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opencv/modules/imgproc/src/grabcut.cpp

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/*M///////////////////////////////////////////////////////////////////////////////////////
//
// IMPORTANT: READ BEFORE DOWNLOADING, COPYING, INSTALLING OR USING.
//
// By downloading, copying, installing or using the software you agree to this license.
// If you do not agree to this license, do not download, install,
// copy or use the software.
//
//
// Intel License Agreement
// For Open Source Computer Vision Library
//
// Copyright (C) 2000, Intel Corporation, all rights reserved.
// Third party copyrights are property of their respective owners.
//
// Redistribution and use in source and binary forms, with or without modification,
// are permitted provided that the following conditions are met:
//
// * Redistribution's of source code must retain the above copyright notice,
// this list of conditions and the following disclaimer.
//
// * Redistribution's in binary form must reproduce the above copyright notice,
// this list of conditions and the following disclaimer in the documentation
// and/or other materials provided with the distribution.
//
// * The name of Intel Corporation may not be used to endorse or promote products
// derived from this software without specific prior written permission.
//
// This software is provided by the copyright holders and contributors "as is" and
// any express or implied warranties, including, but not limited to, the implied
// warranties of merchantability and fitness for a particular purpose are disclaimed.
// In no event shall the Intel Corporation or contributors be liable for any direct,
// indirect, incidental, special, exemplary, or consequential damages
// (including, but not limited to, procurement of substitute goods or services;
// loss of use, data, or profits; or business interruption) however caused
// and on any theory of liability, whether in contract, strict liability,
// or tort (including negligence or otherwise) arising in any way out of
// the use of this software, even if advised of the possibility of such damage.
//
//M*/
#include "precomp.hpp"
#include "opencv2/imgproc/detail/gcgraph.hpp"
#include <limits>
using namespace cv;
using namespace detail;
namespace {
/*
This is implementation of image segmentation algorithm GrabCut described in
"GrabCut - Interactive Foreground Extraction using Iterated Graph Cuts".
Carsten Rother, Vladimir Kolmogorov, Andrew Blake.
*/
/*
GMM - Gaussian Mixture Model
*/
class GMM
{
public:
static const int componentsCount = 5;
GMM( Mat& _model );
double operator()( const Vec3d color ) const;
double operator()( int ci, const Vec3d color ) const;
int whichComponent( const Vec3d color ) const;
void initLearning();
void addSample( int ci, const Vec3d color );
void endLearning();
private:
void calcInverseCovAndDeterm(int ci, double singularFix);
Mat model;
double* coefs;
double* mean;
double* cov;
double inverseCovs[componentsCount][3][3];
double covDeterms[componentsCount];
double sums[componentsCount][3];
double prods[componentsCount][3][3];
int sampleCounts[componentsCount];
int totalSampleCount;
};
GMM::GMM( Mat& _model )
{
const int modelSize = 3/*mean*/ + 9/*covariance*/ + 1/*component weight*/;
if( _model.empty() )
{
_model.create( 1, modelSize*componentsCount, CV_64FC1 );
_model.setTo(Scalar(0));
}
else if( (_model.type() != CV_64FC1) || (_model.rows != 1) || (_model.cols != modelSize*componentsCount) )
CV_Error( CV_StsBadArg, "_model must have CV_64FC1 type, rows == 1 and cols == 13*componentsCount" );
model = _model;
coefs = model.ptr<double>(0);
mean = coefs + componentsCount;
cov = mean + 3*componentsCount;
for( int ci = 0; ci < componentsCount; ci++ )
if( coefs[ci] > 0 )
calcInverseCovAndDeterm(ci, 0.0);
totalSampleCount = 0;
}
double GMM::operator()( const Vec3d color ) const
{
double res = 0;
for( int ci = 0; ci < componentsCount; ci++ )
res += coefs[ci] * (*this)(ci, color );
return res;
}
double GMM::operator()( int ci, const Vec3d color ) const
{
double res = 0;
if( coefs[ci] > 0 )
{
CV_Assert( covDeterms[ci] > std::numeric_limits<double>::epsilon() );
Vec3d diff = color;
double* m = mean + 3*ci;
diff[0] -= m[0]; diff[1] -= m[1]; diff[2] -= m[2];
double mult = diff[0]*(diff[0]*inverseCovs[ci][0][0] + diff[1]*inverseCovs[ci][1][0] + diff[2]*inverseCovs[ci][2][0])
+ diff[1]*(diff[0]*inverseCovs[ci][0][1] + diff[1]*inverseCovs[ci][1][1] + diff[2]*inverseCovs[ci][2][1])
+ diff[2]*(diff[0]*inverseCovs[ci][0][2] + diff[1]*inverseCovs[ci][1][2] + diff[2]*inverseCovs[ci][2][2]);
res = 1.0f/sqrt(covDeterms[ci]) * exp(-0.5f*mult);
}
return res;
}
int GMM::whichComponent( const Vec3d color ) const
{
int k = 0;
double max = 0;
for( int ci = 0; ci < componentsCount; ci++ )
{
double p = (*this)( ci, color );
if( p > max )
{
k = ci;
max = p;
}
}
return k;
}
void GMM::initLearning()
{
for( int ci = 0; ci < componentsCount; ci++)
{
sums[ci][0] = sums[ci][1] = sums[ci][2] = 0;
prods[ci][0][0] = prods[ci][0][1] = prods[ci][0][2] = 0;
prods[ci][1][0] = prods[ci][1][1] = prods[ci][1][2] = 0;
prods[ci][2][0] = prods[ci][2][1] = prods[ci][2][2] = 0;
sampleCounts[ci] = 0;
}
totalSampleCount = 0;
}
void GMM::addSample( int ci, const Vec3d color )
{
sums[ci][0] += color[0]; sums[ci][1] += color[1]; sums[ci][2] += color[2];
prods[ci][0][0] += color[0]*color[0]; prods[ci][0][1] += color[0]*color[1]; prods[ci][0][2] += color[0]*color[2];
prods[ci][1][0] += color[1]*color[0]; prods[ci][1][1] += color[1]*color[1]; prods[ci][1][2] += color[1]*color[2];
prods[ci][2][0] += color[2]*color[0]; prods[ci][2][1] += color[2]*color[1]; prods[ci][2][2] += color[2]*color[2];
sampleCounts[ci]++;
totalSampleCount++;
}
void GMM::endLearning()
{
for( int ci = 0; ci < componentsCount; ci++ )
{
int n = sampleCounts[ci];
if( n == 0 )
coefs[ci] = 0;
else
{
CV_Assert(totalSampleCount > 0);
double inv_n = 1.0 / n;
coefs[ci] = (double)n/totalSampleCount;
double* m = mean + 3*ci;
m[0] = sums[ci][0] * inv_n; m[1] = sums[ci][1] * inv_n; m[2] = sums[ci][2] * inv_n;
double* c = cov + 9*ci;
c[0] = prods[ci][0][0] * inv_n - m[0]*m[0]; c[1] = prods[ci][0][1] * inv_n - m[0]*m[1]; c[2] = prods[ci][0][2] * inv_n - m[0]*m[2];
c[3] = prods[ci][1][0] * inv_n - m[1]*m[0]; c[4] = prods[ci][1][1] * inv_n - m[1]*m[1]; c[5] = prods[ci][1][2] * inv_n - m[1]*m[2];
c[6] = prods[ci][2][0] * inv_n - m[2]*m[0]; c[7] = prods[ci][2][1] * inv_n - m[2]*m[1]; c[8] = prods[ci][2][2] * inv_n - m[2]*m[2];
calcInverseCovAndDeterm(ci, 0.01);
}
}
}
void GMM::calcInverseCovAndDeterm(int ci, const double singularFix)
{
if( coefs[ci] > 0 )
{
double *c = cov + 9*ci;
double dtrm = c[0]*(c[4]*c[8]-c[5]*c[7]) - c[1]*(c[3]*c[8]-c[5]*c[6]) + c[2]*(c[3]*c[7]-c[4]*c[6]);
if (dtrm <= 1e-6 && singularFix > 0)
{
// Adds the white noise to avoid singular covariance matrix.
c[0] += singularFix;
c[4] += singularFix;
c[8] += singularFix;
dtrm = c[0] * (c[4] * c[8] - c[5] * c[7]) - c[1] * (c[3] * c[8] - c[5] * c[6]) + c[2] * (c[3] * c[7] - c[4] * c[6]);
}
covDeterms[ci] = dtrm;
CV_Assert( dtrm > std::numeric_limits<double>::epsilon() );
double inv_dtrm = 1.0 / dtrm;
inverseCovs[ci][0][0] = (c[4]*c[8] - c[5]*c[7]) * inv_dtrm;
inverseCovs[ci][1][0] = -(c[3]*c[8] - c[5]*c[6]) * inv_dtrm;
inverseCovs[ci][2][0] = (c[3]*c[7] - c[4]*c[6]) * inv_dtrm;
inverseCovs[ci][0][1] = -(c[1]*c[8] - c[2]*c[7]) * inv_dtrm;
inverseCovs[ci][1][1] = (c[0]*c[8] - c[2]*c[6]) * inv_dtrm;
inverseCovs[ci][2][1] = -(c[0]*c[7] - c[1]*c[6]) * inv_dtrm;
inverseCovs[ci][0][2] = (c[1]*c[5] - c[2]*c[4]) * inv_dtrm;
inverseCovs[ci][1][2] = -(c[0]*c[5] - c[2]*c[3]) * inv_dtrm;
inverseCovs[ci][2][2] = (c[0]*c[4] - c[1]*c[3]) * inv_dtrm;
}
}
} // namespace
/*
Calculate beta - parameter of GrabCut algorithm.
beta = 1/(2*avg(sqr(||color[i] - color[j]||)))
*/
static double calcBeta( const Mat& img )
{
double beta = 0;
for( int y = 0; y < img.rows; y++ )
{
for( int x = 0; x < img.cols; x++ )
{
Vec3d color = img.at<Vec3b>(y,x);
if( x>0 ) // left
{
Vec3d diff = color - (Vec3d)img.at<Vec3b>(y,x-1);
beta += diff.dot(diff);
}
if( y>0 && x>0 ) // upleft
{
Vec3d diff = color - (Vec3d)img.at<Vec3b>(y-1,x-1);
beta += diff.dot(diff);
}
if( y>0 ) // up
{
Vec3d diff = color - (Vec3d)img.at<Vec3b>(y-1,x);
beta += diff.dot(diff);
}
if( y>0 && x<img.cols-1) // upright
{
Vec3d diff = color - (Vec3d)img.at<Vec3b>(y-1,x+1);
beta += diff.dot(diff);
}
}
}
if( beta <= std::numeric_limits<double>::epsilon() )
beta = 0;
else
beta = 1.f / (2 * beta/(4*img.cols*img.rows - 3*img.cols - 3*img.rows + 2) );
return beta;
}
/*
Calculate weights of noterminal vertices of graph.
beta and gamma - parameters of GrabCut algorithm.
*/
static void calcNWeights( const Mat& img, Mat& leftW, Mat& upleftW, Mat& upW, Mat& uprightW, double beta, double gamma )
{
const double gammaDivSqrt2 = gamma / std::sqrt(2.0f);
leftW.create( img.rows, img.cols, CV_64FC1 );
upleftW.create( img.rows, img.cols, CV_64FC1 );
upW.create( img.rows, img.cols, CV_64FC1 );
uprightW.create( img.rows, img.cols, CV_64FC1 );
for( int y = 0; y < img.rows; y++ )
{
for( int x = 0; x < img.cols; x++ )
{
Vec3d color = img.at<Vec3b>(y,x);
if( x-1>=0 ) // left
{
Vec3d diff = color - (Vec3d)img.at<Vec3b>(y,x-1);
leftW.at<double>(y,x) = gamma * exp(-beta*diff.dot(diff));
}
else
leftW.at<double>(y,x) = 0;
if( x-1>=0 && y-1>=0 ) // upleft
{
Vec3d diff = color - (Vec3d)img.at<Vec3b>(y-1,x-1);
upleftW.at<double>(y,x) = gammaDivSqrt2 * exp(-beta*diff.dot(diff));
}
else
upleftW.at<double>(y,x) = 0;
if( y-1>=0 ) // up
{
Vec3d diff = color - (Vec3d)img.at<Vec3b>(y-1,x);
upW.at<double>(y,x) = gamma * exp(-beta*diff.dot(diff));
}
else
upW.at<double>(y,x) = 0;
if( x+1<img.cols && y-1>=0 ) // upright
{
Vec3d diff = color - (Vec3d)img.at<Vec3b>(y-1,x+1);
uprightW.at<double>(y,x) = gammaDivSqrt2 * exp(-beta*diff.dot(diff));
}
else
uprightW.at<double>(y,x) = 0;
}
}
}
/*
Check size, type and element values of mask matrix.
*/
static void checkMask( const Mat& img, const Mat& mask )
{
if( mask.empty() )
CV_Error( CV_StsBadArg, "mask is empty" );
if( mask.type() != CV_8UC1 )
CV_Error( CV_StsBadArg, "mask must have CV_8UC1 type" );
if( mask.cols != img.cols || mask.rows != img.rows )
CV_Error( CV_StsBadArg, "mask must have as many rows and cols as img" );
for( int y = 0; y < mask.rows; y++ )
{
for( int x = 0; x < mask.cols; x++ )
{
uchar val = mask.at<uchar>(y,x);
if( val!=GC_BGD && val!=GC_FGD && val!=GC_PR_BGD && val!=GC_PR_FGD )
CV_Error( CV_StsBadArg, "mask element value must be equal "
"GC_BGD or GC_FGD or GC_PR_BGD or GC_PR_FGD" );
}
}
}
/*
Initialize mask using rectangular.
*/
static void initMaskWithRect( Mat& mask, Size imgSize, Rect rect )
{
mask.create( imgSize, CV_8UC1 );
mask.setTo( GC_BGD );
rect.x = std::max(0, rect.x);
rect.y = std::max(0, rect.y);
rect.width = std::min(rect.width, imgSize.width-rect.x);
rect.height = std::min(rect.height, imgSize.height-rect.y);
(mask(rect)).setTo( Scalar(GC_PR_FGD) );
}
/*
Initialize GMM background and foreground models using kmeans algorithm.
*/
static void initGMMs( const Mat& img, const Mat& mask, GMM& bgdGMM, GMM& fgdGMM )
{
const int kMeansItCount = 10;
const int kMeansType = KMEANS_PP_CENTERS;
Mat bgdLabels, fgdLabels;
std::vector<Vec3f> bgdSamples, fgdSamples;
Point p;
for( p.y = 0; p.y < img.rows; p.y++ )
{
for( p.x = 0; p.x < img.cols; p.x++ )
{
if( mask.at<uchar>(p) == GC_BGD || mask.at<uchar>(p) == GC_PR_BGD )
bgdSamples.push_back( (Vec3f)img.at<Vec3b>(p) );
else // GC_FGD | GC_PR_FGD
fgdSamples.push_back( (Vec3f)img.at<Vec3b>(p) );
}
}
CV_Assert( !bgdSamples.empty() && !fgdSamples.empty() );
{
Mat _bgdSamples( (int)bgdSamples.size(), 3, CV_32FC1, &bgdSamples[0][0] );
int num_clusters = GMM::componentsCount;
num_clusters = std::min(num_clusters, (int)bgdSamples.size());
kmeans( _bgdSamples, num_clusters, bgdLabels,
TermCriteria( CV_TERMCRIT_ITER, kMeansItCount, 0.0), 0, kMeansType );
}
{
Mat _fgdSamples( (int)fgdSamples.size(), 3, CV_32FC1, &fgdSamples[0][0] );
int num_clusters = GMM::componentsCount;
num_clusters = std::min(num_clusters, (int)fgdSamples.size());
kmeans( _fgdSamples, num_clusters, fgdLabels,
TermCriteria( CV_TERMCRIT_ITER, kMeansItCount, 0.0), 0, kMeansType );
}
bgdGMM.initLearning();
for( int i = 0; i < (int)bgdSamples.size(); i++ )
bgdGMM.addSample( bgdLabels.at<int>(i,0), bgdSamples[i] );
bgdGMM.endLearning();
fgdGMM.initLearning();
for( int i = 0; i < (int)fgdSamples.size(); i++ )
fgdGMM.addSample( fgdLabels.at<int>(i,0), fgdSamples[i] );
fgdGMM.endLearning();
}
/*
Assign GMMs components for each pixel.
*/
static void assignGMMsComponents( const Mat& img, const Mat& mask, const GMM& bgdGMM, const GMM& fgdGMM, Mat& compIdxs )
{
Point p;
for( p.y = 0; p.y < img.rows; p.y++ )
{
for( p.x = 0; p.x < img.cols; p.x++ )
{
Vec3d color = img.at<Vec3b>(p);
compIdxs.at<int>(p) = mask.at<uchar>(p) == GC_BGD || mask.at<uchar>(p) == GC_PR_BGD ?
bgdGMM.whichComponent(color) : fgdGMM.whichComponent(color);
}
}
}
/*
Learn GMMs parameters.
*/
static void learnGMMs( const Mat& img, const Mat& mask, const Mat& compIdxs, GMM& bgdGMM, GMM& fgdGMM )
{
bgdGMM.initLearning();
fgdGMM.initLearning();
Point p;
for( int ci = 0; ci < GMM::componentsCount; ci++ )
{
for( p.y = 0; p.y < img.rows; p.y++ )
{
for( p.x = 0; p.x < img.cols; p.x++ )
{
if( compIdxs.at<int>(p) == ci )
{
if( mask.at<uchar>(p) == GC_BGD || mask.at<uchar>(p) == GC_PR_BGD )
bgdGMM.addSample( ci, img.at<Vec3b>(p) );
else
fgdGMM.addSample( ci, img.at<Vec3b>(p) );
}
}
}
}
bgdGMM.endLearning();
fgdGMM.endLearning();
}
/*
Construct GCGraph
*/
static void constructGCGraph( const Mat& img, const Mat& mask, const GMM& bgdGMM, const GMM& fgdGMM, double lambda,
const Mat& leftW, const Mat& upleftW, const Mat& upW, const Mat& uprightW,
GCGraph<double>& graph )
{
int vtxCount = img.cols*img.rows,
edgeCount = 2*(4*img.cols*img.rows - 3*(img.cols + img.rows) + 2);
graph.create(vtxCount, edgeCount);
Point p;
for( p.y = 0; p.y < img.rows; p.y++ )
{
for( p.x = 0; p.x < img.cols; p.x++)
{
// add node
int vtxIdx = graph.addVtx();
Vec3b color = img.at<Vec3b>(p);
// set t-weights
double fromSource, toSink;
if( mask.at<uchar>(p) == GC_PR_BGD || mask.at<uchar>(p) == GC_PR_FGD )
{
fromSource = -log( bgdGMM(color) );
toSink = -log( fgdGMM(color) );
}
else if( mask.at<uchar>(p) == GC_BGD )
{
fromSource = 0;
toSink = lambda;
}
else // GC_FGD
{
fromSource = lambda;
toSink = 0;
}
graph.addTermWeights( vtxIdx, fromSource, toSink );
// set n-weights
if( p.x>0 )
{
double w = leftW.at<double>(p);
graph.addEdges( vtxIdx, vtxIdx-1, w, w );
}
if( p.x>0 && p.y>0 )
{
double w = upleftW.at<double>(p);
graph.addEdges( vtxIdx, vtxIdx-img.cols-1, w, w );
}
if( p.y>0 )
{
double w = upW.at<double>(p);
graph.addEdges( vtxIdx, vtxIdx-img.cols, w, w );
}
if( p.x<img.cols-1 && p.y>0 )
{
double w = uprightW.at<double>(p);
graph.addEdges( vtxIdx, vtxIdx-img.cols+1, w, w );
}
}
}
}
/*
Estimate segmentation using MaxFlow algorithm
*/
static void estimateSegmentation( GCGraph<double>& graph, Mat& mask )
{
graph.maxFlow();
Point p;
for( p.y = 0; p.y < mask.rows; p.y++ )
{
for( p.x = 0; p.x < mask.cols; p.x++ )
{
if( mask.at<uchar>(p) == GC_PR_BGD || mask.at<uchar>(p) == GC_PR_FGD )
{
if( graph.inSourceSegment( p.y*mask.cols+p.x /*vertex index*/ ) )
mask.at<uchar>(p) = GC_PR_FGD;
else
mask.at<uchar>(p) = GC_PR_BGD;
}
}
}
}
void cv::grabCut( InputArray _img, InputOutputArray _mask, Rect rect,
InputOutputArray _bgdModel, InputOutputArray _fgdModel,
int iterCount, int mode )
{
CV_INSTRUMENT_REGION();
Mat img = _img.getMat();
Mat& mask = _mask.getMatRef();
Mat& bgdModel = _bgdModel.getMatRef();
Mat& fgdModel = _fgdModel.getMatRef();
if( img.empty() )
CV_Error( CV_StsBadArg, "image is empty" );
if( img.type() != CV_8UC3 )
CV_Error( CV_StsBadArg, "image must have CV_8UC3 type" );
GMM bgdGMM( bgdModel ), fgdGMM( fgdModel );
Mat compIdxs( img.size(), CV_32SC1 );
if( mode == GC_INIT_WITH_RECT || mode == GC_INIT_WITH_MASK )
{
if( mode == GC_INIT_WITH_RECT )
initMaskWithRect( mask, img.size(), rect );
else // flag == GC_INIT_WITH_MASK
checkMask( img, mask );
initGMMs( img, mask, bgdGMM, fgdGMM );
}
if( iterCount <= 0)
return;
if( mode == GC_EVAL_FREEZE_MODEL )
iterCount = 1;
if( mode == GC_EVAL || mode == GC_EVAL_FREEZE_MODEL )
checkMask( img, mask );
const double gamma = 50;
const double lambda = 9*gamma;
const double beta = calcBeta( img );
Mat leftW, upleftW, upW, uprightW;
calcNWeights( img, leftW, upleftW, upW, uprightW, beta, gamma );
for( int i = 0; i < iterCount; i++ )
{
GCGraph<double> graph;
assignGMMsComponents( img, mask, bgdGMM, fgdGMM, compIdxs );
if( mode != GC_EVAL_FREEZE_MODEL )
learnGMMs( img, mask, compIdxs, bgdGMM, fgdGMM );
constructGCGraph(img, mask, bgdGMM, fgdGMM, lambda, leftW, upleftW, upW, uprightW, graph );
estimateSegmentation( graph, mask );
}
}