOhz5q0T0zOhoB86VCGjDnFmRTOhoNiSWqlrWZoS1wcJuWG7Ha56GrNK0g3APcSrNrea2UOS3g/sNbM9wC3AZyTtI2Y4djXHS3ocOAPoSnoDcDXwA+CeFMhz4KvAJ1ery3qC+ZPN4s0pjfJUKh/mZwcp73QzwBk62/91jasUHONUs7awMlCz1JtqUCWoRF3l9MuCI2WXg+UM2/JZ5rIBM1lJjgGHKVXRST1dAOYt54gVHAozHAk9DtWzHA1d+qFgvu5Qhoy6zrC0kMXC6y9sln4dpNa5NYtUtL6IPLhPpxH9bzezu4G7l5Td1Lo/D7x5hWMvXuG0Lz3VeqwnmDc/Hf443X6xVX6DpDuAlwPPt9IxbkKYxdV7zAzVYeGxgqXpZ0XWWrtTpagHGfODDke7HQ6WM8zmJb2sopNGftaI+WyeLrEfeo0oLY9BPMzyL/U2DtUzHK57HKm69OuCfllQVxlU2XErE6mOk241AT222O2Elrl5umVqaRoXp5B0O/AqYhed/cD7iEH8c5KuJ/4seEva/W7g9cA+4CjwzhHX2W02C9AE8pBa5nW8n1VGVqfbslnqLc6RUg8yykHB0X6Xg3lNN4tD9IHFwJ31mNHiDIqlxYulB8Msz1XbeK6a4/lyloPlDEfLDoOqCebpdZq1QutYp+ZWdfzl0HzxNPV3U2zC/vcPFczN7LoVnrpqmX0NePd6KuXGRAhxtfs6pAUgQgygpcXWeGsB5qwUYZBR93Pmiw6H8po8myOTUVsM5EfzHjvyeXpZSU4TzGOuvJk98dnBNp4fzHB40ONov8ugXxD6ORpki69Xpteum9smoNexznUd1wENFr+Y3NQZsqfKWPHh/G5tLAZFgsUFH0KIC0GUAVVxcYh8IMLACF3FdTuLjLowyrzgaNZb6B1YhYxBKDhWdHg+n2UmKxe6HQYUuzFWPQ5WPQ4OZnl+MMOhfpdj/Q5Vv4BBlhZ5btYJNfJ0m1WGygBVWPjSoU6rDXkgn24+n7mbemYx12yxtWshoKqGskZlTVbm5AMjdIx6IPJ+nPQqL8DyjKCCfrPWZxBlnTNfdzhU9JgrBnQUKFL6pQp5uthZcLjscbTscrjf5eh8l8F8B5vPyeYz8j5k/fQrYJAC+sDIykBWBVTWsY7NOqAhLPwNbkpN2P96D+ZubZq8eV2jqoIybioLskFN1hF5RxQFWEGa+KpZfDkjUDAwCE0wrwpmih69IubRmznLg4ky5PSrgvmqiEvH9QuqfoEdK1IgF/l8/NLI+0Y+IAVyIxukQJ7qZ1WF1TVWB2+ZTzlPszgHi2mKpqVbVaisyAYV1snIO1mcvTDP4syFeTO8vlmvMyNYQVll1FXOYFBwrBsXnyjycNzizk3rvSxzqrKg7ufQz2IgnxfF0SaQQzEPRd/I+zGQZ2WN+imYV2nzFIuzKe3N4txyLFjMP5cVFNVC6zcbxBWHslzkhbDclgTyuF5nXeeEGRHKjEE3pxrkKLc410qzq4GFjFCLUOZQCg0ysr4WW+TzUByD4pillnmIW78VyMsKK0usDrFl7ikWN2H/+z2Yu7WzEC8ipZY5VYUGJRR5DORZeybFLM2XooX5WlRDqLO4KtBAhE4GmVHntji3igF1XOJLlVDq5pgPSAE9tsbzY0YxH7d83siP1WT9+EtBgxLKMtax+SXhLXPnwdy5pLkQ2rTO8zKusTkoUZaRZ9nCghDWJCibeVvSAJ9QitBtVgSi1Ypn2f0X+66zcNGzCeIxkAfy+RjINaigP1hslZeVt8rdAs+ZO9fWbp2XFZaVca5zCdLKbPFDViATsgyFOF9LVsV1QusyrQpUkC6S2pJgHtMyquJo0qwktswH6WJnfzGQF8dq8vkqBvP5EvVLLAV0b5W7SebB3K2PxR4twOKK982ScmkuckgfNMvTfC2iroSquGZnNlAK5GlrFpSAxZZ5O5hXRjaAvGyCeYi58vkUyI+V6NgA9QfYYADlIPViiflyb5U7wNMszp2gSbeUFRDjsKVbzOKaEAbURqhyVGdkVUZextZ43WExmGfLBXNrzcIYg3kzKCgfBLJ+IO+HmCOfL1OLfBBTLIOUXkkpFg/kDvDeLM6tKNTHNXSWBnTVBqGIw/2rjGyQEboZoRN7vDQLMFvG4mpBkOZHbwXzhXlfFvuRZ4OUI+/XqD9A86lFPiixwWChb7mnV9xxJux73YO5Gx0LWL34UKS5z9PEVlka8m9ljro5VmaEIlscUJSngC6dGMzr1EKvaY3qTNMHDOLFTvXLGMD7KbXSDBIqq5Tbn7B/vW7NhF8AdW5lZsCSgB4Ms4DqOk50VRao20Fl6oveybE8DjCylG9fOmWGFlIthqo486GaIfplvPCqQQrkZbqt2qkVD+RuGRP2kfBg7kbLDKyVcgmhmYQlzqzY7cTJroocdQoszyEXVsT1RE1AtrhmZ9Oql8VzqTao4pcD1fHD9JsgTmtwkAdyt6xpnDVR0q3ENeieMrMXp7L/BvwyMAAeBd5pZv8i6WLg+8Aj6fBvmdlvbUTF3RYXasxCuqppkFrmFmqoClQU0C9RkWNFjrIM8iz1ST++ab6wQlAd0uyMaSrbqo7Buzp+3pWFKW49iLuTmbBLKMO0zD8FfAz4dKvsK8B70vp3HwLeA/yn9NyjZnbFKCvpxlTTbTFY2uJcLsqr1CLPUFHEgUbSQjDXkmC+sDpQ6xxWh4URnYsB3FvjbnhT1zI3s2+mFne77Muth98irjjt3ImatEvTSq8DllUxgKfRouR5HF0kgdJIo7ZmabeQvhjqOq4S1Exlm2ZA9Na4OyUT9lEZRc78N4A7W48vkfQd4CDwX8zs/yx3kKTdwG6AGeZGUA23pS0MLqpjwK7TbR5z5XHEaBxitLRlvrC8W5N/D2EhmFt7tSAP5G5YhgfzNkn/GaiAP09FTwA/ZmbPSHop8L8kvcjMDi491sxuBm4GOENnT9jb6pbVBFurMRMozYeepRY5xIufyx3btM4tLC7C7OkUtw5Tl2ZZiaRfJ14YvSqt+4mZ9YF+un+/pEeBnwT2rr+qbqKk9Eu8K6DdnzFbZv/W1SoP4G4UJuxjtKZgLuka4D8C/9bMjrbKzwWeNbNa0o8DlwGPjaSmbnItDc7tjurObZCpG84v6XbgVcBOSfuB9xF7r/SAr6T8ZtMF8ZXA+yWVxI4/v2Vmz25Q3Z1zbm2mMWduZtctU3zLCvt+Hvj8eivlnHMbqT39z6TwEaDOuek0bS1z55ybRJPWm2WZbgPOOTcFbMhtFZKukfSIpH2Sblzm+Z6kO9Pz9zaDMCWdI+kbkg5L+tiSY14q6XvpmI/qhGHRJ/Jg7pybPu0VrFbZTkZSDnwceB1wOXCdpMuX7HY98JyZXQp8BPhQKp8H3gv8h2VO/QngN4k9Ai8DrlntT/Jg7pybTqNpmb8M2Gdmj5nZALgDuHbJPtcCt6X7dwFXSZKZHTGzvyUG9QWSzgfOMLNvpTE8nwbesFpFPJg756aSbLiN2C17b2vb3TrNBcAPW4/3pzKW28fMKuB54JyTVO2CdJ6TnfMEfgHUOTedhr8A+rSZXbmBNRkJb5k756bSKbTMT+YAcFHr8YWpbNl9JBXAmcAzq5zzwlXOeQIP5s656RNXOBxuO7n7gMskXSKpC+wC9izZZw/wjnT/TcDXzVaeYMjMngAOSnpF6sXyduCLq1XE0yzOuakzqgWd0wI9NwD3ADlwq5k9JOn9wF4z20McMf8ZSfuAZ4kBP9ZDehw4A+hKegNwtZk9DPw2cWGgWeCv03ZSHsydc9NpRIOGzOxu4O4lZTe17s8Db17h2ItXKN8LvPhU6uHB3Dk3lTRhUyl7MHfOTZ8JnDVx1Qugkm6V9JSkB1tlfyjpgKQH0vb61nPvSUNQH5H02o2quHPOrceIerNsGcP0ZvkUyw8l/YiZXZG2uwHSMNZdwIvSMX+ahrs659yWMorh/FvJqsHczL5JvAI7jGuBO8ysb2b/BOwjDnd1zrmtZUQTbW0V6+lnfoOk76Y0zAtS2TBDWwGQtLsZHlvGZUOdc+70GDLFMmlpluV8AvgJ4ArgCeDDp3oCM7vZzK40sys79NZYDeecW6MJa5mvqTeLmT3Z3Jf0SeAv08NhhrY659ymGtWgoa1kTS3zNEVj441A09NlD7ArTcZ+CXEe3r9fXxWdc270FGyobVys2jKXdDvwKuI0kPuB9wGvknQF8UfI48C7ANIw1s8BDwMV8G4zqzek5s45t1ZjlkIZxqrB3MyuW6b4lpPs/0Hgg+uplHPObbRx6nY4DB8B6pybTtPWMnfOuUk0aRdAPZg756aPAT7RlnPOjT/PmTvn3JibxH7mHsydc9PHzNMszjk3Cbxl7pxzk8CDuXPOjT9vmTvn3LgzoJ6saO7B3Dk3lbxl7pxzk8B7szjn3PibtJb5qvOZp2XhnpL0YKvsTkkPpO1xSQ+k8oslHWs99z82sO7OObc2w64yNEYBf5iW+aeAjwGfbgrM7K3NfUkfBp5v7f+omV0xovo559zICdC0XQA1s29Kuni55yQJeAvwiyOul3PObShNWM58rQs6N34BeNLM/rFVdomk70j635J+YaUDJe2WtFfS3pL+OqvhnHOnYALTLOsN5tcBt7cePwH8mJn9LPB7wGclnbHcgWZ2s5ldaWZXduitsxrOOXcqbHF+ltW2VUi6RtIjkvZJunGZ53vpOuM+Sfe2Mx2S3pPKH5H02lb545K+l6497h3mL1pzbxZJBfDvgZc2ZWbWh9jMNrP7JT0K/CQwVGWcc+50GUVvFkk58HHgNcB+4D5Je8zs4dZu1wPPmdmlknYBHwLeKulyYBfwIuBfAV+V9JOtdZNfbWZPD1uX9bTM/x3wD2a2v/WHnZv+OCT9OHAZ8Ng6XsM55zbGaFrmLwP2mdljZjYA7gCuXbLPtcBt6f5dwFXpeuO1wB1m1jezfwL2pfOtyTBdE28H/i/wU5L2S7o+PbWL41MsAK8Evpu6Kt4F/JaZPbvWyjnn3Iaw2JtlmA3Y2VzfS9vu1pkuAH7Yerw/lbHcPmZWEXv/nbPKsQZ8WdL9S15vRcP0ZrluhfJfX6bs88Dnh3lh55zbVMOnWZ42sys3sCbL+XkzOyDphcBXJP2DmX3zZAes9wKoc86NJZkNta3iAHBR6/GFqWzZfdK1xjOBZ052rJk1t08BX2CI9IsHc+fcdBpNzvw+4DJJl0jqEtPPe5bsswd4R7r/JuDrZmapfFfq7XIJ8Rrj30vaJmkHgKRtwNXAg6zC52Zxzk0fA0awoLOZVZJuAO4BcuBWM3tI0vuBvWa2B7gF+IykfcCzxIBP2u9zwMNABbzbzGpJ5wFfiNdIKYDPmtmXVquLB3Pn3NQRQ6VQhmJmdwN3Lym7qXV/HnjzCsd+EPjgkrLHgJ851Xp4MHfOTacwgqb5FuLB3Dk3fUaUZtlKPJg756bSpE205cHcOTedPJg759y4G24SrXHiwdw5N30MmLbFKZxzbhJ5ztw55yaBB3PnnBtzBgQP5s45N+b8Aqhzzk0GD+bOOTfmDKgnawjolgjmh3ju6a/aXUeAode72wJ2Ml71Ba/z6TBu9YXxq/O/Xv8pDMyD+ciZ2bmS9m7Cah5rNm71Ba/z6TBu9YXxrPNIeJrFOefGnPdmcc65CeEt8w1z82ZX4BSNW33B63w6jFt9YTzrvH4TFsxlE/YHOefcas7svND+zc5lF/85wZd+9Kf3j8M1ha3UMnfOudNnwhqyHsydc9NpwoJ5ttkVkHSNpEck7ZN042bXZyWSHpf0PUkPSNqbys6W9BVJ/5huX7DJdbxV0lOSHmyVLVtHRR9N7/t3Jb1ki9T3DyUdSO/zA5Je33ruPam+j0h67emub6rDRZK+IelhSQ9J+p1UviXf55PUd0u/zxvPYm+WYbYxsanBXFIOfBx4HXA5cJ2kyzezTqt4tZld0cqf3Qh8zcwuA76WHm+mTwHXLClbqY6vAy5L227gE6epjm2f4sT6Anwkvc9XpJXPSZ+LXcCL0jF/mj4/p1sF/L6ZXQ68Anh3qttWfZ9Xqi9s7fd5YxmYhaG2cbHZLfOXAfvM7DEzGwB3ANducp1OxbXAben+bcAbNq8qYGbfBJ5dUrxSHa8FPm3Rt4CzJJ1/WiqarFDflVwL3GFmfTP7J2Af8fNzWpnZE2b27XT/EPB94AK26Pt8kvquZEu8z6dFHYbbxsRmB/MLgB+2Hu/n5B+0zWTAlyXdL2l3KjvPzJ5I938EnLc5VTupleq4ld/7G1JK4tZW6mrL1VfSxcDPAvcyBu/zkvrCmLzPG8IMQhhuGxObHczHyc+b2UuIP5vfLemV7Sct9vHc0gm2cagjMQ3xE8AVwBPAhze1NiuQtB34PPC7Znaw/dxWfJ+Xqe9YvM8bymy4bUxsdjA/AFzUenxhKttyzOxAun0K+ALxp+eTzU/mdPvU5tVwRSvVcUu+92b2pJnVFpOVn2TxJ/6Wqa+kDjEw/rmZ/UUq3rLv83L1HYf3eaNZCENt42Kzg/l9wGWSLpHUJV542bPJdTqBpG2SdjT3gauBB4l1fUfa7R3AFzenhie1Uh33AG9PvS1eATzfShNsmiX55DcS32eI9d0lqSfpEuIFxb/fhPoJuAX4vpn999ZTW/J9Xqm+W/193nhDtsrHqGW+qf3MzaySdANwD5ADt5rZQ5tZpxWcB3wh/rugAD5rZl+SdB/wOUnXAz8A3rKJdUTS7cCrgJ2S9gPvA/6Y5et4N/B64gWuo8A7t0h9XyXpCmKa4nHgXQBm9pCkzwEPE3tovNvM6tNdZ+DngF8DvifpgVT2B2zd93ml+l63xd/njTWBE235cH7n3NQ5IzvHXlEM14X+K+XtYzGcf7PTLM45d/pZWpximG0VWmXgY0pZ3Zmevzf1KmqeW3aA1mrnXI4Hc+fcVLJgQ20nM+TAx+uB58zsUuAjwIfSscsO0FrrYEoP5s656TSalvkwAx/bA8ruAq5KF6ZXGqC1psGUPtGWc27qHOK5e75qd+0ccvcZpfmYkpvNrJkDfrlBVi9fcvzCPqnTx/PAOan8W0uObQZorXbOE3gwd85NHTNbbk6gseZpFuecW7thBlkt7COpAM4EnjnJsWsauOXB3Dnn1m6YgY/tAWVvAr6epnxYaYDWmgZTeprFOefWaKWBj5LeD+w1sz3EEbifkbSPOEvornTsigO01jKY0gcNOefcBPA0i3POTQAP5s45NwE8mDvn3ATwYO6ccxPAg7lzzk0AD+bOOTcBPJg759wE+P/1K9RDj1jh4QAAAABJRU5ErkJggg==", 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", 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", 170 | "text/plain": [ 171 | "
" 172 | ] 173 | }, 174 | "metadata": { 175 | "needs_background": "light" 176 | }, 177 | "output_type": "display_data" 178 | } 179 | ], 180 | "source": [ 181 | "# visualizing results\n", 182 | "from pylab import *\n", 183 | "for i in result:\n", 184 | " figure()\n", 185 | " imshow(i)\n", 186 | " colorbar()" 187 | ] 188 | }, 189 | { 190 | "cell_type": "code", 191 | "execution_count": null, 192 | "metadata": {}, 193 | "outputs": [], 194 | "source": [] 195 | } 196 | ], 197 | "metadata": { 198 | "kernelspec": { 199 | "display_name": "base", 200 | "language": "python", 201 | "name": "python3" 202 | }, 203 | "language_info": { 204 | "codemirror_mode": { 205 | "name": "ipython", 206 | "version": 3 207 | }, 208 | "file_extension": ".py", 209 | "mimetype": "text/x-python", 210 | "name": "python", 211 | "nbconvert_exporter": "python", 212 | "pygments_lexer": "ipython3", 213 | "version": "3.9.12" 214 | } 215 | }, 216 | "nbformat": 4, 217 | "nbformat_minor": 2 218 | } 219 | -------------------------------------------------------------------------------- /examples/example_files/example_1_0.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/gxli/Constrained-Diffusion-Decomposition/314202764c43d15cc859f8cdbc64637e99b50066/examples/example_files/example_1_0.png -------------------------------------------------------------------------------- /examples/example_files/example_3_0.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/gxli/Constrained-Diffusion-Decomposition/314202764c43d15cc859f8cdbc64637e99b50066/examples/example_files/example_3_0.png -------------------------------------------------------------------------------- /examples/example_files/example_3_1.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/gxli/Constrained-Diffusion-Decomposition/314202764c43d15cc859f8cdbc64637e99b50066/examples/example_files/example_3_1.png -------------------------------------------------------------------------------- /examples/example_files/example_3_2.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/gxli/Constrained-Diffusion-Decomposition/314202764c43d15cc859f8cdbc64637e99b50066/examples/example_files/example_3_2.png -------------------------------------------------------------------------------- /examples/example_files/example_3_3.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/gxli/Constrained-Diffusion-Decomposition/314202764c43d15cc859f8cdbc64637e99b50066/examples/example_files/example_3_3.png -------------------------------------------------------------------------------- /examples/example_files/example_3_4.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/gxli/Constrained-Diffusion-Decomposition/314202764c43d15cc859f8cdbc64637e99b50066/examples/example_files/example_3_4.png -------------------------------------------------------------------------------- /examples/example_files/example_3_5.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/gxli/Constrained-Diffusion-Decomposition/314202764c43d15cc859f8cdbc64637e99b50066/examples/example_files/example_3_5.png -------------------------------------------------------------------------------- /pyproject.toml: -------------------------------------------------------------------------------- 1 | [build-system] 2 | requires = ["setuptools>=61.0", "wheel"] 3 | build-backend = "setuptools.build_meta" 4 | 5 | [project] 6 | name = "constrained_diffusion" 7 | version = "1.0.1" 8 | description = "Constrained diffusion decomposition: Diffusion-based Multi-Scale Analysis of Complex Iages" 9 | readme = "README.md" 10 | requires-python = ">=3.9" 11 | license = { file = "LICENSE" } 12 | authors = [ 13 | { name = "Guang-Xing Li", email = "ligx.ngc7293@gmail.com" } 14 | ] 15 | classifiers = [ 16 | "Programming Language :: Python :: 3", 17 | "Operating System :: OS Independent", 18 | ] 19 | dependencies = [ 20 | "astropy>=5.0", 21 | "numpy>=1.20", 22 | "scipy>=1.7", 23 | ] 24 | 25 | [project.urls] 26 | Homepage = "https://gxli.github.io/Constrained-Diffusion-Decomposition/" 27 | 28 | 29 | 30 | -------------------------------------------------------------------------------- /requirements.txt: -------------------------------------------------------------------------------- 1 | numpy>=1.20 2 | scipy>=1.7 3 | -------------------------------------------------------------------------------- /src/__init__.py: -------------------------------------------------------------------------------- 1 | # Package initialization for src 2 | from .constrained_diffusion_decomposition import constrained_diffusion_decomposition 3 | from .scripts.script import main 4 | -------------------------------------------------------------------------------- /src/__pycache__/__init__.cpython-39.pyc: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/gxli/Constrained-Diffusion-Decomposition/314202764c43d15cc859f8cdbc64637e99b50066/src/__pycache__/__init__.cpython-39.pyc -------------------------------------------------------------------------------- /src/constrained_diffusion.egg-info/PKG-INFO: -------------------------------------------------------------------------------- 1 | Metadata-Version: 2.4 2 | Name: constrained_diffusion 3 | Version: 1.0.1 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. 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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: >=3.9 684 | Description-Content-Type: text/markdown 685 | License-File: LICENSE 686 | Requires-Dist: astropy>=5.0 687 | Requires-Dist: numpy>=1.20 688 | Requires-Dist: scipy>=1.7 689 | Dynamic: license-file 690 | 691 | 692 | 693 | # Constrained diffusion decomposition: A new PDE-based image decomposition method 694 | 695 | 696 | # General Design 697 | A natural image often contains components of different scales. 698 | 699 | This project decomposition to numpy.ndarray data, decomposing it into scale components, or scales, 1, 2, 4, 8, 16, ... pixels, enabling multi-scale analysis. 700 | 701 | The code is based on 702 | Li 2022, Multi-Scale Decomposition of Astronomical Maps -- Constrained Diffusion Method . 703 | 704 | 705 | Assuuming an input of I(x, y), the decomposition is achieved by solving the equation 706 | 707 | ```math 708 | \frac{\partial I_t }{\partial t} ={\rm sgn}(I_t) \mathcal{H}({- \rm sgn}(I_t) \nabla^2 I_t) \nabla^2 I_t ;, 709 | ``` 710 | where t is related to the scale l by t = l**2. 711 | 712 | 713 | 714 | 715 | # Installation 716 | 717 | 1. Use git clone 718 | ```bash 719 | git clone https://github.com/gxli/Constrained-Diffusion-Decomposition.git 720 | cd constrained_diffusion 721 | pip install . 722 | ``` 723 | 724 | 2. Use pip 725 | 726 | ```bash 727 | pip install -i https://test.pypi.org/simple/ constrained-diffusion==1.0.0 728 | ``` 729 | 730 | # Usage: 731 | 732 | ### Input: 733 | 734 | numpy nd array, of shape e.g. (nx, ny, nz) 735 | 736 | ### Output: 737 | 738 | result: numpy nd array, of shape (m, nx, ny, nz). The mth commponent contain structures of sizes 2$^(m-1)$ to 2$^m$ pixels. residual: numpy nd array, of shape (nx, ny, nz) the input data will be recovered as input = sum_i result[i] + residual 739 | 740 | 741 | 742 | ```python 743 | import constrained_diffusion as cdd 744 | 745 | result, residual = cdd.constrained_diffusion_decomposition(data) 746 | ``` 747 | 748 | 749 | 750 | 751 | # Example 752 | 753 | ```python 754 | import matplotlib.pyplot as plt 755 | from matplotlib import cm 756 | import numpy as np 757 | from astropy.io import fits 758 | from constrained_diffusion import constrained_diffusion_decomposition 759 | 760 | def multivariate_gaussian(pos, mu, Sigma): 761 | """Return the multivariate Gaussian distribution on array pos. 762 | 763 | pos is an array constructed by packing the meshed arrays of variables 764 | x_1, x_2, x_3, ..., x_k into its _last_ dimension. 765 | 766 | """ 767 | 768 | n = mu.shape[0] 769 | Sigma_det = np.linalg.det(Sigma) 770 | Sigma_inv = np.linalg.inv(Sigma) 771 | N = np.sqrt((2*np.pi)**n * Sigma_det) 772 | 773 | fac = np.einsum('...k,kl,...l->...', pos-mu, Sigma_inv, pos-mu) 774 | 775 | return np.exp(-fac / 2) / N 776 | ``` 777 | 778 | 779 | ```python 780 | # Preparing sample input 781 | N_x = 300 782 | N_y = 200 783 | X = np.linspace(0, 300, N_x) 784 | Y = np.linspace(0, 200, N_y) 785 | X, Y = np.meshgrid(X, Y) 786 | 787 | mu = np.array([150., 100.]) 788 | Sigma = np.array([[200, 0], [0, 200]]) 789 | 790 | pos = np.empty(X.shape + (2,)) 791 | pos[:, :, 0] = X 792 | pos[:, :, 1] = Y 793 | 794 | 795 | Z1 = multivariate_gaussian(pos, mu, Sigma) * 100 796 | Z3 = multivariate_gaussian(pos, mu - 10 , Sigma * 0.03) * 3 797 | 798 | Z = Z1 + Z3 799 | 800 | plt.figure() 801 | plt.imshow(Z) 802 | plt.colorbar() 803 | plt.show() 804 | ``` 805 | 806 | 807 | 808 | 809 | 810 | 811 | 812 | 813 | ```python 814 | # performing decomposition 815 | result, residual = constrained_diffusion_decomposition(Z) 816 | ``` 817 | 818 | ntot 6 819 | i = 0 820 | kernel_size 0.31622776601683794 821 | i = 1 822 | kernel_size 0.34641016151377546 823 | i = 2 824 | kernel_size 0.6928203230275509 825 | i = 3 826 | kernel_size 1.3856406460551018 827 | i = 4 828 | kernel_size 2.7712812921102037 829 | i = 5 830 | kernel_size 5.542562584220407 831 | 832 | 833 | 834 | ```python 835 | # visualizing results 836 | from pylab import * 837 | for i in result: 838 | figure() 839 | imshow(i) 840 | colorbar() 841 | ``` 842 | 843 | 844 | 845 | 846 | 847 | 848 | 849 | 850 | 851 | 852 | 853 | 854 | 855 | 856 | 857 | 858 | 859 | 860 | 861 | 862 | 863 | 864 | 865 | 866 | ## License 867 | See the [LICENSE](LICENSE) file for details. 868 | 869 | -------------------------------------------------------------------------------- /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 | src/tests/__init__.py 12 | src/tests/test_constrained_diffusion_decomposition.py -------------------------------------------------------------------------------- /src/constrained_diffusion.egg-info/dependency_links.txt: -------------------------------------------------------------------------------- 1 | 2 | -------------------------------------------------------------------------------- /src/constrained_diffusion.egg-info/requires.txt: -------------------------------------------------------------------------------- 1 | astropy>=5.0 2 | numpy>=1.20 3 | scipy>=1.7 4 | -------------------------------------------------------------------------------- /src/constrained_diffusion.egg-info/top_level.txt: -------------------------------------------------------------------------------- 1 | __init__ 2 | constrained_diffusion 3 | tests 4 | -------------------------------------------------------------------------------- /src/constrained_diffusion.py: -------------------------------------------------------------------------------- 1 | from scipy import ndimage 2 | import numpy as np 3 | from math import log 4 | 5 | def constrained_diffusion_decomposition(data, 6 | e_rel=3e-2, 7 | max_n=None, 8 | sm_mode='reflect'): 9 | """ 10 | Perform constrained diffusion decomposition on n-dimensional data. 11 | 12 | Args: 13 | data: n-dimensional array 14 | e_rel: Relative error (smaller e_rel increases accuracy but computational cost) 15 | max_n: Maximum number of channels (if None, calculated automatically) 16 | sm_mode: Mode for array boundary extension in convolution ('reflect', 'constant', 17 | 'nearest', 'mirror', 'wrap'). Default is 'reflect'. 18 | 19 | Returns: 20 | tuple: (results, residual) 21 | - results: n+1 dimensional array where results[i] contains structures of 22 | sizes between 2**i and 2**(i+1) pixels 23 | - residual: Structures too large to be contained in results 24 | """ 25 | if data.size == 0: 26 | raise ValueError("Input data array is empty") 27 | 28 | ntot = int(log(min(data.shape)) / log(2) - 1) 29 | if max_n is not None: 30 | ntot = min(ntot, max_n) 31 | print("total number of scales", ntot) 32 | 33 | result = [] 34 | diff_image = data.copy() * 0 35 | 36 | for i in range(ntot): 37 | # print("number of scale", i+1) 38 | channel_image = data.copy() * 0 39 | scale_end = float(pow(2, i + 1)) 40 | scale_beginning = float(pow(2, i)) 41 | t_end = scale_end**2 / 2 42 | t_beginning = scale_beginning**2 / 2 43 | 44 | if i == 0: 45 | delta_t_max = t_beginning * 0.1 46 | else: 47 | delta_t_max = t_beginning * e_rel 48 | 49 | niter = int((t_end - t_beginning) / delta_t_max + 0.5) 50 | delta_t = (t_end - t_beginning) / niter 51 | kernel_size = np.sqrt(2 * delta_t) 52 | 53 | print("current channel", i, "current scale", 2**i) 54 | 55 | for kk in range(niter): 56 | smooth_image = ndimage.gaussian_filter(data, kernel_size, mode=sm_mode) 57 | sm_image_1 = np.minimum(data, smooth_image) 58 | sm_image_2 = np.maximum(data, smooth_image) 59 | 60 | diff_image_1 = data - sm_image_1 61 | diff_image_2 = data - sm_image_2 62 | 63 | diff_image = diff_image * 0 64 | 65 | positions_1 = np.where(np.logical_and(diff_image_1 > 0, data > 0)) 66 | positions_2 = np.where(np.logical_and(diff_image_2 < 0, data < 0)) 67 | 68 | diff_image[positions_1] = diff_image_1[positions_1] 69 | diff_image[positions_2] = diff_image_2[positions_2] 70 | 71 | channel_image = channel_image + diff_image 72 | data = data - diff_image 73 | 74 | result.append(channel_image) 75 | 76 | residual = data 77 | return result, residual 78 | -------------------------------------------------------------------------------- /src/tests/__init__.py: -------------------------------------------------------------------------------- 1 | # Package initialization for tests 2 | -------------------------------------------------------------------------------- /src/tests/test_constrained_diffusion_decomposition.py: -------------------------------------------------------------------------------- 1 | import pytest 2 | import numpy as np 3 | from src.constrained_diffusion_decomposition import constrained_diffusion_decomposition 4 | 5 | def test_constrained_diffusion_decomposition(): 6 | # Create a small 2D test array 7 | data = np.ones((16, 16)) 8 | result, residual = constrained_diffusion_decomposition(data, e_rel=3e-2, max_n=2) 9 | 10 | # Check that result is a list of arrays 11 | assert isinstance(result, list) 12 | assert len(result) <= 2 # max_n=2 13 | assert all(isinstance(r, np.ndarray) for r in result) 14 | 15 | # Check residual is an array 16 | assert isinstance(residual, np.ndarray) 17 | assert residual.shape == data.shape 18 | 19 | THOUGH# Check that the sum of results and residual approximates the input 20 | reconstructed = np.sum(result, axis=0) + residual 21 | np.testing.assert_allclose(reconstructed, data, rtol=1e-5) 22 | 23 | def test_invalid_input(): 24 | with pytest.raises(ValueError): 25 | constrained_diffusion_decomposition(np.array([])) # Empty array 26 | --------------------------------------------------------------------------------