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243 lines
12 KiB
C
243 lines
12 KiB
C
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/*
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#
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# File : nlmeans.h
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# ( C++ header file - CImg plug-in )
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#
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# Description : CImg plugin that implements the non-local mean filter.
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# This file is a part of the CImg Library project.
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# ( http://cimg.eu )
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#
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# [1] Buades, A.; Coll, B.; Morel, J.-M.: A non-local algorithm for image denoising
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# IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 2005. CVPR 2005.
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# Volume 2, 20-25 June 2005 Page(s):60 - 65 vol. 2
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#
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# [2] Buades, A. Coll, B. and Morel, J.: A review of image denoising algorithms, with a new one.
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# Multiscale Modeling and Simulation: A SIAM Interdisciplinary Journal 4 (2004) 490-530
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#
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# [3] Gasser, T. Sroka,L. Jennen Steinmetz,C. Residual variance and residual pattern nonlinear regression.
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# Biometrika 73 (1986) 625-659
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#
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# Copyright : Jerome Boulanger
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# ( http://www.irisa.fr/vista/Equipe/People/Jerome.Boulanger.html )
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#
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# License : CeCILL v2.0
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# ( http://www.cecill.info/licences/Licence_CeCILL_V2-en.html )
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#
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# This software is governed by the CeCILL license under French law and
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# abiding by the rules of distribution of free software. You can use,
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# modify and/ or redistribute the software under the terms of the CeCILL
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# license as circulated by CEA, CNRS and INRIA at the following URL
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# "http://www.cecill.info".
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#
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# As a counterpart to the access to the source code and rights to copy,
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# modify and redistribute granted by the license, users are provided only
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# with a limited warranty and the software's author, the holder of the
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# economic rights, and the successive licensors have only limited
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# liability.
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#
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# In this respect, the user's attention is drawn to the risks associated
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# with loading, using, modifying and/or developing or reproducing the
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# software by the user in light of its specific status of free software,
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# that may mean that it is complicated to manipulate, and that also
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# therefore means that it is reserved for developers and experienced
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# professionals having in-depth computer knowledge. Users are therefore
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# encouraged to load and test the software's suitability as regards their
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# requirements in conditions enabling the security of their systems and/or
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# data to be ensured and, more generally, to use and operate it in the
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# same conditions as regards security.
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#
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# The fact that you are presently reading this means that you have had
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# knowledge of the CeCILL license and that you accept its terms.
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#
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*/
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#ifndef cimg_plugin_nlmeans
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#define cimg_plugin_nlmeans
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//! NL-Means denoising algorithm.
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/**
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This is the in-place version of get_nlmean().
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**/
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CImg<T>& nlmeans(int patch_size=1, double lambda=-1, double alpha=3, double sigma=-1, int sampling=1){
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if (!is_empty()){
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if (sigma<0) sigma = std::sqrt(variance_noise()); // noise variance estimation
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const double np = (2*patch_size + 1)*(2*patch_size + 1)*spectrum()/(double)sampling;
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if (lambda<0) {// Bandwidth estimation
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if (np<100)
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lambda = ((((((1.1785e-12*np - 5.1827e-10)*np + 9.5946e-08)*np -
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9.7798e-06)*np + 6.0756e-04)*np - 0.0248)*np + 1.9203)*np + 7.9599;
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else
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lambda = (-7.2611e-04*np + 1.3213)*np + 15.2726;
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}
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#if cimg_debug>=1
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std::fprintf(stderr,"Size of the patch : %dx%d \n",
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2*patch_size + 1,2*patch_size + 1);
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std::fprintf(stderr,"Size of window where similar patch are looked for : %dx%d \n",
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(int)(alpha*(2*patch_size + 1)),(int)(alpha*(2*patch_size + 1)));
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std::fprintf(stderr,"Bandwidth of the kernel : %fx%f^2 \n",
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lambda,sigma);
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std::fprintf(stderr,"Noise standard deviation estimated to : %f \n",
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sigma);
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#endif
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CImg<T> dest(width(),height(),depth(),spectrum(),0);
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double *uhat = new double[spectrum()];
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const double h2 = -.5/(lambda*sigma*sigma); // [Kervrann] notations
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if (depth()!=1){ // 3D case
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const CImg<> P = (*this).get_blur(1); // inspired from Mahmoudi&Sapiro SPletter dec 05
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const int n_simu = 64;
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CImg<> tmp(n_simu,n_simu,n_simu);
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const double sig = std::sqrt(tmp.fill(0.f).noise(sigma).blur(1).pow(2.).sum()/(n_simu*n_simu*n_simu));
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const int
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patch_size_z = 0,
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pxi = (int)(alpha*patch_size),
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pyi = (int)(alpha*patch_size),
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pzi = 2; //Define the size of the neighborhood in z
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for (int zi = 0; zi<depth(); ++zi) {
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#if cimg_debug>=1
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std::fprintf(stderr,"\rProcessing : %3d %%",(int)((float)zi/(float)depth()*100.));fflush(stdout);
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#endif
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for (int yi = 0; yi<height(); ++yi)
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for (int xi = 0; xi<width(); ++xi) {
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cimg_forC(*this,v) uhat[v] = 0;
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float sw = 0, wmax = -1;
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for (int zj = std::max(0,zi - pzi); zj<std::min(depth(),zi + pzi + 1); ++zj)
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for (int yj = std::max(0,yi - pyi); yj<std::min(height(),yi + pyi + 1); ++yj)
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for (int xj = std::max(0,xi - pxi); xj<std::min(width(),xi + pxi + 1); ++xj)
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if (cimg::abs(P(xi,yi,zi) - P(xj,yj,zj))/sig<3) {
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double d = 0;
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int n = 0;
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if (xi!=xj && yi!=yj && zi!=zj){
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for (int kz = -patch_size_z; kz<patch_size_z + 1; kz+=sampling) {
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int
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zj_ = zj + kz,
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zi_ = zi + kz;
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if (zj_>=0 && zj_<depth() && zi_>=0 && zi_<depth())
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for (int ky = -patch_size; ky<=patch_size; ky+=sampling) {
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int
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yj_ = yj + ky,
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yi_ = yi + ky;
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if (yj_>=0 && yj_<height() && yi_>=0 && yi_<height())
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for (int kx = -patch_size; kx<=patch_size; kx+=sampling) {
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int
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xj_ = xj + kx,
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xi_ = xi + kx;
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if (xj_>=0 && xj_<width() && xi_>=0 && xi_<width())
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cimg_forC(*this,v) {
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double d1 = (*this)(xj_,yj_,zj_,v) - (*this)(xi_,yi_,zi_,v);
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d+=d1*d1;
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++n;
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}
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}
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}
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}
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float w = (float)std::exp(d*h2);
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wmax = w>wmax?w:wmax;
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cimg_forC(*this,v) uhat[v]+=w*(*this)(xj,yj,zj,v);
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sw+=w;
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}
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}
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// add the central pixel
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cimg_forC(*this,v) uhat[v]+=wmax*(*this)(xi,yi,zi,v);
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sw+=wmax;
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if (sw) cimg_forC(*this,v) dest(xi,yi,zi,v) = (T)(uhat[v]/=sw);
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else cimg_forC(*this,v) dest(xi,yi,zi,v) = (*this)(xi,yi,zi,v);
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}
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}
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}
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else { // 2D case
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const CImg<> P = (*this).get_blur(1); // inspired from Mahmoudi&Sapiro SPletter dec 05
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const int n_simu = 512;
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CImg<> tmp(n_simu,n_simu);
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const double sig = std::sqrt(tmp.fill(0.f).noise(sigma).blur(1).pow(2.).sum()/(n_simu*n_simu));
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const int
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pxi = (int)(alpha*patch_size),
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pyi = (int)(alpha*patch_size); //Define the size of the neighborhood
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for (int yi = 0; yi<height(); ++yi) {
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#if cimg_debug>=1
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std::fprintf(stderr,"\rProcessing : %3d %%",(int)((float)yi/(float)height()*100.));fflush(stdout);
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#endif
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for (int xi = 0; xi<width(); ++xi) {
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cimg_forC(*this,v) uhat[v] = 0;
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float sw = 0, wmax = -1;
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for (int yj = std::max(0,yi - pyi); yj<std::min(height(),yi + pyi + 1); ++yj)
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for (int xj = std::max(0,xi - pxi); xj<std::min(width(),xi + pxi + 1); ++xj)
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if (cimg::abs(P(xi,yi) - P(xj,yj))/sig<3.) {
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double d = 0;
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int n = 0;
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if (!(xi==xj && yi==yj)) //{
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for (int ky = -patch_size; ky<patch_size + 1; ky+=sampling) {
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int
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yj_ = yj + ky,
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yi_ = yi + ky;
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if (yj_>=0 && yj_<height() && yi_>=0 && yi_<height())
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for (int kx = -patch_size; kx<patch_size + 1; kx+=sampling) {
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int
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xj_ = xj + kx,
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xi_ = xi + kx;
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if (xj_>=0 && xj_<width() && xi_>=0 && xi_<width())
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cimg_forC(*this,v) {
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double d1 = (*this)(xj_,yj_,v) - (*this)(xi_,yi_,v);
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d+=d1*d1;
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n++;
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}
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}
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//}
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float w = (float)std::exp(d*h2);
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cimg_forC(*this,v) uhat[v]+=w*(*this)(xj,yj,v);
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wmax = w>wmax?w:wmax; // Store the maximum of the weights
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sw+=w; // Compute the sum of the weights
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}
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}
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// add the central pixel with the maximum weight
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cimg_forC(*this,v) uhat[v]+=wmax*(*this)(xi,yi,v);
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sw+=wmax;
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// Compute the estimate for the current pixel
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if (sw) cimg_forC(*this,v) dest(xi,yi,v) = (T)(uhat[v]/=sw);
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else cimg_forC(*this,v) dest(xi,yi,v) = (*this)(xi,yi,v);
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}
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} // main loop
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} // 2d
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delete [] uhat;
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dest.move_to(*this);
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#if cimg_debug>=1
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std::fprintf(stderr,"\n"); // make a new line
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#endif
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} // is empty
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return *this;
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}
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//! Get the result of the NL-Means denoising algorithm.
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/**
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\param patch_size = radius of the patch (1=3x3 by default)
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\param lambda = bandwidth ( -1 by default : automatic selection)
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\param alpha = size of the region where similar patch are searched (3 x patch_size = 9x9 by default)
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\param sigma = noise standard deviation (-1 = estimation)
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\param sampling = sampling of the patch (1 = uses all point, 2 = uses one point on 4, etc)
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If the image has three dimensions then the patch is only in 2D and the neighborhood extent in time is only 5.
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If the image has several channel (color images), the distance between the two patch is computed using
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all the channels.
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The greater the patch is the best is the result.
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Lambda parameter is function of the size of the patch size. The automatic Lambda parameter is taken
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in the Chi2 table at a significiance level of 0.01. This diffear from the original paper [1].
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The weighted average becomes then:
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\f$$ \hat{f}(x,y) = \sum_{x',y'} \frac{1}{Z} exp(\frac{P(x,y)-P(x',y')}{2 \lambda \sigma^2}) f(x',y') $$\f
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where \f$ P(x,y) $\f denotes the patch in (x,y) location.
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An a priori is also used to increase the speed of the algorithm in the spirit of Sapiro et al. SPletter dec 05
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This very basic version of the Non-Local Means algorithm provides an output image which contains
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some residual noise with a relatively small variance (\f$\sigma<5$\f).
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[1] A non-local algorithm for image denoising
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Buades, A.; Coll, B.; Morel, J.-M.;
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Computer Vision and Pattern Recognition, 2005. CVPR 2005. IEEE Computer Society Conference on
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Volume 2, 20-25 June 2005 Page(s):60 - 65 vol. 2
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**/
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CImg<T> get_nlmeans( int patch_size=1, double lambda=-1, double alpha=3 ,double sigma=-1, int sampling=1) const {
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return CImg<T>(*this).nlmeans(patch_size,lambda,alpha,sigma,sampling);
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}
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#endif /* cimg_plugin_nlmeans */
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