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