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173 lines
7.6 KiB
C++
173 lines
7.6 KiB
C++
/*
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#
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# File : gaussian_fit1d.cpp
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# ( C++ source file )
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#
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# Description : Fit a gaussian function on a set of sample points,
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# using the Levenberg-Marquardt algorithm.
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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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# Copyright : David Tschumperlé
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# ( http://tschumperle.users.greyc.fr/ )
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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
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#define cimg_plugin "examples/gaussian_fit1d.cpp"
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#include "CImg.h"
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using namespace cimg_library;
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#undef min
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#undef max
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// Main procedure
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//----------------
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int main(int argc,char **argv) {
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cimg_usage("Fit gaussian function on sample points, using Levenberg-Marquardt algorithm.");
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// Read command line arguments.
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const char *s_params = cimg_option("-p","10,3,4","Amplitude, Mean and Std of the ground truth");
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const unsigned int s_nb = cimg_option("-N",40,"Number of sample points");
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const float s_noise = cimg_option("-n",10.0f,"Pourcentage of noise on the samples points");
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const char *s_xrange = cimg_option("-x","-10,10","X-range allowed for the sample points");
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const char *f_params = cimg_option("-p0",(char*)0,"Amplitude, Mean and Std of the first estimate");
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const float f_lambda0 = cimg_option("-l",100.0f,"Initial damping factor");
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const float f_dlambda = cimg_option("-dl",0.9f,"Damping attenuation");
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float s_xmin = -10, s_xmax = 10, s_amp = 1, s_mean = 1, s_std = 1;
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std::sscanf(s_xrange,"%f%*c%f",&s_xmin,&s_xmax);
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std::sscanf(s_params,"%f%*c%f%*c%f",&s_amp,&s_mean,&s_std);
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// Create noisy samples of a Gaussian function.
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const float s_std2 = 2*s_std*s_std, s_fact = s_amp/((float)std::sqrt(2*cimg::PI)*s_std);
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CImg<> samples(s_nb,2);
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cimg_forX(samples,i) {
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const float
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x = (float)(s_xmin + (s_xmax - s_xmin)*cimg::rand()),
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y = s_fact*(float)(1 + s_noise*cimg::grand()/100)*std::exp(-cimg::sqr(x - s_mean)/s_std2);
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samples(i,0) = x;
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samples(i,1) = y;
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}
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// Fit Gaussian function on the sample points and display curve iterations.
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CImgDisplay disp(640,480,"Levenberg-Marquardt Gaussian Fitting",0);
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float f_amp = 1, f_mean = 1, f_std = 1, f_lambda = f_lambda0;
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if (f_params) std::sscanf(f_params,"%f%*c%f%*c%f",&f_amp,&f_mean,&f_std);
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else {
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const float& vmax = samples.get_shared_row(1).max();
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float cmax = 0; samples.contains(vmax,cmax);
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f_mean = samples((int)cmax,0);
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f_std = (s_xmax - s_xmin)/10;
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f_amp = vmax*(float)std::sqrt(2*cimg::PI)*f_std;
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}
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CImg<> beta = CImg<>::vector(f_amp,f_mean,f_std);
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for (unsigned int iter = 0; !disp.is_closed() && !disp.is_keyQ() && !disp.is_keyESC(); ++iter) {
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// Do one iteration of the Levenberg-Marquardt algorithm.
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CImg<> YmF(1,s_nb), J(beta.height(),s_nb);
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const float
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_f_amp = beta(0), _f_mean = beta(1), _f_std = beta(2),
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_f_std2 = 2*_f_std*_f_std, _f_fact = (float)std::sqrt(2*cimg::PI)*_f_std;
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float _f_error = 0;
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cimg_forY(J,i) {
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const float
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x = samples(i,0),
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_f_exp = std::exp(-cimg::sqr(x - _f_mean)/_f_std2),
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delta = samples(i,1) - _f_amp*_f_exp/_f_fact;
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YmF(i) = delta;
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J(0,i) = _f_exp/_f_fact;
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J(1,i) = _f_amp*_f_exp/_f_fact*(x - _f_mean)*2/_f_std2;
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J(2,i) = _f_amp*_f_exp/_f_fact*(cimg::sqr(x - _f_mean)/(_f_std*_f_std*_f_std));
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_f_error+=cimg::sqr(delta);
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}
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CImg<> Jt = J.get_transpose(), M = Jt*J;
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cimg_forX(M,x) M(x,x)*=1 + f_lambda;
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beta+=M.get_invert()*Jt*YmF;
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if (beta(0)<=0) beta(0) = 0.1f;
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if (beta(2)<=0) beta(2) = 0.1f;
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f_lambda*=f_dlambda;
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// Display fitting curves.
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const unsigned char black[] = { 0,0,0 }, gray[] = { 228,228,228 };
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CImg<unsigned char>(disp.width(),disp.height(),1,3,255).
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draw_gaussfit(samples,beta(0),beta(1),beta(2),s_amp,s_mean,s_std).
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draw_rectangle(5,7,150,100,gray,0.9f).draw_rectangle(5,7,150,100,black,1,~0U).
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draw_text(10,10,"Iteration : %d",black,0,1,13,iter).
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draw_text(10,25,"Amplitude : %.4g (%.4g)",black,0,1,13,beta(0),s_amp).
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draw_text(10,40,"Mean : %.4g (%.4g)",black,0,1,13,beta(1),s_mean).
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draw_text(10,55,"Std : %.4g (%.4g)",black,0,1,13,beta(2),s_std).
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draw_text(10,70,"Error : %.4g",black,0,1,13,std::sqrt(_f_error)).
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draw_text(10,85,"Lambda : %.4g",black,0,1,13,f_lambda).
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display(disp.resize(false).wait(20));
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}
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return 0;
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}
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#else
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// Draw sample points, ideal and fitted gaussian curves on the instance image.
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// (defined as a CImg plug-in function).
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template<typename t>
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CImg<T>& draw_gaussfit(const CImg<t>& samples,
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const float f_amp, const float f_mean, const float f_std,
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const float i_amp, const float i_mean, const float i_std) {
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if (is_empty()) return *this;
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const unsigned char black[] = { 0,0,0 }, green[] = { 10,155,20 }, orange[] = { 155,20,0 }, purple[] = { 200,10,200 };
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float
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xmin, xmax = samples.get_shared_row(0).max_min(xmin), deltax = xmax - xmin,
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ymin, ymax = samples.get_shared_row(1).max_min(ymin), deltay = ymax - ymin;
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xmin-=0.2f*deltax; xmax+=0.2f*deltax; ymin-=0.2f*deltay; ymax+=0.2f*deltay;
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deltax = xmax - xmin; deltay = ymax - ymin;
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draw_grid(64,64,0,0,false,false,black,0.3f,0x55555555,0x55555555).draw_axes(xmin,xmax,ymax,ymin,black,0.8f);
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CImg<> nsamples(samples);
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(nsamples.get_shared_row(0)-=xmin)*=width()/deltax;
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(nsamples.get_shared_row(1)-=ymax)*=-height()/deltay;
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cimg_forX(nsamples,i) draw_circle((int)nsamples(i,0),(int)nsamples(i,1),3,orange,1,~0U);
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CImg<int> truth(width(),2), fit(width(),2);
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const float
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i_std2 = 2*i_std*i_std, i_fact = i_amp/((float)std::sqrt(2*cimg::PI)*i_std),
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f_std2 = 2*f_std*f_std, f_fact = f_amp/((float)std::sqrt(2*cimg::PI)*f_std);
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cimg_forX(*this,x) {
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const float
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x0 = xmin + x*deltax/width(),
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ys0 = i_fact*std::exp(-cimg::sqr(x0 - i_mean)/i_std2),
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yf0 = f_fact*std::exp(-cimg::sqr(x0 - f_mean)/f_std2);
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fit(x,0) = truth(x,0) = x;
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truth(x,1) = (int)((ymax - ys0)*height()/deltay);
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fit(x,1) = (int)((ymax - yf0)*height()/deltay);
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}
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return draw_line(truth,green,0.7f,0xCCCCCCCC).draw_line(fit,purple);
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}
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#endif
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