bgfg_gaussmix.cpp

/*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
//
// 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"

/////////////////////////////////////// MOG model //////////////////////////////////////////

static void CV_CDECL
icvReleaseGaussianBGModel( CvGaussBGModel** bg_model )
{
    if( !bg_model )
        CV_Error( CV_StsNullPtr, "" );

    if( *bg_model )
    {
        delete (cv::Ptr<cv::BackgroundSubtractor>*)((*bg_model)->mog);
        cvReleaseImage( &(*bg_model)->background );
        cvReleaseImage( &(*bg_model)->foreground );
        memset( *bg_model, 0, sizeof(**bg_model) );
        delete *bg_model;
        *bg_model = 0;
    }
}


static int CV_CDECL
icvUpdateGaussianBGModel( IplImage* curr_frame, CvGaussBGModel*  bg_model, double learningRate )
{
    cv::Mat image = cv::cvarrToMat(curr_frame), mask = cv::cvarrToMat(bg_model->foreground);

    cv::Ptr<cv::BackgroundSubtractor>* mog = (cv::Ptr<cv::BackgroundSubtractor>*)(bg_model->mog);
    CV_Assert(mog != 0);

    (*mog)->apply(image, mask, learningRate);
    bg_model->countFrames++;

    return 0;
}

CV_IMPL CvBGStatModel*
cvCreateGaussianBGModel( IplImage* first_frame, CvGaussBGStatModelParams* parameters )
{
    CvGaussBGStatModelParams params;

    CV_Assert( CV_IS_IMAGE(first_frame) );

    //init parameters
    if( parameters == NULL )
    {                        // These constants are defined in cvaux/include/cvaux.h
        params.win_size      = CV_BGFG_MOG_WINDOW_SIZE;
        params.bg_threshold  = CV_BGFG_MOG_BACKGROUND_THRESHOLD;

        params.std_threshold = CV_BGFG_MOG_STD_THRESHOLD;
        params.weight_init   = CV_BGFG_MOG_WEIGHT_INIT;

        params.variance_init = CV_BGFG_MOG_SIGMA_INIT*CV_BGFG_MOG_SIGMA_INIT;
        params.minArea       = CV_BGFG_MOG_MINAREA;
        params.n_gauss       = CV_BGFG_MOG_NGAUSSIANS;
    }
    else
        params = *parameters;

    CvGaussBGModel* bg_model = new CvGaussBGModel;
    memset( bg_model, 0, sizeof(*bg_model) );
    bg_model->type = CV_BG_MODEL_MOG;
    bg_model->release = (CvReleaseBGStatModel)icvReleaseGaussianBGModel;
    bg_model->update = (CvUpdateBGStatModel)icvUpdateGaussianBGModel;

    bg_model->params = params;

    cv::Ptr<cv::BackgroundSubtractor> mog = cv::createBackgroundSubtractorMOG(params.win_size, params.n_gauss,
                                                                              params.bg_threshold);
    cv::Ptr<cv::BackgroundSubtractor>* pmog = new cv::Ptr<cv::BackgroundSubtractor>;
    *pmog = mog;
    bg_model->mog = pmog;

    CvSize sz = cvGetSize(first_frame);
    bg_model->background = cvCreateImage(sz, IPL_DEPTH_8U, first_frame->nChannels);
    bg_model->foreground = cvCreateImage(sz, IPL_DEPTH_8U, 1);

    bg_model->countFrames = 0;

    icvUpdateGaussianBGModel( first_frame, bg_model, 1 );

    return (CvBGStatModel*)bg_model;
}


//////////////////////////////////////////// MOG2 //////////////////////////////////////////////

/*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
 //
 // 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*/

/*//Implementation of the Gaussian mixture model background subtraction from:
 //
 //"Improved adaptive Gausian mixture model for background subtraction"
 //Z.Zivkovic
 //International Conference Pattern Recognition, UK, August, 2004
 //http://www.zoranz.net/Publications/zivkovic2004ICPR.pdf
 //The code is very fast and performs also shadow detection.
 //Number of Gausssian components is adapted per pixel.
 //
 // and
 //
 //"Efficient Adaptive Density Estimapion per Image Pixel for the Task of Background Subtraction"
 //Z.Zivkovic, F. van der Heijden
 //Pattern Recognition Letters, vol. 27, no. 7, pages 773-780, 2006.
 //
 //The algorithm similar to the standard Stauffer&Grimson algorithm with
 //additional selection of the number of the Gaussian components based on:
 //
 //"Recursive unsupervised learning of finite mixture models "
 //Z.Zivkovic, F.van der Heijden
 //IEEE Trans. on Pattern Analysis and Machine Intelligence, vol.26, no.5, pages 651-656, 2004
 //http://www.zoranz.net/Publications/zivkovic2004PAMI.pdf
 //
 //
 //Example usage with as cpp class
 // BackgroundSubtractorMOG2 bg_model;
 //For each new image the model is updates using:
 // bg_model(img, fgmask);
 //
 //Example usage as part of the CvBGStatModel:
 // CvBGStatModel* bg_model = cvCreateGaussianBGModel2( first_frame );
 //
 // //update for each frame
 // cvUpdateBGStatModel( tmp_frame, bg_model );//segmentation result is in bg_model->foreground
 //
 // //release at the program termination
 // cvReleaseBGStatModel( &bg_model );
 //
 //Author: Z.Zivkovic, www.zoranz.net
 //Date: 7-April-2011, Version:1.0
 ///////////*/

#include "precomp.hpp"


/*
 Interface of Gaussian mixture algorithm from:

 "Improved adaptive Gausian mixture model for background subtraction"
 Z.Zivkovic
 International Conference Pattern Recognition, UK, August, 2004
 http://www.zoranz.net/Publications/zivkovic2004ICPR.pdf

 Advantages:
 -fast - number of Gausssian components is constantly adapted per pixel.
 -performs also shadow detection (see bgfg_segm_test.cpp example)

 */


#define CV_BG_MODEL_MOG2            3                 /* "Mixture of Gaussians 2".  */


/* default parameters of gaussian background detection algorithm */
#define CV_BGFG_MOG2_STD_THRESHOLD            4.0f     /* lambda=2.5 is 99% */
#define CV_BGFG_MOG2_WINDOW_SIZE              500      /* Learning rate; alpha = 1/CV_GBG_WINDOW_SIZE */
#define CV_BGFG_MOG2_BACKGROUND_THRESHOLD     0.9f     /* threshold sum of weights for background test */
#define CV_BGFG_MOG2_STD_THRESHOLD_GENERATE   3.0f     /* lambda=2.5 is 99% */
#define CV_BGFG_MOG2_NGAUSSIANS               5        /* = K = number of Gaussians in mixture */
#define CV_BGFG_MOG2_VAR_INIT                 15.0f    /* initial variance for new components*/
#define CV_BGFG_MOG2_VAR_MIN                    4.0f
#define CV_BGFG_MOG2_VAR_MAX                      5*CV_BGFG_MOG2_VAR_INIT
#define CV_BGFG_MOG2_MINAREA                  15.0f    /* for postfiltering */

/* additional parameters */
#define CV_BGFG_MOG2_CT                               0.05f     /* complexity reduction prior constant 0 - no reduction of number of components*/
#define CV_BGFG_MOG2_SHADOW_VALUE             127       /* value to use in the segmentation mask for shadows, sot 0 not to do shadow detection*/
#define CV_BGFG_MOG2_SHADOW_TAU               0.5f      /* Tau - shadow threshold, see the paper for explanation*/

typedef struct CvGaussBGStatModel2Params
{
    //image info
    int nWidth;
    int nHeight;
    int nND;//number of data dimensions (image channels)

    bool bPostFiltering;//defult 1 - do postfiltering - will make shadow detection results also give value 255
    double  minArea; // for postfiltering

    bool bInit;//default 1, faster updates at start

    /////////////////////////
    //very important parameters - things you will change
    ////////////////////////
    float fAlphaT;
    //alpha - speed of update - if the time interval you want to average over is T
    //set alpha=1/T. It is also usefull at start to make T slowly increase
    //from 1 until the desired T
    float fTb;
    //Tb - threshold on the squared Mahalan. dist. to decide if it is well described
    //by the background model or not. Related to Cthr from the paper.
    //This does not influence the update of the background. A typical value could be 4 sigma
    //and that is Tb=4*4=16;

    /////////////////////////
    //less important parameters - things you might change but be carefull
    ////////////////////////
    float fTg;
    //Tg - threshold on the squared Mahalan. dist. to decide
    //when a sample is close to the existing components. If it is not close
    //to any a new component will be generated. I use 3 sigma => Tg=3*3=9.
    //Smaller Tg leads to more generated components and higher Tg might make
    //lead to small number of components but they can grow too large
    float fTB;//1-cf from the paper
    //TB - threshold when the component becomes significant enough to be included into
    //the background model. It is the TB=1-cf from the paper. So I use cf=0.1 => TB=0.
    //For alpha=0.001 it means that the mode should exist for approximately 105 frames before
    //it is considered foreground
    float fVarInit;
    float fVarMax;
    float fVarMin;
    //initial standard deviation  for the newly generated components.
    //It will will influence the speed of adaptation. A good guess should be made.
    //A simple way is to estimate the typical standard deviation from the images.
    //I used here 10 as a reasonable value
    float fCT;//CT - complexity reduction prior
    //this is related to the number of samples needed to accept that a component
    //actually exists. We use CT=0.05 of all the samples. By setting CT=0 you get
    //the standard Stauffer&Grimson algorithm (maybe not exact but very similar)

    //even less important parameters
    int nM;//max number of modes - const - 4 is usually enough

    //shadow detection parameters
    bool bShadowDetection;//default 1 - do shadow detection
    unsigned char nShadowDetection;//do shadow detection - insert this value as the detection result
    float fTau;
    // Tau - shadow threshold. The shadow is detected if the pixel is darker
    //version of the background. Tau is a threshold on how much darker the shadow can be.
    //Tau= 0.5 means that if pixel is more than 2 times darker then it is not shadow
    //See: Prati,Mikic,Trivedi,Cucchiarra,"Detecting Moving Shadows...",IEEE PAMI,2003.
} CvGaussBGStatModel2Params;

#define CV_BGFG_MOG2_NDMAX 3

typedef struct CvPBGMMGaussian
{
    float weight;
    float mean[CV_BGFG_MOG2_NDMAX];
    float variance;
}CvPBGMMGaussian;

typedef struct CvGaussBGStatModel2Data
{
    CvPBGMMGaussian* rGMM; //array for the mixture of Gaussians
    unsigned char* rnUsedModes;//number of Gaussian components per pixel (maximum 255)
} CvGaussBGStatModel2Data;


/*
 //only foreground image is updated
 //no filtering included
 typedef struct CvGaussBGModel2
 {
 CV_BG_STAT_MODEL_FIELDS();
 CvGaussBGStatModel2Params params;
 CvGaussBGStatModel2Data   data;
 int                       countFrames;
 } CvGaussBGModel2;

 CVAPI(CvBGStatModel*) cvCreateGaussianBGModel2( IplImage* first_frame,
 CvGaussBGStatModel2Params* params CV_DEFAULT(NULL) );
 */

//shadow detection performed per pixel
// should work for rgb data, could be usefull for gray scale and depth data as well
//  See: Prati,Mikic,Trivedi,Cucchiarra,"Detecting Moving Shadows...",IEEE PAMI,2003.
CV_INLINE int _icvRemoveShadowGMM(float* data, int nD,
                                  unsigned char nModes,
                                  CvPBGMMGaussian* pGMM,
                                  float m_fTb,
                                  float m_fTB,
                                  float m_fTau)
{
    float tWeight = 0;
    float numerator, denominator;
    // check all the components  marked as background:
    for (int iModes=0;iModes<nModes;iModes++)
    {

        CvPBGMMGaussian g=pGMM[iModes];

        numerator = 0.0f;
        denominator = 0.0f;
        for (int iD=0;iD<nD;iD++)
        {
            numerator   += data[iD]  * g.mean[iD];
            denominator += g.mean[iD]* g.mean[iD];
        }

        // no division by zero allowed
        if (denominator == 0)
        {
            return 0;
        };
        float a = numerator / denominator;

        // if tau < a < 1 then also check the color distortion
        if ((a <= 1) && (a >= m_fTau))
        {

            float dist2a=0.0f;

            for (int iD=0;iD<nD;iD++)
            {
                float dD= a*g.mean[iD] - data[iD];
                dist2a += (dD*dD);
            }

            if (dist2a<m_fTb*g.variance*a*a)
            {
                return 2;
            }
        };

        tWeight += g.weight;
        if (tWeight > m_fTB)
        {
            return 0;
        };
    };
    return 0;
}

//update GMM - the base update function performed per pixel
//
//"Efficient Adaptive Density Estimapion per Image Pixel for the Task of Background Subtraction"
//Z.Zivkovic, F. van der Heijden
//Pattern Recognition Letters, vol. 27, no. 7, pages 773-780, 2006.
//
//The algorithm similar to the standard Stauffer&Grimson algorithm with
//additional selection of the number of the Gaussian components based on:
//
//"Recursive unsupervised learning of finite mixture models "
//Z.Zivkovic, F.van der Heijden
//IEEE Trans. on Pattern Analysis and Machine Intelligence, vol.26, no.5, pages 651-656, 2004
//http://www.zoranz.net/Publications/zivkovic2004PAMI.pdf

CV_INLINE int _icvUpdateGMM(float* data, int nD,
                            unsigned char* pModesUsed,
                            CvPBGMMGaussian* pGMM,
                            int m_nM,
                            float m_fAlphaT,
                            float m_fTb,
                            float m_fTB,
                            float m_fTg,
                            float m_fVarInit,
                            float m_fVarMax,
                            float m_fVarMin,
                            float m_fPrune)
{
    //calculate distances to the modes (+ sort)
    //here we need to go in descending order!!!
    bool bBackground=0;//return value -> true - the pixel classified as background

    //internal:
    bool bFitsPDF=0;//if it remains zero a new GMM mode will be added
    float m_fOneMinAlpha=1-m_fAlphaT;
    unsigned char nModes=*pModesUsed;//current number of modes in GMM
    float totalWeight=0.0f;

    //////
    //go through all modes
    int iMode=0;
    CvPBGMMGaussian* pGauss=pGMM;
    for (;iMode<nModes;iMode++,pGauss++)
    {
        float weight = pGauss->weight;//need only weight if fit is found
        weight=m_fOneMinAlpha*weight+m_fPrune;

        ////
        //fit not found yet
        if (!bFitsPDF)
        {
            //check if it belongs to some of the remaining modes
            float var=pGauss->variance;

            //calculate difference and distance
            float dist2=0.0f;
#if (CV_BGFG_MOG2_NDMAX==1)
            float dData=pGauss->mean[0]-data[0];
            dist2=dData*dData;
#else
            float dData[CV_BGFG_MOG2_NDMAX];

            for (int iD=0;iD<nD;iD++)
            {
                dData[iD]=pGauss->mean[iD]-data[iD];
                dist2+=dData[iD]*dData[iD];
            }
#endif
            //background? - m_fTb - usually larger than m_fTg
            if ((totalWeight<m_fTB)&&(dist2<m_fTb*var))
                bBackground=1;

            //check fit
            if (dist2<m_fTg*var)
            {
                /////
                //belongs to the mode - bFitsPDF becomes 1
                bFitsPDF=1;

                //update distribution

                //update weight
                weight+=m_fAlphaT;

                float k = m_fAlphaT/weight;

                //update mean
#if (CV_BGFG_MOG2_NDMAX==1)
                pGauss->mean[0]-=k*dData;
#else
                for (int iD=0;iD<nD;iD++)
                {
                    pGauss->mean[iD]-=k*dData[iD];
                }
#endif

                //update variance
                float varnew = var + k*(dist2-var);
                //limit the variance
                pGauss->variance = MIN(m_fVarMax,MAX(varnew,m_fVarMin));

                //sort
                //all other weights are at the same place and
                //only the matched (iModes) is higher -> just find the new place for it
                for (int iLocal = iMode;iLocal>0;iLocal--)
                {
                    //check one up
                    if (weight < (pGMM[iLocal-1].weight))
                    {
                        break;
                    }
                    else
                    {
                        //swap one up
                        CvPBGMMGaussian temp = pGMM[iLocal];
                        pGMM[iLocal] = pGMM[iLocal-1];
                        pGMM[iLocal-1] = temp;
                        pGauss--;
                    }
                }
                //belongs to the mode - bFitsPDF becomes 1
                /////
            }
        }//!bFitsPDF)

        //check prune
        if (weight<-m_fPrune)
        {
            weight=0.0;
            nModes--;
        }

        pGauss->weight=weight;//update weight by the calculated value
        totalWeight+=weight;
    }
    //go through all modes
    //////

    //renormalize weights
    for (iMode = 0; iMode < nModes; iMode++)
    {
        pGMM[iMode].weight = pGMM[iMode].weight/totalWeight;
    }

    //make new mode if needed and exit
    if (!bFitsPDF)
    {
        if (nModes==m_nM)
        {
            //replace the weakest
            pGauss=pGMM+m_nM-1;
        }
        else
        {
            //add a new one
            pGauss=pGMM+nModes;
            nModes++;
        }

        if (nModes==1)
        {
            pGauss->weight=1;
        }
        else
        {
            pGauss->weight=m_fAlphaT;

            //renormalize all weights
            for (iMode = 0; iMode < nModes-1; iMode++)
            {
                pGMM[iMode].weight *=m_fOneMinAlpha;
            }
        }

        //init
        memcpy(pGauss->mean,data,nD*sizeof(float));
        pGauss->variance=m_fVarInit;

        //sort
        //find the new place for it
        for (int iLocal = nModes-1;iLocal>0;iLocal--)
        {
            //check one up
            if (m_fAlphaT < (pGMM[iLocal-1].weight))
            {
                break;
            }
            else
            {
                //swap one up
                CvPBGMMGaussian temp = pGMM[iLocal];
                pGMM[iLocal] = pGMM[iLocal-1];
                pGMM[iLocal-1] = temp;
            }
        }
    }

    //set the number of modes
    *pModesUsed=nModes;

    return bBackground;
}

// a bit more efficient implementation for common case of 3 channel (rgb) images
CV_INLINE int _icvUpdateGMM_C3(float r,float g, float b,
                               unsigned char* pModesUsed,
                               CvPBGMMGaussian* pGMM,
                               int m_nM,
                               float m_fAlphaT,
                               float m_fTb,
                               float m_fTB,
                               float m_fTg,
                               float m_fVarInit,
                               float m_fVarMax,
                               float m_fVarMin,
                               float m_fPrune)
{
    //calculate distances to the modes (+ sort)
    //here we need to go in descending order!!!
    bool bBackground=0;//return value -> true - the pixel classified as background

    //internal:
    bool bFitsPDF=0;//if it remains zero a new GMM mode will be added
    float m_fOneMinAlpha=1-m_fAlphaT;
    unsigned char nModes=*pModesUsed;//current number of modes in GMM
    float totalWeight=0.0f;

    //////
    //go through all modes
    int iMode=0;
    CvPBGMMGaussian* pGauss=pGMM;
    for (;iMode<nModes;iMode++,pGauss++)
    {
        float weight = pGauss->weight;//need only weight if fit is found
        weight=m_fOneMinAlpha*weight+m_fPrune;

        ////
        //fit not found yet
        if (!bFitsPDF)
        {
            //check if it belongs to some of the remaining modes
            float var=pGauss->variance;

            //calculate difference and distance
            float muR = pGauss->mean[0];
            float muG = pGauss->mean[1];
            float muB = pGauss->mean[2];

            float dR=muR - r;
            float dG=muG - g;
            float dB=muB - b;

            float dist2=(dR*dR+dG*dG+dB*dB);

            //background? - m_fTb - usually larger than m_fTg
            if ((totalWeight<m_fTB)&&(dist2<m_fTb*var))
                bBackground=1;

            //check fit
            if (dist2<m_fTg*var)
            {
                /////
                //belongs to the mode - bFitsPDF becomes 1
                bFitsPDF=1;

                //update distribution

                //update weight
                weight+=m_fAlphaT;

                float k = m_fAlphaT/weight;

                //update mean
                pGauss->mean[0] = muR - k*(dR);
                pGauss->mean[1] = muG - k*(dG);
                pGauss->mean[2] = muB - k*(dB);

                //update variance
                float varnew = var + k*(dist2-var);
                //limit the variance
                pGauss->variance = MIN(m_fVarMax,MAX(varnew,m_fVarMin));

                //sort
                //all other weights are at the same place and
                //only the matched (iModes) is higher -> just find the new place for it
                for (int iLocal = iMode;iLocal>0;iLocal--)
                {
                    //check one up
                    if (weight < (pGMM[iLocal-1].weight))
                    {
                        break;
                    }
                    else
                    {
                        //swap one up
                        CvPBGMMGaussian temp = pGMM[iLocal];
                        pGMM[iLocal] = pGMM[iLocal-1];
                        pGMM[iLocal-1] = temp;
                        pGauss--;
                    }
                }
                //belongs to the mode - bFitsPDF becomes 1
                /////
            }

        }//!bFitsPDF)

        //check prunning
        if (weight<-m_fPrune)
        {
            weight=0.0;
            nModes--;
        }

        pGauss->weight=weight;
        totalWeight+=weight;
    }
    //go through all modes
    //////

    //renormalize weights
    for (iMode = 0; iMode < nModes; iMode++)
    {
        pGMM[iMode].weight = pGMM[iMode].weight/totalWeight;
    }

    //make new mode if needed and exit
    if (!bFitsPDF)
    {
        if (nModes==m_nM)
        {
            //replace the weakest
            pGauss=pGMM+m_nM-1;
        }
        else
        {
            //add a new one
            pGauss=pGMM+nModes;
            nModes++;
        }

        if (nModes==1)
        {
            pGauss->weight=1;
        }
        else
        {
            pGauss->weight=m_fAlphaT;

            //renormalize all weights
            for (iMode = 0; iMode < nModes-1; iMode++)
            {
                pGMM[iMode].weight *=m_fOneMinAlpha;
            }
        }

        //init
        pGauss->mean[0]=r;
        pGauss->mean[1]=g;
        pGauss->mean[2]=b;

        pGauss->variance=m_fVarInit;

        //sort
        //find the new place for it
        for (int iLocal = nModes-1;iLocal>0;iLocal--)
        {
            //check one up
            if (m_fAlphaT < (pGMM[iLocal-1].weight))
            {
                break;
            }
            else
            {
                //swap one up
                CvPBGMMGaussian temp = pGMM[iLocal];
                pGMM[iLocal] = pGMM[iLocal-1];
                pGMM[iLocal-1] = temp;
            }
        }
    }

    //set the number of modes
    *pModesUsed=nModes;

    return bBackground;
}

//the main function to update the background model
static void icvUpdatePixelBackgroundGMM2( const CvArr* srcarr, CvArr* dstarr ,
                                  CvPBGMMGaussian *pGMM,
                                  unsigned char *pUsedModes,
                                  //CvGaussBGStatModel2Params* pGMMPar,
                                  int nM,
                                  float fTb,
                                  float fTB,
                                  float fTg,
                                  float fVarInit,
                                  float fVarMax,
                                  float fVarMin,
                                  float fCT,
                                  float fTau,
                                  bool bShadowDetection,
                                  unsigned char  nShadowDetection,
                                  float alpha)
{
    CvMat sstub, *src = cvGetMat(srcarr, &sstub);
    CvMat dstub, *dst = cvGetMat(dstarr, &dstub);
    CvSize size = cvGetMatSize(src);
    int nD=CV_MAT_CN(src->type);

    //reshape if possible
    if( CV_IS_MAT_CONT(src->type & dst->type) )
    {
        size.width *= size.height;
        size.height = 1;
    }

    int x, y;
    float data[CV_BGFG_MOG2_NDMAX];
    float prune=-alpha*fCT;

    //general nD

    if (nD!=3)
    {
        switch (CV_MAT_DEPTH(src->type))
        {
            case CV_8U:
                for( y = 0; y < size.height; y++ )
                {
                    uchar* sptr = src->data.ptr + src->step*y;
                    uchar* pDataOutput = dst->data.ptr + dst->step*y;
                    for( x = 0; x < size.width; x++,
                        pGMM+=nM,pUsedModes++,pDataOutput++,sptr+=nD)
                    {
                        //convert data
                        for (int iD=0;iD<nD;iD++) data[iD]=float(sptr[iD]);
                        //update GMM model
                        int result = _icvUpdateGMM(data,nD,pUsedModes,pGMM,nM,alpha, fTb, fTB, fTg, fVarInit, fVarMax, fVarMin,prune);
                        //detect shadows in the foreground
                        if (bShadowDetection)
                            if (result==0) result= _icvRemoveShadowGMM(data,nD,(*pUsedModes),pGMM,fTb,fTB,fTau);
                        //generate output
                        (* pDataOutput)= (result==1) ? 0 : (result==2) ? (nShadowDetection) : 255;
                    }
                }
                break;
            case CV_16S:
                for( y = 0; y < size.height; y++ )
                {
                    short* sptr = src->data.s + src->step*y;
                    uchar* pDataOutput = dst->data.ptr + dst->step*y;
                    for( x = 0; x < size.width; x++,
                        pGMM+=nM,pUsedModes++,pDataOutput++,sptr+=nD)
                    {
                        //convert data
                        for (int iD=0;iD<nD;iD++) data[iD]=float(sptr[iD]);
                        //update GMM model
                        int result = _icvUpdateGMM(data,nD,pUsedModes,pGMM,nM,alpha, fTb, fTB, fTg, fVarInit, fVarMax, fVarMin,prune);
                        //detect shadows in the foreground
                        if (bShadowDetection)
                            if (result==0) result= _icvRemoveShadowGMM(data,nD,(*pUsedModes),pGMM,fTb,fTB,fTau);
                        //generate output
                        (* pDataOutput)= (result==1) ? 0 : (result==2) ? (nShadowDetection) : 255;
                    }
                }
                break;
            case CV_16U:
                for( y = 0; y < size.height; y++ )
                {
                    unsigned short* sptr = (unsigned short*) (src->data.s + src->step*y);
                    uchar* pDataOutput = dst->data.ptr + dst->step*y;
                    for( x = 0; x < size.width; x++,
                        pGMM+=nM,pUsedModes++,pDataOutput++,sptr+=nD)
                    {
                        //convert data
                        for (int iD=0;iD<nD;iD++) data[iD]=float(sptr[iD]);
                        //update GMM model
                        int result = _icvUpdateGMM(data,nD,pUsedModes,pGMM,nM,alpha, fTb, fTB, fTg, fVarInit, fVarMax, fVarMin,prune);
                        //detect shadows in the foreground
                        if (bShadowDetection)
                            if (result==0) result= _icvRemoveShadowGMM(data,nD,(*pUsedModes),pGMM,fTb,fTB,fTau);
                        //generate output
                        (* pDataOutput)= (result==1) ? 0 : (result==2) ? (nShadowDetection) : 255;
                    }
                }
                break;
            case CV_32S:
                for( y = 0; y < size.height; y++ )
                {
                    int* sptr = src->data.i + src->step*y;
                    uchar* pDataOutput = dst->data.ptr + dst->step*y;
                    for( x = 0; x < size.width; x++,
                        pGMM+=nM,pUsedModes++,pDataOutput++,sptr+=nD)
                    {
                        //convert data
                        for (int iD=0;iD<nD;iD++) data[iD]=float(sptr[iD]);
                        //update GMM model
                        int result = _icvUpdateGMM(data,nD,pUsedModes,pGMM,nM,alpha, fTb, fTB, fTg, fVarInit, fVarMax, fVarMin,prune);
                        //detect shadows in the foreground
                        if (bShadowDetection)
                            if (result==0) result= _icvRemoveShadowGMM(data,nD,(*pUsedModes),pGMM,fTb,fTB,fTau);
                        //generate output
                        (* pDataOutput)= (result==1) ? 0 : (result==2) ? (nShadowDetection) : 255;
                    }
                }
                break;
            case CV_32F:
                for( y = 0; y < size.height; y++ )
                {
                    float* sptr = src->data.fl + src->step*y;
                    uchar* pDataOutput = dst->data.ptr + dst->step*y;
                    for( x = 0; x < size.width; x++,
                        pGMM+=nM,pUsedModes++,pDataOutput++,sptr+=nD)
                    {
                        //update GMM model
                        int result = _icvUpdateGMM(sptr,nD,pUsedModes,pGMM,nM,alpha, fTb, fTB, fTg, fVarInit, fVarMax, fVarMin,prune);
                        //detect shadows in the foreground
                        if (bShadowDetection)
                            if (result==0) result= _icvRemoveShadowGMM(data,nD,(*pUsedModes),pGMM,fTb,fTB,fTau);
                        //generate output
                        (* pDataOutput)= (result==1) ? 0 : (result==2) ? (nShadowDetection) : 255;
                    }
                }
                break;
            case CV_64F:
                for( y = 0; y < size.height; y++ )
                {
                    double* sptr = src->data.db + src->step*y;
                    uchar* pDataOutput = dst->data.ptr + dst->step*y;
                    for( x = 0; x < size.width; x++,
                        pGMM+=nM,pUsedModes++,pDataOutput++,sptr+=nD)
                    {
                        //convert data
                        for (int iD=0;iD<nD;iD++) data[iD]=float(sptr[iD]);
                        //update GMM model
                        int result = _icvUpdateGMM(data,nD,pUsedModes,pGMM,nM,alpha, fTb, fTB, fTg, fVarInit, fVarMax, fVarMin,prune);
                        //detect shadows in the foreground
                        if (bShadowDetection)
                            if (result==0) result= _icvRemoveShadowGMM(data,nD,(*pUsedModes),pGMM,fTb,fTB,fTau);
                        //generate output
                        (* pDataOutput)= (result==1) ? 0 : (result==2) ? (nShadowDetection) : 255;
                    }
                }
                break;
        }
    }else ///if (nD==3) - a bit faster
    {
        switch (CV_MAT_DEPTH(src->type))
        {
            case CV_8U:
                for( y = 0; y < size.height; y++ )
                {
                    uchar* sptr = src->data.ptr + src->step*y;
                    uchar* pDataOutput = dst->data.ptr + dst->step*y;
                    for( x = 0; x < size.width; x++,
                        pGMM+=nM,pUsedModes++,pDataOutput++,sptr+=nD)
                    {
                        //convert data
                        data[0]=float(sptr[0]),data[1]=float(sptr[1]),data[2]=float(sptr[2]);
                        //update GMM model
                        int result = _icvUpdateGMM_C3(data[0],data[1],data[2],pUsedModes,pGMM,nM,alpha, fTb, fTB, fTg, fVarInit, fVarMax, fVarMin,prune);
                        //detect shadows in the foreground
                        if (bShadowDetection)
                            if (result==0) result= _icvRemoveShadowGMM(data,nD,(*pUsedModes),pGMM,fTb,fTB,fTau);
                        //generate output
                        (* pDataOutput)= (result==1) ? 0 : (result==2) ? (nShadowDetection) : 255;
                    }
                }
                break;
            case CV_16S:
                for( y = 0; y < size.height; y++ )
                {
                    short* sptr = src->data.s + src->step*y;
                    uchar* pDataOutput = dst->data.ptr + dst->step*y;
                    for( x = 0; x < size.width; x++,
                        pGMM+=nM,pUsedModes++,pDataOutput++,sptr+=nD)
                    {
                        //convert data
                        data[0]=float(sptr[0]),data[1]=float(sptr[1]),data[2]=float(sptr[2]);
                        //update GMM model
                        int result = _icvUpdateGMM_C3(data[0],data[1],data[2],pUsedModes,pGMM,nM,alpha, fTb, fTB, fTg, fVarInit, fVarMax, fVarMin,prune);
                        //detect shadows in the foreground
                        if (bShadowDetection)
                            if (result==0) result= _icvRemoveShadowGMM(data,nD,(*pUsedModes),pGMM,fTb,fTB,fTau);
                        //generate output
                        (* pDataOutput)= (result==1) ? 0 : (result==2) ? (nShadowDetection) : 255;
                    }
                }
                break;
            case CV_16U:
                for( y = 0; y < size.height; y++ )
                {
                    unsigned short* sptr = (unsigned short*) src->data.s + src->step*y;
                    uchar* pDataOutput = dst->data.ptr + dst->step*y;
                    for( x = 0; x < size.width; x++,
                        pGMM+=nM,pUsedModes++,pDataOutput++,sptr+=nD)
                    {
                        //convert data
                        data[0]=float(sptr[0]),data[1]=float(sptr[1]),data[2]=float(sptr[2]);
                        //update GMM model
                        int result = _icvUpdateGMM_C3(data[0],data[1],data[2],pUsedModes,pGMM,nM,alpha, fTb, fTB, fTg, fVarInit, fVarMax, fVarMin,prune);
                        //detect shadows in the foreground
                        if (bShadowDetection)
                            if (result==0) result= _icvRemoveShadowGMM(data,nD,(*pUsedModes),pGMM,fTb,fTB,fTau);
                        //generate output
                        (* pDataOutput)= (result==1) ? 0 : (result==2) ? (nShadowDetection) : 255;
                    }
                }
                break;
            case CV_32S:
                for( y = 0; y < size.height; y++ )
                {
                    int* sptr = src->data.i + src->step*y;
                    uchar* pDataOutput = dst->data.ptr + dst->step*y;
                    for( x = 0; x < size.width; x++,
                        pGMM+=nM,pUsedModes++,pDataOutput++,sptr+=nD)
                    {
                        //convert data
                        data[0]=float(sptr[0]),data[1]=float(sptr[1]),data[2]=float(sptr[2]);
                        //update GMM model
                        int result = _icvUpdateGMM_C3(data[0],data[1],data[2],pUsedModes,pGMM,nM,alpha, fTb, fTB, fTg, fVarInit, fVarMax, fVarMin,prune);
                        //detect shadows in the foreground
                        if (bShadowDetection)
                            if (result==0) result= _icvRemoveShadowGMM(data,nD,(*pUsedModes),pGMM,fTb,fTB,fTau);
                        //generate output
                        (* pDataOutput)= (result==1) ? 0 : (result==2) ? (nShadowDetection) : 255;
                    }
                }
                break;
            case CV_32F:
                for( y = 0; y < size.height; y++ )
                {
                    float* sptr = src->data.fl + src->step*y;
                    uchar* pDataOutput = dst->data.ptr + dst->step*y;
                    for( x = 0; x < size.width; x++,
                        pGMM+=nM,pUsedModes++,pDataOutput++,sptr+=nD)
                    {
                        //update GMM model
                        int result = _icvUpdateGMM_C3(sptr[0],sptr[1],sptr[2],pUsedModes,pGMM,nM,alpha, fTb, fTB, fTg, fVarInit, fVarMax, fVarMin,prune);
                        //detect shadows in the foreground
                        if (bShadowDetection)
                            if (result==0) result= _icvRemoveShadowGMM(data,nD,(*pUsedModes),pGMM,fTb,fTB,fTau);
                        //generate output
                        (* pDataOutput)= (result==1) ? 0 : (result==2) ? (nShadowDetection) : 255;
                    }
                }
                break;
            case CV_64F:
                for( y = 0; y < size.height; y++ )
                {
                    double* sptr = src->data.db + src->step*y;
                    uchar* pDataOutput = dst->data.ptr + dst->step*y;
                    for( x = 0; x < size.width; x++,
                        pGMM+=nM,pUsedModes++,pDataOutput++,sptr+=nD)
                    {
                        //convert data
                        data[0]=float(sptr[0]),data[1]=float(sptr[1]),data[2]=float(sptr[2]);
                        //update GMM model
                        int result = _icvUpdateGMM_C3(data[0],data[1],data[2],pUsedModes,pGMM,nM,alpha, fTb, fTB, fTg, fVarInit, fVarMax, fVarMin,prune);
                        //detect shadows in the foreground
                        if (bShadowDetection)
                            if (result==0) result= _icvRemoveShadowGMM(data,nD,(*pUsedModes),pGMM,fTb,fTB,fTau);
                        //generate output
                        (* pDataOutput)= (result==1) ? 0 : (result==2) ? (nShadowDetection) : 255;
                    }
                }
                break;
        }
    }//a bit faster for nD=3;
}


//only foreground image is updated
//no filtering included
typedef struct CvGaussBGModel2
{
    CV_BG_STAT_MODEL_FIELDS();
    CvGaussBGStatModel2Params params;
    CvGaussBGStatModel2Data   data;
    int                       countFrames;
} CvGaussBGModel2;

CVAPI(CvBGStatModel*) cvCreateGaussianBGModel2( IplImage* first_frame,
                                               CvGaussBGStatModel2Params* params CV_DEFAULT(NULL) );

//////////////////////////////////////////////
//implementation as part of the CvBGStatModel
static void CV_CDECL icvReleaseGaussianBGModel2( CvGaussBGModel2** bg_model );
static int CV_CDECL icvUpdateGaussianBGModel2( IplImage* curr_frame, CvGaussBGModel2*  bg_model );


CV_IMPL CvBGStatModel*
cvCreateGaussianBGModel2( IplImage* first_frame, CvGaussBGStatModel2Params* parameters )
{
    CvGaussBGModel2* bg_model = 0;
    int w,h;

    CV_FUNCNAME( "cvCreateGaussianBGModel2" );

    __BEGIN__;

    CvGaussBGStatModel2Params params;

    if( !CV_IS_IMAGE(first_frame) )
        CV_ERROR( CV_StsBadArg, "Invalid or NULL first_frame parameter" );

    if( first_frame->nChannels>CV_BGFG_MOG2_NDMAX )
        CV_ERROR( CV_StsBadArg, "Maxumum number of channels in the image is excedded (change CV_BGFG_MOG2_MAXBANDS constant)!" );


    CV_CALL( bg_model = (CvGaussBGModel2*)cvAlloc( sizeof(*bg_model) ));
    memset( bg_model, 0, sizeof(*bg_model) );
    bg_model->type    = CV_BG_MODEL_MOG2;
    bg_model->release = (CvReleaseBGStatModel) icvReleaseGaussianBGModel2;
    bg_model->update  = (CvUpdateBGStatModel)  icvUpdateGaussianBGModel2;

    //init parameters
    if( parameters == NULL )
    {
        memset(&params, 0, sizeof(params));

        // These constants are defined in cvaux/include/cvaux.h
        params.bShadowDetection = 1;
        params.bPostFiltering=0;
        params.minArea=CV_BGFG_MOG2_MINAREA;

        //set parameters
        // K - max number of Gaussians per pixel
        params.nM = CV_BGFG_MOG2_NGAUSSIANS;//4;
        // Tb - the threshold - n var
        //pGMM->fTb = 4*4;
        params.fTb = CV_BGFG_MOG2_STD_THRESHOLD*CV_BGFG_MOG2_STD_THRESHOLD;
        // Tbf - the threshold
        //pGMM->fTB = 0.9f;//1-cf from the paper
        params.fTB = CV_BGFG_MOG2_BACKGROUND_THRESHOLD;
        // Tgenerate - the threshold
        params.fTg = CV_BGFG_MOG2_STD_THRESHOLD_GENERATE*CV_BGFG_MOG2_STD_THRESHOLD_GENERATE;//update the mode or generate new
        //pGMM->fSigma= 11.0f;//sigma for the new mode
        params.fVarInit = CV_BGFG_MOG2_VAR_INIT;
        params.fVarMax = CV_BGFG_MOG2_VAR_MAX;
        params.fVarMin = CV_BGFG_MOG2_VAR_MIN;
        // alpha - the learning factor
        params.fAlphaT = 1.0f/CV_BGFG_MOG2_WINDOW_SIZE;//0.003f;
        // complexity reduction prior constant
        params.fCT = CV_BGFG_MOG2_CT;//0.05f;

        //shadow
        // Shadow detection
        params.nShadowDetection = (unsigned char)CV_BGFG_MOG2_SHADOW_VALUE;//value 0 to turn off
        params.fTau = CV_BGFG_MOG2_SHADOW_TAU;//0.5f;// Tau - shadow threshold
    }
    else
    {
        params = *parameters;
    }

    bg_model->params = params;

    //image data
    w = first_frame->width;
    h = first_frame->height;

    bg_model->params.nWidth = w;
    bg_model->params.nHeight = h;

    bg_model->params.nND = first_frame->nChannels;


    //allocate GMM data

    //GMM for each pixel
    bg_model->data.rGMM = (CvPBGMMGaussian*) malloc(w*h * params.nM * sizeof(CvPBGMMGaussian));
    //used modes per pixel
    bg_model->data.rnUsedModes = (unsigned char* ) malloc(w*h);
    memset(bg_model->data.rnUsedModes,0,w*h);//no modes used

    //prepare storages
    CV_CALL( bg_model->background = cvCreateImage(cvSize(w,h), IPL_DEPTH_8U, first_frame->nChannels));
    CV_CALL( bg_model->foreground = cvCreateImage(cvSize(w,h), IPL_DEPTH_8U, 1));

    //for eventual filtering
    CV_CALL( bg_model->storage = cvCreateMemStorage());

    bg_model->countFrames = 0;

    __END__;

    if( cvGetErrStatus() < 0 )
    {
        CvBGStatModel* base_ptr = (CvBGStatModel*)bg_model;

        if( bg_model && bg_model->release )
            bg_model->release( &base_ptr );
        else
            cvFree( &bg_model );
        bg_model = 0;
    }

    return (CvBGStatModel*)bg_model;
}


static void CV_CDECL
icvReleaseGaussianBGModel2( CvGaussBGModel2** _bg_model )
{
    CV_FUNCNAME( "icvReleaseGaussianBGModel2" );

    __BEGIN__;

    if( !_bg_model )
        CV_ERROR( CV_StsNullPtr, "" );

    if( *_bg_model )
    {
        CvGaussBGModel2* bg_model = *_bg_model;

        free (bg_model->data.rGMM);
        free (bg_model->data.rnUsedModes);

        cvReleaseImage( &bg_model->background );
        cvReleaseImage( &bg_model->foreground );
        cvReleaseMemStorage(&bg_model->storage);
        memset( bg_model, 0, sizeof(*bg_model) );
        cvFree( _bg_model );
    }

    __END__;
}


static int CV_CDECL
icvUpdateGaussianBGModel2( IplImage* curr_frame, CvGaussBGModel2*  bg_model )
{
    //checks
    if ((curr_frame->height!=bg_model->params.nHeight)||(curr_frame->width!=bg_model->params.nWidth)||(curr_frame->nChannels!=bg_model->params.nND))
        CV_Error( CV_StsBadSize, "the image not the same size as the reserved GMM background model");

    float alpha=bg_model->params.fAlphaT;
    bg_model->countFrames++;

    //faster initial updates - increase value of alpha
    if (bg_model->params.bInit){
        float alphaInit=(1.0f/(2*bg_model->countFrames+1));
        if (alphaInit>alpha)
        {
            alpha = alphaInit;
        }
        else
        {
            bg_model->params.bInit = 0;
        }
    }

    //update background
    //icvUpdatePixelBackgroundGMM2( curr_frame, bg_model->foreground, bg_model->data.rGMM,bg_model->data.rnUsedModes,&(bg_model->params),alpha);
    icvUpdatePixelBackgroundGMM2( curr_frame, bg_model->foreground, bg_model->data.rGMM,bg_model->data.rnUsedModes,
                                 bg_model->params.nM,
                                 bg_model->params.fTb,
                                 bg_model->params.fTB,
                                 bg_model->params.fTg,
                                 bg_model->params.fVarInit,
                                 bg_model->params.fVarMax,
                                 bg_model->params.fVarMin,
                                 bg_model->params.fCT,
                                 bg_model->params.fTau,
                                 bg_model->params.bShadowDetection,
                                 bg_model->params.nShadowDetection,
                                 alpha);

    //foreground filtering
    if (bg_model->params.bPostFiltering==1)
    {
        int region_count = 0;
        CvSeq *first_seq = NULL, *prev_seq = NULL, *seq = NULL;


        //filter small regions
        cvClearMemStorage(bg_model->storage);

        cvMorphologyEx( bg_model->foreground, bg_model->foreground, 0, 0, CV_MOP_OPEN, 1 );
        cvMorphologyEx( bg_model->foreground, bg_model->foreground, 0, 0, CV_MOP_CLOSE, 1 );

        cvFindContours( bg_model->foreground, bg_model->storage, &first_seq, sizeof(CvContour), CV_RETR_LIST );
        for( seq = first_seq; seq; seq = seq->h_next )
        {
            CvContour* cnt = (CvContour*)seq;
            if( cnt->rect.width * cnt->rect.height < bg_model->params.minArea )
            {
                //delete small contour
                prev_seq = seq->h_prev;
                if( prev_seq )
                {
                    prev_seq->h_next = seq->h_next;
                    if( seq->h_next ) seq->h_next->h_prev = prev_seq;
                }
                else
                {
                    first_seq = seq->h_next;
                    if( seq->h_next ) seq->h_next->h_prev = NULL;
                }
            }
            else
            {
                region_count++;
            }
        }
        bg_model->foreground_regions = first_seq;
        cvZero(bg_model->foreground);
        cvDrawContours(bg_model->foreground, first_seq, CV_RGB(0, 0, 255), CV_RGB(0, 0, 255), 10, -1);

        return region_count;
    }

    return 1;
}

/* End of file. */