/*-------------------------------------------------------------------------------------------  File        : mcf_levelsets.cpp  Description : Implementation of the Mean Curvature Flow (classical 2d curve evolution),                using the framework of Level Sets  Copyright  : David Tschumperle - http://www.greyc.ensicaen.fr/~dtschump/  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.-----------------------------------------------------------------------------------------*/#include "../CImg.h"using namespace cimg_library;// The undef below is necessary when using a non-standard compiler.#ifdef cimg_use_visualcpp6#define std#endif// get_level0() : Retrieve the curve corresponding to the zero level set of the distance function//-------------CImg<unsigned char> get_level0(const CImg<>& img) {  CImg<unsigned char> dest(img);  CImg_2x2(I,float);  cimg_for2x2(img,x,y,0,0,I) if (Icc*Inc<0 || Icc*Icn<0) dest(x,y) = 255; else dest(x,y) = Icc<0?100:0;  return dest;}// init_distance_function() : Init distance function (PDE-based approach).//-------------------------void init_distance_function(CImg<>& img, unsigned int nb_iter,CImgDisplay* disp=NULL) {  const float dt = 1;  CImg_3x3(I,float);  img.blur(0.5);  for (unsigned int iter=0; iter<nb_iter; iter++) {    CImg<> veloc(img.dimx(),img.dimy(),img.dimz(),img.dimv());    cimg_for3x3(img,x,y,0,0,I) {      const float	gx = 0.5f*(Inc-Ipc),	gy = 0.5f*(Icn-Icp),	sgn = -cimg::sign(Icc),	ix = (gx*sgn)>0?(Inc-Icc):(Icc-Ipc),	iy = (gy*sgn)>0?(Icn-Icc):(Icc-Icp),	ng = (float)std::sqrt(gx*gx+gy*gy),	ngx = ng>1e-5?gx/ng:gx,	ngy = ng>1e-5?gy/ng:gy;      veloc(x,y) = sgn*(ngx*ix + ngy*iy - 1);    }    const CImgStats stats(veloc);    const double xdt = dt/cimg::max(cimg::abs(stats.min),cimg::abs(stats.max));    img+=xdt*veloc;    if (disp && !(iter%40)) img.display(*disp);  }}//-----------------// Main procedure//-----------------int main(int argc,char **argv) {  cimg_usage("Perform a Mean Curvature Flow on closed curves, using Level Sets");  const float dt = cimg_option("-dt",0.8f,"PDE time step");  const unsigned int nb_iter = cimg_option("-iter",10000,"Number of iterations");  // Create a user-defined closed curve  CImg<unsigned char> curve(256,256,1,2,0);  unsigned char col1[2]={0,255}, col2[2]={200,255}, col3[2]={255,255};  curve.draw_grid(20,20,0,0,col3,0xCCCCCCCC,0xCCCCCCCC,false,false,0.4f).    draw_text("Please draw your curve\nin this window\n(Use your mouse)",5,5,col1);  CImgDisplay disp(curve,"Mean curvature flow",0);  int xo=-1,yo=-1,x0=-1,y0=-1,x1=-1,y1=-1;  while (!disp.is_closed && (x0<0 || disp.button)) {    if (disp.button && disp.mouse_x>=0 && disp.mouse_y>=0) {      if (x0<0) { xo = x0 = disp.mouse_x; yo = y0 = disp.mouse_y; } else {	x1 = disp.mouse_x; y1 = disp.mouse_y;	curve.draw_line(x0,y0,x1,y1,col2).display(disp);	x0 = x1; y0 = y1;      }    }    disp.wait();    if (disp.is_resized) disp.resize(disp);  }  curve.draw_line(x1,y1,xo,yo,col2).channel(0).draw_fill(0,0,col3);  CImg<> img = CImg<>(curve.get_shared_channel(0)).normalize(-1,1);  // Init distance function  init_distance_function(img,10,&disp);  // Perform the "Mean Curvature Flow"  CImg_3x3(I,float);  for (unsigned int iter=0; iter<nb_iter && !disp.is_closed && disp.key!=cimg::keyQ; iter++) {    CImg<> veloc(img.dimx(),img.dimy(),img.dimz(),img.dimv());    cimg_for3x3(img,x,y,0,0,I) {      const float	ix = 0.5f*(Inc-Ipc),	iy = 0.5f*(Icn-Icp),	ixx = Inc+Ipc-2*Icc,	iyy = Icn+Icp-2*Icc,	ixy = 0.25f*(Ipp+Inn-Inp-Ipn),	ngrad = ix*ix+iy*iy,	iee = (ngrad>1e-5)?(( iy*iy*ixx - 2*ix*iy*ixy + ix*ix*iyy )/ngrad):0;      veloc(x,y) = iee;    }    const CImgStats stats(veloc);    const double xdt = dt/cimg::max(cimg::abs(stats.min),cimg::abs(stats.max));    img+=xdt*veloc;    if (!(iter%10))      get_level0(img).draw_grid(20,20,0,0,col3,0xCCCCCCCC,0xCCCCCCCC,false,false,0.4f).        draw_text(5,5,col3,0,11,1,"Iteration %d",iter).display(disp);    if (!(iter%30)) init_distance_function(img,1);    if (disp.is_resized) disp.resize(disp);  }  // End of program  return 0;}