实现运动目标检测（opencv3）（一）(2)

该函数的源码：

#include "precomp.hpp"
 
namespace cv
{
 
/*
 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)
*/
 
// default parameters of gaussian background detection algorithm
// 这部分的参数建议把《Improved adaptive Gausian mixture model for background subtraction》读一遍，大部分的就基本理解了
static const int defaultHistory2 = 500; // Learning rate; alpha = 1/defaultHistory2
static const float defaultVarThreshold2 = 4.0f*4.0f;
static const int defaultNMixtures2 = 5; // maximal number of Gaussians in mixture
static const float defaultBackgroundRatio2 = 0.9f; // threshold sum of weights for background test
static const float defaultVarThresholdGen2 = 3.0f*3.0f;
static const float defaultVarInit2 = 15.0f; // initial variance for new components
static const float defaultVarMax2 = 5*defaultVarInit2;
static const float defaultVarMin2 = 4.0f;
 
// additional parameters
static const float defaultfCT2 = 0.05f; // complexity reduction prior constant 0 - no reduction of number of components
static const unsigned char defaultnShadowDetection2 = (unsigned char)127; // value to use in the segmentation mask for shadows, set 0 not to do shadow detection
static const float defaultfTau = 0.5f; // Tau - shadow threshold, see the paper for explanation
 
// 注意这个结构体后面没有用到，不用管它
struct GaussBGStatModel2Params
{
    //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.
};
 
// 定义了高斯模型中有关权重和方差的结构体
struct GMM
{
    float weight;
    float variance;
};
 
// 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.
static CV_INLINE bool
detectShadowGMM(const float* data, int nchannels, int nmodes,
                const GMM* gmm, const float* mean,
                float Tb, float TB, float tau)
{
	// 输入的是像素，函数判断非背景的像素是前景还是阴影
    float tWeight = 0;
 
    // check all the components  marked as background:
    for( int mode = 0; mode < nmodes; mode++, mean += nchannels )
    {
        GMM g = gmm[mode];
 
        float numerator = 0.0f;
        float denominator = 0.0f;
        for( int c = 0; c < nchannels; c++ )
        {
            numerator   += data[c] * mean[c];
            denominator += mean[c] * mean[c];// 使用高斯分布中的均值计算得到近似的不受到前景影响的“背景”
        }
 
        // no division by zero allowed
        if( denominator == 0 )
            return false;
		
		// 大前提是该像素“颜色”相对于“背景”有所衰减
        // if tau < a < 1 then also check the color distortion
        if( numerator <= denominator && numerator >= tau*denominator )
        {
            float a = numerator / denominator;
            float dist2a = 0.0f;
 
            for( int c = 0; c < nchannels; c++ )
            {
                float dD= a*mean[c] - data[c];
                dist2a += dD*dD;
            }
			// 没看懂，感觉像是作者的经验公式
            if (dist2a < Tb*g.variance*a*a)
                return true;
        };
 
        tWeight += g.weight;
        if( tWeight > TB )
            return false;
    };
    return false;
}
 
//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
 
// 通过该结构体实现算法的并行计算，可以百度下parallel_for_大致了解下
struct MOG2Invoker : ParallelLoopBody
{
    MOG2Invoker(const Mat& _src, Mat& _dst,
                GMM* _gmm, float* _mean,
                uchar* _modesUsed,
                int _nmixtures, float _alphaT,
                float _Tb, float _TB, float _Tg,
                float _varInit, float _varMin, float _varMax,
                float _prune, float _tau, bool _detectShadows,
                uchar _shadowVal)
    {
        src = &_src;// 原图
        dst = &_dst;
        gmm0 = _gmm;
        mean0 = _mean;
        modesUsed0 = _modesUsed;
        nmixtures = _nmixtures;
        alphaT = _alphaT;
        Tb = _Tb;
        TB = _TB;
        Tg = _Tg;
        varInit = _varInit;
        varMin = MIN(_varMin, _varMax);
        varMax = MAX(_varMin, _varMax);
        prune = _prune;
        tau = _tau;
        detectShadows = _detectShadows;
        shadowVal = _shadowVal;
 
        cvtfunc = src->depth() != CV_32F ? getConvertFunc(src->depth(), CV_32F) : 0;
    }
 
    void operator()(const Range& range) const
    {
        int y0 = range.start, y1 = range.end;// 每个并行计算单元的输入是一行图像
        int ncols = src->cols, nchannels = src->channels();
        AutoBuffer<float> buf(src->cols*nchannels);
        float alpha1 = 1.f - alphaT;
        float dData[CV_CN_MAX];
 
        for( int y = y0; y < y1; y++ )
        {
            const float* data = buf;
            if( cvtfunc )
                cvtfunc( src->ptr(y), src->step, 0, 0, (uchar*)data, 0, Size(ncols*nchannels, 1), 0);// 转换为1XN的图像,N为原图的列数
            else
                data = src->ptr<float>(y);
 
            float* mean = mean0 + ncols*nmixtures*nchannels*y;
            GMM* gmm = gmm0 + ncols*nmixtures*y;
            uchar* modesUsed = modesUsed0 + ncols*y;
            uchar* mask = dst->ptr(y);
			// 遍历1XN图像的每个像素
            for( int x = 0; x < ncols; x++, data += nchannels, gmm += nmixtures, mean += nmixtures*nchannels )
            {
                //calculate distances to the modes (+ sort)
                //here we need to go in descending order!!!
                bool background = false;//return value -> true - the pixel classified as background
 
                //internal:
                bool fitsPDF = false;//if it remains zero a new GMM mode will be added
                int nmodes = modesUsed[x], nNewModes = nmodes;//current number of modes in GMM
                float totalWeight = 0.f;
 
                float* mean_m = mean;
				
                //////
                //go through all modes
				// 1.计算是否符合当前混合模型
                for( int mode = 0; mode < nmodes; mode++, mean_m += nchannels )
                {
                    float weight = alpha1*gmm[mode].weight + prune;//need only weight if fit is found
                    int swap_count = 0;
                    ////
                    //fit not found yet
                    if( !fitsPDF )
                    {
                        //check if it belongs to some of the remaining modes
                        float var = gmm[mode].variance;
 
                        //calculate difference and distance
                        float dist2;
 
                        if( nchannels == 3 )
                        {
                            dData[0] = mean_m[0] - data[0];
                            dData[1] = mean_m[1] - data[1];
                            dData[2] = mean_m[2] - data[2];
                            dist2 = dData[0]*dData[0] + dData[1]*dData[1] + dData[2]*dData[2];
                        }
                        else
                        {
                            dist2 = 0.f;
                            for( int c = 0; c < nchannels; c++ )
                            {
                                dData[c] = mean_m[c] - data[c];
                                dist2 += dData[c]*dData[c];
                            }
                        }
 
                        //background? - Tb - usually larger than Tg
                        if( totalWeight < TB && dist2 < Tb*var )
                            background = true;
 
                        //check fit
                        if( dist2 < Tg*var )
                        {
                            /////
                            //belongs to the mode
                            fitsPDF = true;
 
                            //update distribution
 
                            //update weight
                            weight += alphaT;
                            float k = alphaT/weight;
 
                            //update mean
                            for( int c = 0; c < nchannels; c++ )
                                mean_m[c] -= k*dData[c];
 
                            //update variance
                            float varnew = var + k*(dist2-var);
                            //limit the variance
                            varnew = MAX(varnew, varMin);
                            varnew = MIN(varnew, varMax);
                            gmm[mode].variance = varnew;
 
                            //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 i = mode; i > 0; i-- )
                            {
                                //check one up
                                if( weight < gmm[i-1].weight )
                                    break;
 
                                swap_count++;
                                //swap one up
                                std::swap(gmm[i], gmm[i-1]);
                                for( int c = 0; c < nchannels; c++ )
                                    std::swap(mean[i*nchannels + c], mean[(i-1)*nchannels + c]);
                            }
                            //belongs to the mode - bFitsPDF becomes 1
                            /////
                        }
                    }//!bFitsPDF)
 
                    //check prune
                    if( weight < -prune )// 保证下一次运算中模型的权值非负
                    {
                        weight = 0.0;
                        nmodes--;// 丢弃掉该模型
                    }
 
                    gmm[mode-swap_count].weight = weight;//update weight by the calculated value
                    totalWeight += weight;
                }
                //go through all modes
                //////
 
                //renormalize weights
				// 2.权重归一化
                totalWeight = 1.f/totalWeight;
                for( int mode = 0; mode < nmodes; mode++ )
                {
                    gmm[mode].weight *= totalWeight;
                }
 
                nmodes = nNewModes;
 
                //make new mode if needed and exit
				// 3.根据情况增加新的高斯分布
                if( !fitsPDF )
                {
                    // replace the weakest or add a new one
                    int mode = nmodes == nmixtures ? nmixtures-1 : nmodes++;
 
                    if (nmodes==1)
                        gmm[mode].weight = 1.f;
                    else
                    {
                        gmm[mode].weight = alphaT;
 
                        // renormalize all other weights
                        for( int i = 0; i < nmodes-1; i++ )
                            gmm[i].weight *= alpha1;
                    }
 
                    // init
                    for( int c = 0; c < nchannels; c++ )
                        mean[mode*nchannels + c] = data[c];
 
                    gmm[mode].variance = varInit;
 
                    //sort
                    //find the new place for it
                    for( int i = nmodes - 1; i > 0; i-- )
                    {
                        // check one up
                        if( alphaT < gmm[i-1].weight )
                            break;
 
                        // swap one up
                        std::swap(gmm[i], gmm[i-1]);
                        for( int c = 0; c < nchannels; c++ )
                            std::swap(mean[i*nchannels + c], mean[(i-1)*nchannels + c]);
                    }
                }
 
                //set the number of modes
                modesUsed[x] = uchar(nmodes);// 更新GMM中实际使用的模型个数
				// 4.如果不是背景，根据参数确定是否继续进行阴影判断
                mask[x] = background ? 0 :
                    detectShadows && detectShadowGMM(data, nchannels, nmodes, gmm, mean, Tb, TB, tau) ?
                    shadowVal : 255;
            }
        }
    }
 
    const Mat* src;
    Mat* dst;
    GMM* gmm0;
    float* mean0;
    uchar* modesUsed0;
 
    int nmixtures;
    float alphaT, Tb, TB, Tg;
    float varInit, varMin, varMax, prune, tau;
 
    bool detectShadows;
    uchar shadowVal;
 
    BinaryFunc cvtfunc;
};
 
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_CN_MAX );
 
    // 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 + nchannels), 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);
 
	// 并行计算，应该是分为了image.rows个计算单元，所以每个计算单元只计算每一行的“图像”
    parallel_for_(Range(0, image.rows),
                  MOG2Invoker(image, fgmask,
                              (GMM*)bgmodel.data,
                              (float*)(bgmodel.data + sizeof(GMM)*nmixtures*image.rows*image.cols),
                              bgmodelUsedModes.data, nmixtures, (float)learningRate,
                              (float)varThreshold,
                              backgroundRatio, varThresholdGen,
                              fVarInit, fVarMin, fVarMax, float(-learningRate*fCT), fTau,
                              bShadowDetection, nShadowDetection));
}
 
// 可以调用该函数得到视频中每一帧的不受前景物体存在影响的近似背景图像
void BackgroundSubtractorMOG2::getBackgroundImage(OutputArray backgroundImage) const
{
    int nchannels = CV_MAT_CN(frameType);
    CV_Assert(nchannels == 1 || nchannels == 3);
    Mat meanBackground(frameSize, CV_MAKETYPE(CV_8U, nchannels), Scalar::all(0));
    int firstGaussianIdx = 0;
    const GMM* gmm = (GMM*)bgmodel.data;
    const float* mean = reinterpret_cast<const float*>(gmm + frameSize.width*frameSize.height*nmixtures);
    std::vector<float> meanVal(nchannels, 0.f);
    for(int row=0; row<meanBackground.rows; row++)
    {
        for(int col=0; col<meanBackground.cols; col++)
        {
            int nmodes = bgmodelUsedModes.at<uchar>(row, col);
            float totalWeight = 0.f;
            for(int gaussianIdx = firstGaussianIdx; gaussianIdx < firstGaussianIdx + nmodes; gaussianIdx++)
            {
                GMM gaussian = gmm[gaussianIdx];
                size_t meanPosition = gaussianIdx*nchannels;
                for(int chn = 0; chn < nchannels; chn++)
                {
                    meanVal[chn] += gaussian.weight * mean[meanPosition + chn];// 核心代码，就是利用多个高斯分布的权值、均值的加权和作为背景像素值
                }
                totalWeight += gaussian.weight;
 
                if(totalWeight > backgroundRatio)
                    break;
            }
            float invWeight = 1.f/totalWeight;
            switch(nchannels)
            {
            case 1:
                meanBackground.at<uchar>(row, col) = (uchar)(meanVal[0] * invWeight);
                meanVal[0] = 0.f;
                break;
            case 3:
                Vec3f& meanVec = *reinterpret_cast<Vec3f*>(&meanVal[0]);
                meanBackground.at<Vec3b>(row, col) = Vec3b(meanVec * invWeight);
                meanVec = 0.f;
                break;
            }
            firstGaussianIdx += nmixtures;
        }
    }
    meanBackground.copyTo(backgroundImage);
}
 
}

经过实验可以看出，GMM是分离前景和背景，输出为前景二值掩码。 要经过一些形态学运算，找轮廓后会得到检测部分，即目标检测。结果如下图：

到现在目标检测算是初步完成了。

https://blog.csdn.net/angelasan/article/details/44917283。转载自：https://blog.csdn.net/javazejian/article/details/51932554。转载自：https://blog.csdn.net/a19881029/article/details/26348627。

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