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