我的OpenCV学习笔记（25）：c++版本的高斯混合模型的源代码完全注释

之前看到过C版本的，感觉写的很长，没有仔细看，但是C++版本的写的还是很不错的。我仔细看了一下，并对内容进行了仔细的注释，如果有人没有看懂，欢迎留言讨论。

先看一眼头文件，在background_segm.hpp中

class CV_EXPORTS_W BackgroundSubtractorMOG : public BackgroundSubtractor
{
public:
    //! the default constructor
    CV_WRAP BackgroundSubtractorMOG();
    //! the full constructor that takes the length of the history, the number of gaussian mixtures, the background ratio parameter and the noise strength
    CV_WRAP BackgroundSubtractorMOG(int history, int nmixtures, double backgroundRatio, double noiseSigma=0);
    //! the destructor
    virtual ~BackgroundSubtractorMOG();
    //! the update operator
    virtual void operator()(InputArray image, OutputArray fgmask, double learningRate=0);
    
    //! re-initiaization method
    virtual void initialize(Size frameSize, int frameType);
    
    virtual AlgorithmInfo* info() const;

protected:    
    Size frameSize;
    int frameType;
    Mat bgmodel;
    int nframes;
    int history;//利用历史帧数计算学习速率，不是主要参数
    int nmixtures;//高斯模型的个数
    double varThreshold;//方差门限
    double backgroundRatio;//背景门限
    double noiseSigma;//噪声方差
};	

再看一眼源文件，在bgfg_gaussmix.cpp中：

static const int defaultNMixtures = 5;//默认混合模型个数
static const int defaultHistory = 200;//默认历史帧数
static const double defaultBackgroundRatio = 0.7;//默认背景门限
static const double defaultVarThreshold = 2.5*2.5;//默认方差门限
static const double defaultNoiseSigma = 30*0.5;//默认噪声方差
static const double defaultInitialWeight = 0.05;//默认初始权值
 //不带参数的构造函数，使用默认值  
BackgroundSubtractorMOG::BackgroundSubtractorMOG()
{
    frameSize = Size(0,0);
    frameType = 0;
    
    nframes = 0;
    nmixtures = defaultNMixtures;
    history = defaultHistory;
    varThreshold = defaultVarThreshold;
    backgroundRatio = defaultBackgroundRatio;
    noiseSigma = defaultNoiseSigma;
}
//带参数的构造函数，使用参数传进来的值    
BackgroundSubtractorMOG::BackgroundSubtractorMOG(int _history, int _nmixtures,
                                                 double _backgroundRatio,
                                                 double _noiseSigma)
{
    frameSize = Size(0,0);
    frameType = 0;
    
    nframes = 0;
    nmixtures = min(_nmixtures > 0 ? _nmixtures : defaultNMixtures, 8);//不能超过8个，否则就用默认的
    history = _history > 0 ? _history : defaultHistory;//不能小于0，否则就用默认的
    varThreshold = defaultVarThreshold;//门限使用默认的
    backgroundRatio = min(_backgroundRatio > 0 ? _backgroundRatio : 0.95, 1.);//背景门限必须大于0，小于1，否则使用0.95
    noiseSigma = _noiseSigma <= 0 ? defaultNoiseSigma : _noiseSigma;//噪声门限大于0
}
    
BackgroundSubtractorMOG::~BackgroundSubtractorMOG()
{
}


void BackgroundSubtractorMOG::initialize(Size _frameSize, int _frameType)
{
    frameSize = _frameSize;
    frameType = _frameType;
    nframes = 0;
    
    int nchannels = CV_MAT_CN(frameType);
    CV_Assert( CV_MAT_DEPTH(frameType) == CV_8U );
    
    // for each gaussian mixture of each pixel bg model we store ...
    // the mixture sort key (w/sum_of_variances), the mixture weight (w),
    // the mean (nchannels values) and
    // the diagonal covariance matrix (another nchannels values)
    bgmodel.create( 1, frameSize.height*frameSize.width*nmixtures*(2 + 2*nchannels), CV_32F );//初始化一个1行*XX列的矩阵
	//XX是这样计算的：图像的行*列*混合模型的个数*（1（优先级） + 1（权值） + 2（均值 + 方差） * 通道数）
    bgmodel = Scalar::all(0);//清零
}

//设为模版，就是考虑到了彩色图像与灰度图像两种情况    
template<typename VT> struct MixData
{
    float sortKey;
    float weight;
    VT mean;
    VT var;
};

    
static void process8uC1( const Mat& image, Mat& fgmask, double learningRate,
                         Mat& bgmodel, int nmixtures, double backgroundRatio,
                         double varThreshold, double noiseSigma )
{
    int x, y, k, k1, rows = image.rows, cols = image.cols;
    float alpha = (float)learningRate, T = (float)backgroundRatio, vT = (float)varThreshold;//学习速率、背景门限、方差门限
    int K = nmixtures;//混合模型个数
    MixData<float>* mptr = (MixData<float>*)bgmodel.data;
    
    const float w0 = (float)defaultInitialWeight;//初始权值
    const float sk0 = (float)(w0/(defaultNoiseSigma*2));//初始优先级
    const float var0 = (float)(defaultNoiseSigma*defaultNoiseSigma*4);//初始方差
    const float minVar = (float)(noiseSigma*noiseSigma);//最小方差
    
    for( y = 0; y < rows; y++ )
    {
        const uchar* src = image.ptr<uchar>(y);
        uchar* dst = fgmask.ptr<uchar>(y);
        
        if( alpha > 0 )//如果学习速率为0，则退化为背景相减
        {
            for( x = 0; x < cols; x++, mptr += K )
            {
                float wsum = 0;
                float pix = src[x];//每个像素
                int kHit = -1, kForeground = -1;//是否属于模型，是否属于前景
                
                for( k = 0; k < K; k++ )//每个高斯模型
                {
                    float w = mptr[k].weight;//当前模型的权值
                    wsum += w;//权值累加
                    if( w < FLT_EPSILON )
                        break;
                    float mu = mptr[k].mean;//当前模型的均值
                    float var = mptr[k].var;//当前模型的方差
                    float diff = pix - mu;//当前像素与模型均值之差
                    float d2 = diff*diff;//平方
                    if( d2 < vT*var )//是否小于方门限，即是否属于该模型
                    {
                        wsum -= w;//如果匹配，则把它减去，因为之后会更新它
                        float dw = alpha*(1.f - w);
                        mptr[k].weight = w + dw;//增加权值
						//注意源文章中涉及概率的部分多进行了简化，将概率变为1
                        mptr[k].mean = mu + alpha*diff;//修正均值		
                        var = max(var + alpha*(d2 - var), minVar);//开始时方差清零0，所以这里使用噪声方差作为默认方差，否则使用上一次方差
                        mptr[k].var = var;//修正方差
                        mptr[k].sortKey = w/sqrt(var);//重新计算优先级，貌似这里不对，应该使用更新后的mptr[k].weight而不是w
                        
                        for( k1 = k-1; k1 >= 0; k1-- )//从匹配的第k个模型开始向前比较，如果更新后的单高斯模型优先级超过他前面的那个，则交换顺序
                        {
                            if( mptr[k1].sortKey >= mptr[k1+1].sortKey )//如果优先级没有发生改变，则停止比较
                                break;
                            std::swap( mptr[k1], mptr[k1+1] );//交换它们的顺序，始终保证优先级最大的在前面
                        }
                        
                        kHit = k1+1;//记录属于哪个模型
                        break;
                    }
                }
                
                if( kHit < 0 ) // no appropriate gaussian mixture found at all, remove the weakest mixture and create a new one
								//当前像素不属于任何一个模型
                {
					//初始化一个新模型
                    kHit = k = min(k, K-1);//有两种情况，当最开始的初始化时，k并不是等于K-1的
                    wsum += w0 - mptr[k].weight;//从权值总和中减去原来的那个模型，并加上默认权值
                    mptr[k].weight = w0;//初始化权值
                    mptr[k].mean = pix;//初始化均值
                    mptr[k].var = var0;	//初始化方差
                    mptr[k].sortKey = sk0;//初始化权值
                }
                else
                    for( ; k < K; k++ )
                        wsum += mptr[k].weight;//求出剩下的总权值
                
                float wscale = 1.f/wsum;//归一化
                wsum = 0;
                for( k = 0; k < K; k++ )
                {
                    wsum += mptr[k].weight *= wscale;
                    mptr[k].sortKey *= wscale;//计算归一化权值
                    if( wsum > T && kForeground < 0 )
                        kForeground = k+1;//第几个模型之后就判为前景了
                }
                
                dst[x] = (uchar)(-(kHit >= kForeground));//判决：(ucahr)(-true) = 255;(uchar)(-(false)) = 0;
            }
        }
        else//如果学习速率小于等于0，则没有背景更新过程，其他过程类似
        {
            for( x = 0; x < cols; x++, mptr += K )
            {
                float pix = src[x];
                int kHit = -1, kForeground = -1;
                
                for( k = 0; k < K; k++ )
                {
                    if( mptr[k].weight < FLT_EPSILON )
                        break;
                    float mu = mptr[k].mean;
                    float var = mptr[k].var;
                    float diff = pix - mu;
                    float d2 = diff*diff;
                    if( d2 < vT*var )
                    {
                        kHit = k;
                        break;
                    }
                }
                
                if( kHit >= 0 )
                {
                    float wsum = 0;
                    for( k = 0; k < K; k++ )
                    {
                        wsum += mptr[k].weight;
                        if( wsum > T )
                        {
                            kForeground = k+1;
                            break;
                        }
                    }
                }
                
                dst[x] = (uchar)(kHit < 0 || kHit >= kForeground ? 255 : 0);
            }
        }
    }
}

    
static void process8uC3( const Mat& image, Mat& fgmask, double learningRate,
                         Mat& bgmodel, int nmixtures, double backgroundRatio,
                         double varThreshold, double noiseSigma )
{
    int x, y, k, k1, rows = image.rows, cols = image.cols;
    float alpha = (float)learningRate, T = (float)backgroundRatio, vT = (float)varThreshold;
    int K = nmixtures;
    
    const float w0 = (float)defaultInitialWeight;
    const float sk0 = (float)(w0/(defaultNoiseSigma*2*sqrt(3.)));
    const float var0 = (float)(defaultNoiseSigma*defaultNoiseSigma*4);
    const float minVar = (float)(noiseSigma*noiseSigma);
    MixData<Vec3f>* mptr = (MixData<Vec3f>*)bgmodel.data;
    
    for( y = 0; y < rows; y++ )
    {
        const uchar* src = image.ptr<uchar>(y);
        uchar* dst = fgmask.ptr<uchar>(y);
        
        if( alpha > 0 )
        {
            for( x = 0; x < cols; x++, mptr += K )
            {
                float wsum = 0;
                Vec3f pix(src[x*3], src[x*3+1], src[x*3+2]);
                int kHit = -1, kForeground = -1;
                
                for( k = 0; k < K; k++ )
                {
                    float w = mptr[k].weight;
                    wsum += w;
                    if( w < FLT_EPSILON )
                        break;
                    Vec3f mu = mptr[k].mean;
                    Vec3f var = mptr[k].var;
                    Vec3f diff = pix - mu;
                    float d2 = diff.dot(diff);
                    if( d2 < vT*(var[0] + var[1] + var[2]) )
                    {
                        wsum -= w;
                        float dw = alpha*(1.f - w);
                        mptr[k].weight = w + dw;
                        mptr[k].mean = mu + alpha*diff;
                        var = Vec3f(max(var[0] + alpha*(diff[0]*diff[0] - var[0]), minVar),
                                    max(var[1] + alpha*(diff[1]*diff[1] - var[1]), minVar),
                                    max(var[2] + alpha*(diff[2]*diff[2] - var[2]), minVar));
                        mptr[k].var = var;
                        mptr[k].sortKey = w/sqrt(var[0] + var[1] + var[2]);
                        
                        for( k1 = k-1; k1 >= 0; k1-- )
                        {
                            if( mptr[k1].sortKey >= mptr[k1+1].sortKey )
                                break;
                            std::swap( mptr[k1], mptr[k1+1] );
                        }
                        
                        kHit = k1+1;
                        break;
                    }
                }
                
                if( kHit < 0 ) // no appropriate gaussian mixture found at all, remove the weakest mixture and create a new one
                {
                    kHit = k = min(k, K-1);
                    wsum += w0 - mptr[k].weight;
                    mptr[k].weight = w0;
                    mptr[k].mean = pix;
                    mptr[k].var = Vec3f(var0, var0, var0);
                    mptr[k].sortKey = sk0;
                }
                else
                    for( ; k < K; k++ )
                        wsum += mptr[k].weight;
            
                float wscale = 1.f/wsum;
                wsum = 0;
                for( k = 0; k < K; k++ )
                {
                    wsum += mptr[k].weight *= wscale;
                    mptr[k].sortKey *= wscale;
                    if( wsum > T && kForeground < 0 )
                        kForeground = k+1;
                }
                
                dst[x] = (uchar)(-(kHit >= kForeground));
            }
        }
        else
        {
            for( x = 0; x < cols; x++, mptr += K )
            {
                Vec3f pix(src[x*3], src[x*3+1], src[x*3+2]);
                int kHit = -1, kForeground = -1;
                
                for( k = 0; k < K; k++ )
                {
                    if( mptr[k].weight < FLT_EPSILON )
                        break;
                    Vec3f mu = mptr[k].mean;
                    Vec3f var = mptr[k].var;
                    Vec3f diff = pix - mu;
                    float d2 = diff.dot(diff);
                    if( d2 < vT*(var[0] + var[1] + var[2]) )
                    {
                        kHit = k;
                        break;
                    }
                }
 
                if( kHit >= 0 )
                {
                    float wsum = 0;
                    for( k = 0; k < K; k++ )
                    {
                        wsum += mptr[k].weight;
                        if( wsum > T )
                        {
                            kForeground = k+1;
                            break;
                        }
                    }
                }
                
                dst[x] = (uchar)(kHit < 0 || kHit >= kForeground ? 255 : 0);
            }
        }
    }
}

void BackgroundSubtractorMOG::operator()(InputArray _image, OutputArray _fgmask, double learningRate)
{
    Mat image = _image.getMat();
    bool needToInitialize = nframes == 0 || learningRate >= 1 || image.size() != frameSize || image.type() != frameType;//是否需要初始化
    
    if( needToInitialize )
        initialize(image.size(), image.type());//初始化
    
    CV_Assert( image.depth() == CV_8U );
    _fgmask.create( image.size(), CV_8U );
    Mat fgmask = _fgmask.getMat();
    
    ++nframes;
    learningRate = learningRate >= 0 && nframes > 1 ? learningRate : 1./min( nframes, history );
    CV_Assert(learningRate >= 0);
    
    if( image.type() == CV_8UC1 )//处理灰度图像
        process8uC1( image, fgmask, learningRate, bgmodel, nmixtures, backgroundRatio, varThreshold, noiseSigma );
    else if( image.type() == CV_8UC3 )//处理彩色图像
        process8uC3( image, fgmask, learningRate, bgmodel, nmixtures, backgroundRatio, varThreshold, noiseSigma );
    else
        CV_Error( CV_StsUnsupportedFormat, "Only 1- and 3-channel 8-bit images are supported in BackgroundSubtractorMOG" );
}
    
}

其中处理3通道彩色图像与处理单通道灰度图像类似，我就没有进行注释了。

其中有几点需要注意：

1.在高斯混合模型中需要使用概率更新参数的地方，程序中都简化成为了1处理，否则计算一个正态分布的概率还是挺花时间的。（程序作者在注释中也指出了他不是完全按照论文写成的，而是做了一些小的修改）。但是除了将概率换成1，其他地方还是严格按照公式的，大家可以仔细推导一下，就会看出其中的差异。

2.作者原文中是如果没有一个高斯模型与该像素点匹配，则去掉一个一个概率最小的，而用当前像素初始化的分布来替代他，而在这里变成了去掉优先级最小的。

3.程序中为了避免多次做循环，把一些步骤拆开做了，比如归一化权值需要先求出总权值，调整权值后的排序之类的，计算背景模型个数等等。减少了遍历的次数。其中的巧妙之处也不得不佩服作者的良苦用心。

3.就是似乎更新优先级的计算有点小问题，也可能是我理解不对。

4.在初始化时，可以使用多种方式，大家一看程序就明白了。

最后附上一个小的示例程序，教你如何使用高斯混合模型：

int main()
{
	VideoCapture capture("D:/videos/shadow/use3.MPG");
	if( !capture.isOpened() )
	{
		cout<<"读取视频失败"<<endl;
		return -1;
	}
	//获取整个帧数
	long totalFrameNumber = capture.get(CV_CAP_PROP_FRAME_COUNT);
	cout<<"整个视频共"<<totalFrameNumber<<"帧"<<endl;

	//设置开始帧()
	long frameToStart = 200;
	capture.set( CV_CAP_PROP_POS_FRAMES,frameToStart);
	cout<<"从第"<<frameToStart<<"帧开始读"<<endl;

	//设置结束帧
	int frameToStop = 650;

	if(frameToStop < frameToStart)
	{
		cout<<"结束帧小于开始帧，程序错误，即将退出！"<<endl;
		return -1;
	}
	else
	{
		cout<<"结束帧为：第"<<frameToStop<<"帧"<<endl;
	}

	double rate = capture.get(CV_CAP_PROP_FPS);
	int delay = 1000/rate;

	Mat frame;
	//前景图片
	Mat foreground;


	//使用默认参数调用混合高斯模型
	BackgroundSubtractorMOG mog;
	bool stop(false);
	//currentFrame是在循环体中控制读取到指定的帧后循环结束的变量
	long currentFrame = frameToStart;
	while( !stop )
	{
		if( !capture.read(frame) )
		{
			cout<<"从视频中读取图像失败或者读完整个视频"<<endl;
			return -2;
		}
		cvtColor(frame,frame,CV_RGB2GRAY);
		imshow("输入视频",frame);
		//参数为：输入图像、输出图像、学习速率
		mog(frame,foreground,0.01);


		imshow("前景",foreground);

		//按ESC键退出，按其他键会停止在当前帧

		int c = waitKey(delay);

		if ( (char)c == 27 || currentFrame >= frameToStop)
		{
			stop = true;
		}
		if ( c >= 0)
		{
			waitKey(0);
		}
		currentFrame++;

	}

	waitKey(0);
}

就说这么多吧，虽然我