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