/*
#
# File : mcf_levelsets3d.cpp
# ( C++ source file )
#
# Description : Implementation of the Mean Curvature Flow on Surfaces
# using the framework of Level Sets 3D.
# This file is a part of the CImg Library project.
# ( http://cimg.sourceforge.net )
#
# Copyright : David Tschumperle
# ( 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.
#
*/
#include "CImg.h"
using namespace cimg_library;
#undef min
#undef max
// Apply the Mean curvature flow PDE
//-----------------------------------
template<typename T> CImg<T>& mcf_PDE(CImg<T>& img, const unsigned int nb_iterations,
const float dt=0.25f, const float narrow=4.0f) {
CImg<float> velocity(img.width(),img.height(),img.depth(),img.spectrum());
CImg_3x3x3(I,float);
for (unsigned int iteration = 0; iteration<nb_iterations; ++iteration) {
float *ptrd = velocity.data(), veloc_max = 0;
cimg_for3x3x3(img,x,y,z,0,I,float) if (cimg::abs(Iccc)<narrow) {
const float
ix = (Incc - Ipcc)/2,
iy = (Icnc - Icpc)/2,
iz = (Iccn - Iccp)/2,
norm = (float)std::sqrt(1e-5f + ix*ix + iy*iy + iz*iz),
ixx = Incc + Ipcc - 2*Iccc,
ixy = (Ippc + Innc - Inpc - Ipnc)/4,
ixz = (Ipcp + Incn - Incp - Ipcn)/4,
iyy = Icnc + Icpc - 2*Iccc,
iyz = (Icpp + Icnn - Icnp - Icpn)/4,
izz = Iccn + Iccp - 2*Iccc,
a = ix/norm,
b = iy/norm,
c = iz/norm,
inn = a*a*ixx + b*b*iyy + c*c*izz + 2*a*b*ixy + 2*a*c*ixz + 2*b*c*iyz,
veloc = ixx + iyy + izz - inn;
*(ptrd++) = veloc;
if (veloc>veloc_max) veloc_max = veloc; else if (-veloc>veloc_max) veloc_max = -veloc;
} else *(ptrd++) = 0;
if (veloc_max>0) img+=(velocity*=dt/veloc_max);
}
return img;
}
/*----------------------
Main procedure
--------------------*/
int main(int argc,char **argv) {
cimg_usage("Mean curvature flow of a surface, using 3D level sets");
const char *file_i = cimg_option("-i",(char*)0,"Input image");
const float dt = cimg_option("-dt",0.05f,"PDE Time step");
const float narrow = cimg_option("-band",5.0f,"Size of the narrow band");
const bool both = cimg_option("-both",false,"Show both evolving and initial surface");
// Define the signed distance map of the initial surface.
CImg<> img;
if (file_i) {
const float sigma = cimg_option("-sigma",1.2f,"Segmentation regularity");
const float alpha = cimg_option("-alpha",5.0f,"Region growing tolerance");
img.load(file_i).channel(0);
CImg<int> s;
CImgDisplay disp(img,"Please select a starting point");
while (!s || s[0]<0) s = img.get_select(0,disp);
CImg<> region;
float tmp[] = { 0 };
img.draw_fill(s[0],s[1],s[2],tmp,1,region,alpha);
((img = region.normalize(-1,1))*=-1).blur(sigma);
}
else { // Create synthetic implicit function.
img.assign(60,60,60);
const float exte[] = { 1 }, inte[] = { -1 };
img.fill(*exte).draw_rectangle(15,15,15,45,45,45,inte).draw_rectangle(25,25,0,35,35,img.depth()-1,exte).
draw_rectangle(0,25,25,img.width()-1,35,35,exte).draw_rectangle(25,0,25,35,img.height()-1,35,exte).noise(0.7);
}
img.distance_eikonal(10,0,0.1f);
// Compute corresponding surface triangularization by the marching cube algorithm (isovalue 0).
CImg<> points0;
CImgList<unsigned int> faces0;
if (both) points0 = img.get_isosurface3d(faces0,0);
const CImgList<unsigned char> colors0(faces0.size(),CImg<unsigned char>::vector(100,200,255));
const CImgList<> opacities0(faces0.size(),1,1,1,1,0.2f);
// Perform MCF evolution.
CImgDisplay disp(256,256,0,1), disp3d(512,512,0,0);
float alpha = 0, beta = 0;
for (unsigned int iteration = 0; !disp.is_closed() && !disp3d.is_closed() &&
!disp.is_keyESC() && !disp3d.is_keyESC() && !disp.is_keyQ() && !disp3d.is_keyQ(); ++iteration) {
disp.set_title("3D implicit Function (iter. %u)",iteration);
disp3d.set_title("Mean curvature flow 3D - Isosurface (iter. %u)",iteration);
// Apply PDE on the distance function.
mcf_PDE(img,1,dt,narrow); // Do one iteration of mean curvature flow.
if (!(iteration%10)) img.distance_eikonal(1,narrow,0.5f); // Every 10 steps, do one iteration of distance function re-initialization.
// Compute surface triangularization by the marching cube algorithm (isovalue 0)
CImgList<unsigned int> faces;
CImg<> points = img.get_isosurface3d(faces,0);
CImgList<unsigned char> colors(faces.size(),CImg<unsigned char>::vector(200,128,100));
CImgList<> opacities(faces.size(),CImg<>::vector(1.0f));
const float fact = 3*cimg::max(disp3d.width(),disp3d.height())/(4.0f*cimg::max(img.width(),img.height()));
// Append initial object if necessary.
if (both) {
points.append_object3d(faces,points0,faces0);
colors.insert(colors0);
opacities.insert(opacities0);
}
// Center and rescale the objects
cimg_forX(points,l) {
points(l,0)=(points(l,0)-img.width()/2)*fact;
points(l,1)=(points(l,1)-img.height()/2)*fact;
points(l,2)=(points(l,2)-img.depth()/2)*fact;
}
// Display 3D object on the display window.
CImg<unsigned char> visu(disp3d.width(),disp3d.height(),1,3,0);
const CImg<> rot = CImg<>::rotation_matrix(1,0,0,(beta+=0.01f))*CImg<>::rotation_matrix(0,1,1,(alpha+=0.05f));
if (points.size()) {
visu.draw_object3d(visu.width()/2.0f,visu.height()/2.0f,0.0f,
rot*points,faces,colors,opacities,3,
false,500.0,0.0f,0.0f,-8000.0f).display(disp3d);
} else visu.fill(0).display(disp3d);
img.display(disp.wait(20));
if ((disp3d.button() || disp3d.key()) && points.size() && !disp3d.is_keyESC() && !disp3d.is_keyQ()) {
const unsigned char white[3] = { 255, 255, 255 };
visu.fill(0).draw_text(10,10,"Time stopped, press any key to start again",white).
display_object3d(disp3d,points,faces,colors,opacities,true,4,3,false,500,0,0,-5000,0.4f,0.3f);
disp3d.set_key();
}
if (disp.is_resized()) disp.resize(false);
if (disp3d.is_resized()) disp3d.resize(false);
disp.wait(50);
}
return 0;
}