【OpenCV】SIFT原理与源码分析:关键点描述

wolfoxkao 2012-10-26

《SIFT原理与源码分析》系列文章索引:http://blog.csdn.net/xiaowei_cqu/article/details/8069548

由前一篇《方向赋值》,为找到的关键点即SIFT特征点赋了值,包含位置、尺度和方向的信息。接下来的步骤是关键点描述,即用用一组向量将这个关键点描述出来,这个描述子不但包括关键点,也包括关键点周围对其有贡献的像素点。用来作为目标匹配的依据(所以描述子应该有较高的独特性,以保证匹配率),也可使关键点具有更多的不变特性,如光照变化、3D视点变化等。

SIFT描述子h(x,y,θ)是对关键点附近邻域内高斯图像梯度统计的结果,是一个三维矩阵,但通常用一个矢量来表示。矢量通过对三维矩阵按一定规律排列得到。

描述子采样区域

特征描述子与关键点所在尺度有关,因此对梯度的求取应在特征点对应的高斯图像上进行。将关键点附近划分成d×d个子区域,每个子区域尺寸为mσ个像元(d=4,m=3,σ为尺特征点的尺度值)。考虑到实际计算时需要双线性插值,故计算的图像区域为mσ(d+1),再考虑旋转,则实际计算的图像区域为【OpenCV】SIFT原理与源码分析:关键点描述,如下图所示:
【OpenCV】SIFT原理与源码分析:关键点描述

源码

Point pt(cvRound(ptf.x), cvRound(ptf.y));
	//计算余弦,正弦,CV_PI/180:将角度值转化为幅度值
    float cos_t = cosf(ori*(float)(CV_PI/180));
    float sin_t = sinf(ori*(float)(CV_PI/180));
    float bins_per_rad = n / 360.f;
    float exp_scale = -1.f/(d * d * 0.5f); //d:SIFT_DESCR_WIDTH 4	
    float hist_width = SIFT_DESCR_SCL_FCTR * scl;  // SIFT_DESCR_SCL_FCTR: 3 
	                                               // scl: size*0.5f
	// 计算图像区域半径mσ(d+1)/2*sqrt(2)
	// 1.4142135623730951f 为根号2
    int radius = cvRound(hist_width * 1.4142135623730951f * (d + 1) * 0.5f);
    cos_t /= hist_width;
    sin_t /= hist_width;

区域坐标轴旋转

为了保证特征矢量具有旋转不变性,要以特征点为中心,在附近邻域内旋转θ角,即旋转为特征点的方向。
【OpenCV】SIFT原理与源码分析:关键点描述
旋转后区域内采样点新的坐标为:
【OpenCV】SIFT原理与源码分析:关键点描述

源码

//计算采样区域点坐标旋转
    for( i = -radius, k = 0; i <= radius; i++ )
        for( j = -radius; j <= radius; j++ )
        {
            /*
             Calculate sample's histogram array coords rotated relative to ori.
             Subtract 0.5 so samples that fall e.g. in the center of row 1 (i.e.
             r_rot = 1.5) have full weight placed in row 1 after interpolation.
             */
            float c_rot = j * cos_t - i * sin_t;
            float r_rot = j * sin_t + i * cos_t;
            float rbin = r_rot + d/2 - 0.5f;
            float cbin = c_rot + d/2 - 0.5f;
            int r = pt.y + i, c = pt.x + j;

            if( rbin > -1 && rbin < d && cbin > -1 && cbin < d &&
               r > 0 && r < rows - 1 && c > 0 && c < cols - 1 )
            {
                float dx = (float)(img.at<short>(r, c+1) - img.at<short>(r, c-1));
                float dy = (float)(img.at<short>(r-1, c) - img.at<short>(r+1, c));
                X[k] = dx; Y[k] = dy; RBin[k] = rbin; CBin[k] = cbin;
                W[k] = (c_rot * c_rot + r_rot * r_rot)*exp_scale;
                k++;
            }
        }

计算采样区域梯度直方图

将旋转后区域划分为d×d个子区域(每个区域间隔为mσ像元),在子区域内计算8个方向的梯度直方图,绘制每个方向梯度方向的累加值,形成一个种子点。
与求主方向不同的是,此时,每个子区域梯度方向直方图将0°~360°划分为8个方向区间,每个区间为45°。即每个种子点有8个方向区间的梯度强度信息。由于存在d×d,即4×4个子区域,所以最终共有4×4×8=128个数据,形成128维SIFT特征矢量。
【OpenCV】SIFT原理与源码分析:关键点描述
对特征矢量需要加权处理,加权采用mσd/2的标准高斯函数。为了除去光照变化影响,还有一步归一化处理。

源码

//计算梯度直方图
    for( k = 0; k < len; k++ )
    {
        float rbin = RBin[k], cbin = CBin[k];
        float obin = (Ori[k] - ori)*bins_per_rad;
        float mag = Mag[k]*W[k];

        int r0 = cvFloor( rbin );
        int c0 = cvFloor( cbin );
        int o0 = cvFloor( obin );
        rbin -= r0;
        cbin -= c0;
        obin -= o0;

        //n为SIFT_DESCR_HIST_BINS:8,即将360°分为8个区间
		if( o0 < 0 )
            o0 += n;
        if( o0 >= n )
            o0 -= n;
		

        // histogram update using tri-linear interpolation
		// 双线性插值
        float v_r1 = mag*rbin, v_r0 = mag - v_r1;
        float v_rc11 = v_r1*cbin, v_rc10 = v_r1 - v_rc11;
        float v_rc01 = v_r0*cbin, v_rc00 = v_r0 - v_rc01;
        float v_rco111 = v_rc11*obin, v_rco110 = v_rc11 - v_rco111;
        float v_rco101 = v_rc10*obin, v_rco100 = v_rc10 - v_rco101;
        float v_rco011 = v_rc01*obin, v_rco010 = v_rc01 - v_rco011;
        float v_rco001 = v_rc00*obin, v_rco000 = v_rc00 - v_rco001;

        int idx = ((r0+1)*(d+2) + c0+1)*(n+2) + o0;
        hist[idx] += v_rco000;
        hist[idx+1] += v_rco001;
        hist[idx+(n+2)] += v_rco010;
        hist[idx+(n+3)] += v_rco011;
        hist[idx+(d+2)*(n+2)] += v_rco100;
        hist[idx+(d+2)*(n+2)+1] += v_rco101;
        hist[idx+(d+3)*(n+2)] += v_rco110;
        hist[idx+(d+3)*(n+2)+1] += v_rco111;
    }

关键点描述源码

// SIFT关键点特征描述
// SIFT描述子是关键点领域高斯图像提取统计结果的一种表示
static void calcSIFTDescriptor( const Mat& img, Point2f ptf, float ori, float scl,
                               int d, int n, float* dst )
						   
{
    Point pt(cvRound(ptf.x), cvRound(ptf.y));
	//计算余弦,正弦,CV_PI/180:将角度值转化为幅度值
    float cos_t = cosf(ori*(float)(CV_PI/180));
    float sin_t = sinf(ori*(float)(CV_PI/180));
    float bins_per_rad = n / 360.f;
    float exp_scale = -1.f/(d * d * 0.5f); //d:SIFT_DESCR_WIDTH 4	
    float hist_width = SIFT_DESCR_SCL_FCTR * scl;  // SIFT_DESCR_SCL_FCTR: 3 
	                                               // scl: size*0.5f
	// 计算图像区域半径mσ(d+1)/2*sqrt(2)
	// 1.4142135623730951f 为根号2
    int radius = cvRound(hist_width * 1.4142135623730951f * (d + 1) * 0.5f);
    cos_t /= hist_width;
    sin_t /= hist_width;

    int i, j, k, len = (radius*2+1)*(radius*2+1), histlen = (d+2)*(d+2)*(n+2);
    int rows = img.rows, cols = img.cols;

    AutoBuffer<float> buf(len*6 + histlen);
    float *X = buf, *Y = X + len, *Mag = Y, *Ori = Mag + len, *W = Ori + len;
    float *RBin = W + len, *CBin = RBin + len, *hist = CBin + len;

	//初始化直方图
    for( i = 0; i < d+2; i++ )
    {
        for( j = 0; j < d+2; j++ )
            for( k = 0; k < n+2; k++ )
                hist[(i*(d+2) + j)*(n+2) + k] = 0.;
    }

	//计算采样区域点坐标旋转
    for( i = -radius, k = 0; i <= radius; i++ )
        for( j = -radius; j <= radius; j++ )
        {
            /*
             Calculate sample's histogram array coords rotated relative to ori.
             Subtract 0.5 so samples that fall e.g. in the center of row 1 (i.e.
             r_rot = 1.5) have full weight placed in row 1 after interpolation.
             */
            float c_rot = j * cos_t - i * sin_t;
            float r_rot = j * sin_t + i * cos_t;
            float rbin = r_rot + d/2 - 0.5f;
            float cbin = c_rot + d/2 - 0.5f;
            int r = pt.y + i, c = pt.x + j;

            if( rbin > -1 && rbin < d && cbin > -1 && cbin < d &&
               r > 0 && r < rows - 1 && c > 0 && c < cols - 1 )
            {
                float dx = (float)(img.at<short>(r, c+1) - img.at<short>(r, c-1));
                float dy = (float)(img.at<short>(r-1, c) - img.at<short>(r+1, c));
                X[k] = dx; Y[k] = dy; RBin[k] = rbin; CBin[k] = cbin;
                W[k] = (c_rot * c_rot + r_rot * r_rot)*exp_scale;
                k++;
            }
        }

    len = k;
    fastAtan2(Y, X, Ori, len, true);
    magnitude(X, Y, Mag, len);
    exp(W, W, len);

	
	//计算梯度直方图
    for( k = 0; k < len; k++ )
    {
        float rbin = RBin[k], cbin = CBin[k];
        float obin = (Ori[k] - ori)*bins_per_rad;
        float mag = Mag[k]*W[k];

        int r0 = cvFloor( rbin );
        int c0 = cvFloor( cbin );
        int o0 = cvFloor( obin );
        rbin -= r0;
        cbin -= c0;
        obin -= o0;

        //n为SIFT_DESCR_HIST_BINS:8,即将360°分为8个区间
		if( o0 < 0 )
            o0 += n;
        if( o0 >= n )
            o0 -= n;
		

        // histogram update using tri-linear interpolation
		// 双线性插值
        float v_r1 = mag*rbin, v_r0 = mag - v_r1;
        float v_rc11 = v_r1*cbin, v_rc10 = v_r1 - v_rc11;
        float v_rc01 = v_r0*cbin, v_rc00 = v_r0 - v_rc01;
        float v_rco111 = v_rc11*obin, v_rco110 = v_rc11 - v_rco111;
        float v_rco101 = v_rc10*obin, v_rco100 = v_rc10 - v_rco101;
        float v_rco011 = v_rc01*obin, v_rco010 = v_rc01 - v_rco011;
        float v_rco001 = v_rc00*obin, v_rco000 = v_rc00 - v_rco001;

        int idx = ((r0+1)*(d+2) + c0+1)*(n+2) + o0;
        hist[idx] += v_rco000;
        hist[idx+1] += v_rco001;
        hist[idx+(n+2)] += v_rco010;
        hist[idx+(n+3)] += v_rco011;
        hist[idx+(d+2)*(n+2)] += v_rco100;
        hist[idx+(d+2)*(n+2)+1] += v_rco101;
        hist[idx+(d+3)*(n+2)] += v_rco110;
        hist[idx+(d+3)*(n+2)+1] += v_rco111;
    }

    // finalize histogram, since the orientation histograms are circular
	// 最后确定直方图,目标方向直方图是圆的
    for( i = 0; i < d; i++ )
        for( j = 0; j < d; j++ )
        {
            int idx = ((i+1)*(d+2) + (j+1))*(n+2);
            hist[idx] += hist[idx+n];
            hist[idx+1] += hist[idx+n+1];
            for( k = 0; k < n; k++ )
                dst[(i*d + j)*n + k] = hist[idx+k];
        }
    // copy histogram to the descriptor,
    // apply hysteresis thresholding
    // and scale the result, so that it can be easily converted
    // to byte array
    float nrm2 = 0;
    len = d*d*n;
    for( k = 0; k < len; k++ )
        nrm2 += dst[k]*dst[k];
    float thr = std::sqrt(nrm2)*SIFT_DESCR_MAG_THR;
    for( i = 0, nrm2 = 0; i < k; i++ )
    {
        float val = std::min(dst[i], thr);
        dst[i] = val;
        nrm2 += val*val;
    }
    nrm2 = SIFT_INT_DESCR_FCTR/std::max(std::sqrt(nrm2), FLT_EPSILON);
    for( k = 0; k < len; k++ )
    {
        dst[k] = saturate_cast<uchar>(dst[k]*nrm2);
    }
}
至此SIFT描述子生成,SIFT算法也基本完成了~参见《SIFT原理与源码分析

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