opencv/modules/video/src/bgfg_gaussmix2.cpp

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/*//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
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; 
}



//////////////////////////////////////////////
//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 )
      {                        
		/* 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;
}


namespace cv
{

static const int defaultHistory2 = CV_BGFG_MOG2_WINDOW_SIZE;
static const float defaultVarThreshold2 = CV_BGFG_MOG2_STD_THRESHOLD*CV_BGFG_MOG2_STD_THRESHOLD;
static const int defaultNMixtures2 = CV_BGFG_MOG2_NGAUSSIANS;
static const float defaultBackgroundRatio2 = CV_BGFG_MOG2_BACKGROUND_THRESHOLD;
static const float defaultVarThresholdGen2 = CV_BGFG_MOG2_STD_THRESHOLD_GENERATE*CV_BGFG_MOG2_STD_THRESHOLD_GENERATE;
static const float defaultVarInit2 = CV_BGFG_MOG2_VAR_INIT;
static const float defaultVarMax2 = CV_BGFG_MOG2_VAR_MAX;
static const float defaultVarMin2 = CV_BGFG_MOG2_VAR_MIN;
static const float defaultfCT2 = CV_BGFG_MOG2_CT;
static const unsigned char defaultnShadowDetection2 = (unsigned char)CV_BGFG_MOG2_SHADOW_VALUE;
static const float defaultfTau = CV_BGFG_MOG2_SHADOW_TAU;


BackgroundSubtractorMOG2::BackgroundSubtractorMOG2()
{
    frameSize = Size(0,0);
    frameType = 0;
    
    nframes = 0;
    history = defaultHistory2;
	varThreshold = defaultVarThreshold2;
	bShadowDetection = 1;

	nmixtures = defaultNMixtures2;   
	backgroundRatio = defaultBackgroundRatio2;
	fVarInit = defaultVarInit2;
	fVarMax  = defaultVarMax2;
	fVarMin = defaultVarMin2;

	varThresholdGen = defaultVarThresholdGen2;
	fCT = defaultfCT2;
	nShadowDetection =  defaultnShadowDetection2;
	fTau = defaultfTau;
}
    
BackgroundSubtractorMOG2::BackgroundSubtractorMOG2(int _history,  float _varThreshold, bool _bShadowDetection)
{
    frameSize = Size(0,0);
    frameType = 0;
    
    nframes = 0;
    history = _history > 0 ? _history : defaultHistory2;
	varThreshold = (_varThreshold>0)? _varThreshold : defaultVarThreshold2;
	bShadowDetection = _bShadowDetection;

	nmixtures = defaultNMixtures2;   
	backgroundRatio = defaultBackgroundRatio2;
	fVarInit = defaultVarInit2;
	fVarMax  = defaultVarMax2;
	fVarMin = defaultVarMin2;

	varThresholdGen = defaultVarThresholdGen2;
	fCT = defaultfCT2;
	nShadowDetection =  defaultnShadowDetection2;
	fTau = defaultfTau;
}
    
BackgroundSubtractorMOG2::~BackgroundSubtractorMOG2()
{
}


void BackgroundSubtractorMOG2::initialize(Size _frameSize, int _frameType)
{
    frameSize = _frameSize;
    frameType = _frameType;
    nframes = 0;
    
    int nchannels = CV_MAT_CN(frameType);
	CV_Assert( nchannels <= CV_BGFG_MOG2_NDMAX );
    
    // for each gaussian mixture of each pixel bg model we store ...
    // the mixture weight (w),
    // the mean (nchannels values) and
    // the covariance
    bgmodel.create( 1, frameSize.height*frameSize.width*nmixtures*(2 + CV_BGFG_MOG2_NDMAX), CV_32F );
	//make the array for keeping track of the used modes per pixel - all zeros at start
	bgmodelUsedModes.create(frameSize,CV_8U);
    bgmodelUsedModes = Scalar::all(0);
}

void BackgroundSubtractorMOG2::operator()(InputArray _image, OutputArray _fgmask, double learningRate)
{
    Mat image = _image.getMat();
    bool needToInitialize = nframes == 0 || learningRate >= 1 || image.size() != frameSize || image.type() != frameType;
    
    if( needToInitialize )
        initialize(image.size(), image.type());
    
    _fgmask.create( image.size(), CV_8U );
    Mat fgmask = _fgmask.getMat();
    
    ++nframes;
    learningRate = learningRate >= 0 && nframes > 1 ? learningRate : 1./min( 2*nframes, history );
    CV_Assert(learningRate >= 0);
    CvMat _cimage = image, _cfgmask = fgmask;
    
	if (learningRate > 0) 
		icvUpdatePixelBackgroundGMM2( &_cimage, &_cfgmask, 
		(CvPBGMMGaussian*) bgmodel.data,
		bgmodelUsedModes.data,
		nmixtures,//nM
		varThreshold,//fTb
		backgroundRatio,//fTB
		varThresholdGen,//fTg,
		fVarInit,
		fVarMax,
		fVarMin,
		fCT,
		fTau,
		bShadowDetection,
		nShadowDetection,
		float(learningRate));
}

void BackgroundSubtractorMOG2::getBackgroundImage(OutputArray backgroundImage) const
{
    CV_Assert(CV_BGFG_MOG2_NDMAX == 3);
    Mat meanBackground(frameSize, CV_8UC3, Scalar::all(0));

    int firstGaussianIdx = 0;
    CvPBGMMGaussian* pGMM = (CvPBGMMGaussian*)bgmodel.data;
    for(int row=0; row<meanBackground.rows; row++)
    {
        for(int col=0; col<meanBackground.cols; col++)
        {
            int nModes = static_cast<int>(bgmodelUsedModes.at<uchar>(row, col));
            double meanVal[CV_BGFG_MOG2_NDMAX] = {0.0, 0.0, 0.0};

            double totalWeight = 0.0;
            for(int gaussianIdx = firstGaussianIdx; gaussianIdx < firstGaussianIdx + nModes; gaussianIdx++)
            {
                CvPBGMMGaussian gaussian = pGMM[gaussianIdx];
                totalWeight += gaussian.weight;

                for(int chIdx = 0; chIdx < CV_BGFG_MOG2_NDMAX; chIdx++)
                {
                    meanVal[chIdx] += gaussian.weight * gaussian.mean[chIdx];
                }

                if(totalWeight > backgroundRatio)
                    break;
            }

            Vec3f val = Vec3f(meanVal[0], meanVal[1], meanVal[2]) * (1.0 / totalWeight);
            meanBackground.at<Vec3b>(row, col) = Vec3b(val);
            firstGaussianIdx += nmixtures;
        }
    }

    switch(CV_MAT_CN(frameType))
    {
        case 1:
        {
            vector<Mat> channels;
            split(meanBackground, channels);
            channels[0].copyTo(backgroundImage);
            break;
        }

        case 3:
        {
            meanBackground.copyTo(backgroundImage);
            break;
        }

        default:
            CV_Assert(false);
    }
}

}

/* End of file. */