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/*/////////////////////////////////////////////////////////////////////////////////////
2 phase level set method
0-input image
1-initial phi1
2-dt=>time-step of iteration
3-kappa =>coefficient of the weighted length term L(phi1)
4-lambda1 =>coefficient of insice C term
5-lambda2 =>coefficient of outside C term
6-lambda=>coefficient of the weighted length term L(phi2)
7-mu => coefficient of the internal (penalizing) energy term P(phi1),P(phi2)
8-v=>coefficient of the weighted area term A(phi2)
9-iterations
10-g=>edge indicator
/*/////////////////////////////////////////////////////////////////////////////////////
#include <mex.h>
#include <mat.h>
#include <matrix.h>
#define cimg_plugin "cimgmatlab.h"
#include "CImg.h"
#include <iostream>
#include <string>
#include <math.h>
using namespace cimg_library;
using namespace std;
//globa values
const double epsilon=0.8; // the papamater smooth Dirac function (default value 1.5);
const float precision=0.009f;//precision of the error estimation
//functions
CImg<double> DiracU( CImg<double>& u0) ;
CImg<double> Heaviside(CImg<double>& u0);
CImg<double> ExtractContour(CImg<double> LevelSet);
CImg<unsigned char> get_level0(const CImg<>& img);
CImg<unsigned char> InitialLevelSet(CImg<double>&Img);
CImg<double> DiracF(CImg<double>& u1,CImg<double>& u2);
CImg<double>Heaviside1(CImg<double>& u0);
//-----------------
// Main-MexFunction
//-----------------
void mexFunction(int nlhs, mxArray *plhs[], int nrhs, const mxArray *prhs[]) {
if (nrhs < 13) mexErrMsgTxt("No enough input arguments.");
if (nrhs >13) mexErrMsgTxt("Too many input arguments.");
if (nrhs == 13){
//Input Parameters ( inputs)
CImg<double> Img(prhs[0],true); //input image
CImg<double> phi1(prhs[1],true); //Rib cage approximation
CImg<double> phi2(prhs[2],true);
CImg<int>VolumeMask(prhs[3],true);
const double dt= mxGetScalar( prhs[4]); //time-step of iteration
const double kappa = mxGetScalar(prhs[5]); //coefficient of the weighted length term L(phi1)
const double lambda1 = mxGetScalar(prhs[6]);//coefficient of insice C term
const double lambda2 = mxGetScalar(prhs[7]);//coefficient of outside C term
const double lambda = mxGetScalar(prhs[8]); //coefficient of the weighted length term L(phi2)
const double mu = mxGetScalar(prhs[9]); // coefficient of the internal (penalizing) energy term P(u)
const double v = mxGetScalar(prhs[10]); //coefficient of the weighted area term A(u)
const unsigned int nb_iter = mxGetScalar(prhs[11]);
CImg<double> g(prhs[12],true);
//////////////////////////////////////////////////////////////////////////////////////////////////
unsigned char col1[2]={0,255}, col2[2]={200,255}, col3[2]={255,255};//colors filling
CImg<double>f(phi1.dimx(),phi1.dimy());
cimg_forXY(phi1,x,y) {if(phi1(x,y)==1) phi1(x,y)=200;}
phi1.draw_fill(0,0,col3);
cimg_forXY(phi2,x,y) {if(phi2(x,y)==1) phi2(x,y)=200;}
phi2.draw_fill(0,0,col3);
cimg_forXY(phi1,x,y){
if(phi1(x,y)==200) f(x,y)=0;
if(phi1(x,y)==0) f(x,y)=-5;
if(phi1(x,y)==255) f(x,y)=5;
}
cimg_forXY(phi1,x,y){
phi1(x,y)=floor(phi1(x,y)-phi2(x,y));
if(phi1(x,y)<0) phi1(x,y)=-1;
if(phi1(x,y)==0) phi1(x,y)=1;
if(phi1(x,y)==-55 || phi1(x,y)==200) phi1(x,y)=0;
}
cimg_forXY(phi2,x,y){
if(phi2(x,y)==200) phi2(x,y)=0;
if(phi2(x,y)==0) phi2(x,y)=-5;
if(phi2(x,y)==255) phi2(x,y)=5;
}
CImg<double>HeavisideF10= Heaviside1(f);
// cimg_forXY(phi1,x,y){ phi1(x,y)=phi1(x,y)*phi2(x,y);}
// if (phi1(x,y)*phi2(x,y)>0) phi1(x,y)=-5;
// if (phi1(x,y)*phi2(x,y)==0)phi1(x,y)=0;
//if (phi1(x,y)*phi2(x,y)<0)phi1(x,y)=5;
//}
// phi1.normalize(-1,1);
// CImgDisplay disp2(phi2,"Image",0);
phi1.distance_hamilton(5);//distance function
// phi2.distance_hamilton(30);//distance function
// CImgDisplay disp1(phi1,"Image",0);
//Initializations
CImg<double> dphi1(Img.dimx(),Img.dimy(),2); //derivatives of phi
CImg<double> veloc1(phi1.dimx(),phi1.dimy());
CImg<double> N_dphi1(phi1.dimx(),phi1.dimy(),2); //Normalize gradient of level set function phi1
CImg<double> veloc2(phi2.dimx(),phi2.dimy());
CImg<double> N_dphi2(phi2.dimx(),phi2.dimy(),2); //Normalize gradient of level set function phi2
// const unsigned int nb_iter = 0;//Number of iterations
double c1=0, c2=0, Averagec1=0, Averagec2=0;
//Edge indicator
CImg<double>dg(g.dimx(),g.dimy(),1,2);
cimg_for3XY(g,x,y){
dg(x,y,0)=0.5*(g(_n1x,y)-g(_p1x,y)),
dg(x,y,1)=0.5*(g(x,_n1y)-g(x,_p1y));
}
// CImg<double>HeavisideF10= Heaviside1(phi1);
double E1=1e20f,E2=1e20f;//Initial energy
double Eold1 = 0, Eold2=0;
veloc1.fill(0);
veloc2.fill(0);
//////////////////////////////////////////////////////////////////////////////////////////////
//Main PDEs
for (unsigned int iter=0; iter<=nb_iter; iter++) {
CImg<double> diracF1=DiracU(phi1);
CImg<double>HeavisideF1=Heaviside(phi1);
CImg<double> diracF2=DiracU(phi2);
CImg<double>HeavisideF2=Heaviside1(phi2);
// CImg<double> dirac = DiracF(phi1,phi2);
cimg_for3XY(phi1,x,y)if (VolumeMask(x,y)==0){
//PHI1
const double
phix1=0.5*(phi1(_n1x,y)-phi1(_p1x,y)),
phiy1=0.5*(phi1(x,_n1y)-phi1(x,_p1y)); //derivatives of phi(central)
const double Mag_dphi1= sqrt(pow(phix1,2)+ pow(phiy1,2)+1e-10); //magnitude of grad(phi)
N_dphi1(x,y,0)=phix1/Mag_dphi1;
N_dphi1(x,y,1)=phiy1/Mag_dphi1;
c1+=HeavisideF1(x,y)* Img(x,y);
c2+=(1-HeavisideF1(x,y))*Img(x,y);
Averagec1+=HeavisideF1(x,y);
Averagec2+=HeavisideF1(x,y);
/////////////////////////////////////////////////////////////////////////////////////
//PHI2
const double
phix2=0.5*(phi2(_n1x,y)-phi2(_p1x,y)),
phiy2=0.5*(phi2(x,_n1y)-phi2(x,_p1y)); //derivatives of phi2
const double Mag_dphi2= sqrt(pow(phix2,2)+ pow(phiy2,2)+1e-10); //magnitude of grad(phi2)
N_dphi2(x,y,0)=phix2/Mag_dphi2;
N_dphi2(x,y,1)=phiy2/Mag_dphi2;
}
c1/=(Averagec1+1e-5);
c2/=(Averagec2+1e-5);
cimg_for3XY(Img,x,y)if (VolumeMask(x,y)==0){
//Chan-Vese level set function
const double
dN_phix1=0.5*(N_dphi1(_n1x,y,0)-N_dphi1(_p1x,y,0)),
dN_phiy1=0.5*(N_dphi1(x,_n1y,1)-N_dphi1(x,_p1y,1)),
Laplac_phi1=(phi1(_n1x,y) + phi1(_p1x,y) + phi1(x,_n1y) + phi1(x,_p1y))-4*phi1(x,y),
K1=dN_phix1+dN_phiy1;
const double
phixx1=(phi1(_n1x,y)+phi1(_p1x,y)-2*phi1(x,y)),
phiyy1=(phi1(x,_n1y)+phi1(x,_p1y)-2*phi1(x,y)),
phix1 =0.5*(phi1(_n1x,y)-phi1(_p1x,y)),
phiy1 =0.5*(phi1(x,_n1y)-phi1(x,_p1y)),
Mag_dphi1 = sqrt(pow(phix1,2)+ pow(phiy1,2)+1e-10);
veloc1(x,y)=kappa*diracF1(x,y)*(dg(x,y,0)* N_dphi1(x,y,0) +dg(x,y,1)* N_dphi1(x,y,1)+g(x,y)*K1)+mu*(Laplac_phi1-K1)-lambda1* diracF1(x,y)* pow(Img(x,y)-c1,2)+lambda2*diracF1(x,y)*pow(Img(x,y)-c2,2);//+35*diracF1(x,y);//0.01*diracF1(x,y)*(1-HeavisideF1(x,y))*pow(1-HeavisideF2(x,y),2);//-0.8*diracF2(x,y)*(HeavisideF1(x,y)-1);
// veloc1(x,y)=(1-HeavisideF2(x,y))*veloc1(x,y);
E1+=lambda1*HeavisideF1(x,y)*pow(Img(x,y)-c1,2);//+lambda2*(1-HeavisideF1(x,y))*pow(Img(x,y)-c2,2);
//front propagation level set function
const double
dN_phix2=0.5*(N_dphi2(_n1x,y,0)-N_dphi2(_p1x,y,0)),
dN_phiy2=0.5*(N_dphi2(x,_n1y,1)-N_dphi2(x,_p1y,1)),
Laplac_phi2=(phi2(_n1x,y) + phi2(_p1x,y) + phi2(x,_n1y) + phi2(x,_p1y))-4*phi2(x,y),
K2=dN_phix2+dN_phiy2;
const double
phixx2=(phi2(_n1x,y)+phi2(_p1x,y)-2*phi2(x,y)),
phiyy2=(phi2(x,_n1y)+phi2(x,_p1y)-2*phi2(x,y)),
phix2 =0.5*(phi2(_n1x,y)-phi2(_p1x,y)),
phiy2 =0.5*(phi2(x,_n1y)-phi2(x,_p1y)),//derivatives of u
Mag_dphi2 = sqrt(pow(phix2,2)+ pow(phiy2,2)+1e-10); //magnitude of grad(u)
//if (HeavisideF10(x,y)-HeavisideF2(x,y)>0 && HeavisideF1(x,y)>0){
veloc2(x,y)=lambda* diracF2(x,y)*( dg(x,y,0)* N_dphi2(x,y,0) +dg(x,y,1)* N_dphi2(x,y,1) + g(x,y)*K2)+mu*(Laplac_phi2-K2)+v*g(x,y)*diracF2(x,y);
//}
// else veloc2(x,y)=0;
veloc2(x,y)=veloc2(x,y)*HeavisideF10(x,y)*HeavisideF1(x,y);
//Energy estimation(functionals)
E2+=v*HeavisideF2(x,y)*g(x,y);
// E2+=lambda*g(x,y)*diracF2(x,y)* Mag_dphi2+1/2*mu*pow( Mag_dphi2-1,2)+v*HeavisideF2(x,y)*g(x,y);
}
phi1+=dt*veloc1;
phi2+=dt*veloc2;
if ((abs(Eold1-E1)<0.001f) && (abs(Eold2-E2)<0.001f)) break;
/* if (!(iter%8)) {
get_level0(phi1).resize(disp1.dimx(),disp1.dimy()).draw_grid(20,20,0,0,false,false,col3,0.4f,0xCCCCCCCC,0xCCCCCCCC).
draw_text(5,5,"Iteration %d",col3,0,1,11,iter).display(disp1);
get_level0(phi2).resize(disp2.dimx(),disp2.dimy()).draw_grid(20,20,0,0,false,false,col3,0.4f,0xCCCCCCCC,0xCCCCCCCC).
draw_text(5,5,"Iteration %d",col3,0,1,11,iter).display(disp2);
}*/
//printf ("Energy functional E1: %d \n",E1);
//printf ("Energy functional E2: %d \n",E2);
// printf("E1-Eold1=%d\n",abs(Eold1-E1));
// printf("E2-Eold2=%d\n",abs(E2-Eold2));
// if (!(iter%550)) phi2.distance_hamilton(1,3);// phi1.distance_hamilton(1,10);;
c1=0,Averagec1=0;
c2=0,Averagec2=0;
Eold1 = E1, Eold2=E2;
E1=0;E2=0;
}
// phi2.distance_hamilton(1,10), phi1.distance_hamilton(1,10);
//CImg<double>Contour1 = ExtractContour(phi1);
//CImg<double>Contour2 = ExtractContour(phi2);
// phi2.distance_hamilton(1,3);
// phi1.distance_hamilton(1,3);
plhs[0]= phi1.toMatlab();
plhs[1]= phi2.toMatlab();
}
return;
}
CImg<double> DiracU(CImg<double>& u0) {
CImg<double> u(u0.dimx(),u0.dimy());
u.fill(0);
cimg_forXY(u0,x,y) {
if (u0(x,y)<=epsilon && u0(x,y)>=-epsilon){
u(x,y)=(double)1/(2*epsilon)*(1+cos(3.14*u0(x,y)/epsilon));
}
}
return u;
}
CImg<double> Heaviside(CImg<double>& u0) {
CImg<double> u(u0.dimx(),u0.dimy());
u.fill(0);
/*cimg_forXY(u0,x,y){
u(x,y)=1/2*(1+2/3.14*atan(u(x,y)/epsilon));
}*/
cimg_forXY(u0,x,y) {
if (u0(x,y)>=-epsilon && u0(x,y)<=epsilon){
u(x,y)=(double) 1/2+u0(x,y)/(2*epsilon)+1/(2*3.14)*sin(3.14*u0(x,y)/epsilon);
}
if (u0(x,y)>epsilon) u(x,y)=1;
}
return u;
}
/*******************************************************************************/
CImg<double> ExtractContour(CImg<double> LevelSet)
{
CImg<double> Contour(LevelSet.dimx(),LevelSet.dimy(),1,1);
Contour.fill(0);
CImg_3x3(I,double);
cimg_for3x3(LevelSet,x,y,0,0,I)
{
if(Icc*Icp<=0 || Icc*Icn<=0 || Icc*Ipc<=0 || Icc*Inc<=0)
Contour(x,y) = 1;
}
return Contour;
}
CImg<double> Heaviside1(CImg<double>& u0) {
CImg<double> u(u0.dimx(),u0.dimy());
u.fill(0);
cimg_forXY(u0,x,y) {
if (u0(x,y)<=epsilon && u0(x,y)>=-epsilon){
u(x,y)=(double) 1/2-u0(x,y)/(2*epsilon)+1/(2*3.14)*sin(-3.14*u0(x,y)/epsilon);
}
if (u0(x,y)<-epsilon) u(x,y)=1;
}
return u;
}
//////////////////////////////////////////////////////////////////////////////////////////////
// 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); Inn = 0;
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;
}
/////////////////////////////////////////////////////////////////////////////////////////////////////////////
// // Create a user-defined closed curve (Initial level set fuction)
CImg<unsigned char> InitialLevelSet(CImg<double>&Img){
CImg<unsigned char> curve(Img.dimx(),Img.dimy(),Img.dimz(),2,0);
unsigned char col1[2]={0,255}, col2[2]={200,255}, col3[2]={255,255};//colors
curve.draw_grid(20,20,0,0,false,false,col1,0.4f,0xCCCCCCCC,0xCCCCCCCC).
draw_text(5,5,"Please draw your curve\nin the middle of this window\n(Use your mouse)\n-heart initial curve",col1);
CImgDisplay disp(curve,"Image",0);
CImg<double> tempImg(Img);
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);
tempImg.draw_point(x1,y1,col1).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);
return curve;
}
//////////////////////////////////////////////////////////////////////////////////////////////