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Canny 边缘检测算法

1986年，JOHN CANNY 提出一个很好的边缘检测算法，被称为Canny编边缘检测器[1]。

Canny边缘检测根据对信噪比与定位乘积进行测度，得到最优化逼近算子，也就是Canny算子。类似与 LoG 边缘检测方法，也属于先平滑后求导数的方法。

使用Canny边缘检测器，图象边缘检测必须满足两个条件：

能有效地抑制噪声；
必须尽量精确确定边缘的位置。

算法大致流程：

1、求图像与高斯平滑滤波器卷积:

【OpenCV】Canny 边缘检测

2、使用一阶有限差分计算偏导数的两个阵列P与Q：

3、幅值和方位角:

4、非极大值抑制（NMS ）：细化幅值图像中的屋脊带，即只保留幅值局部变化最大的点。

将梯度角的变化范围减小到圆周的四个扇区之一，方向角和幅值分别为：

非极大值抑制通过抑制梯度线上所有非屋脊峰值的幅值来细化M[i,j],中的梯度幅值屋脊．这一算法首先将梯度角θ[i,j]的变化范围减小到圆周的四个扇区之一,如下图所示：

5、取阈值

将低于阈值的所有值赋零，得到图像的边缘阵列
阈值τ取得太低->假边缘
阈值τ取得太高->部分轮廊丢失
选用两个阈值: 更有效的阈值方案．

相关代码

Canny算法实现：

用高斯滤波器平滑图像（在调用Canny之前自己用blur平滑）
用一阶偏导的有限差分来计算梯度的幅值和方向．
对梯度幅值应用非极大值抑制．
用双阈值算法检测和连接边缘．

void cv::Canny( InputArray _src, OutputArray _dst,
                double low_thresh, double high_thresh,
                int aperture_size, bool L2gradient )
{
    Mat src = _src.getMat();
    CV_Assert( src.depth() == CV_8U );
    
    _dst.create(src.size(), CV_8U);
    Mat dst = _dst.getMat();

    if (!L2gradient && (aperture_size & CV_CANNY_L2_GRADIENT) == CV_CANNY_L2_GRADIENT)
    {
        //backward compatibility
        aperture_size &= ~CV_CANNY_L2_GRADIENT;
        L2gradient = true;
    }

    if ((aperture_size & 1) == 0 || (aperture_size != -1 && (aperture_size < 3 || aperture_size > 7)))
        CV_Error(CV_StsBadFlag, "");

#ifdef HAVE_TEGRA_OPTIMIZATION
    if (tegra::canny(src, dst, low_thresh, high_thresh, aperture_size, L2gradient))
        return;
#endif

    const int cn = src.channels();
    cv::Mat dx(src.rows, src.cols, CV_16SC(cn));
    cv::Mat dy(src.rows, src.cols, CV_16SC(cn));

    cv::Sobel(src, dx, CV_16S, 1, 0, aperture_size, 1, 0, cv::BORDER_REPLICATE);
    cv::Sobel(src, dy, CV_16S, 0, 1, aperture_size, 1, 0, cv::BORDER_REPLICATE);

    if (low_thresh > high_thresh)
        std::swap(low_thresh, high_thresh);

    if (L2gradient)
    {
        low_thresh = std::min(32767.0, low_thresh);
        high_thresh = std::min(32767.0, high_thresh);
		
        if (low_thresh > 0) low_thresh *= low_thresh;
        if (high_thresh > 0) high_thresh *= high_thresh;
    }
    int low = cvFloor(low_thresh);
    int high = cvFloor(high_thresh);

    ptrdiff_t mapstep = src.cols + 2;
    cv::AutoBuffer<uchar> buffer((src.cols+2)*(src.rows+2) + cn * mapstep * 3 * sizeof(int));
    
    int* mag_buf[3];
    mag_buf[0] = (int*)(uchar*)buffer;
    mag_buf[1] = mag_buf[0] + mapstep*cn;
    mag_buf[2] = mag_buf[1] + mapstep*cn;
    memset(mag_buf[0], 0, /* cn* */mapstep*sizeof(int));

    uchar* map = (uchar*)(mag_buf[2] + mapstep*cn);
    memset(map, 1, mapstep);
    memset(map + mapstep*(src.rows + 1), 1, mapstep);

    int maxsize = std::max(1 << 10, src.cols * src.rows / 10);
    std::vector<uchar*> stack(maxsize);
    uchar **stack_top = &stack[0];
    uchar **stack_bottom = &stack[0];

    /* sector numbers
       (Top-Left Origin)

        1   2   3
         *  *  *
          * * *
        0*******0
          * * *
         *  *  *
        3   2   1
    */

    #define CANNY_PUSH(d)    *(d) = uchar(2), *stack_top++ = (d)
    #define CANNY_POP(d)     (d) = *--stack_top

    // calculate magnitude and angle of gradient, perform non-maxima supression.
    // fill the map with one of the following values:
    //   0 - the pixel might belong to an edge
    //   1 - the pixel can not belong to an edge
    //   2 - the pixel does belong to an edge
    for (int i = 0; i <= src.rows; i++)
    {
        int* _norm = mag_buf[(i > 0) + 1] + 1;
        if (i < src.rows)
        {
            short* _dx = dx.ptr<short>(i);
            short* _dy = dy.ptr<short>(i);

            if (!L2gradient)
            {
                for (int j = 0; j < src.cols*cn; j++)
                    _norm[j] = std::abs(int(_dx[j])) + std::abs(int(_dy[j]));
            }
            else
            {
                for (int j = 0; j < src.cols*cn; j++)
                    _norm[j] = int(_dx[j])*_dx[j] + int(_dy[j])*_dy[j];
            }
			
            if (cn > 1)
            {
                for(int j = 0, jn = 0; j < src.cols; ++j, jn += cn)
                {
                    int maxIdx = jn;
                    for(int k = 1; k < cn; ++k)
                        if(_norm[jn + k] > _norm[maxIdx]) maxIdx = jn + k;
                    _norm[j] = _norm[maxIdx];
                    _dx[j] = _dx[maxIdx];
                    _dy[j] = _dy[maxIdx];
                }
            }
            _norm[-1] = _norm[src.cols] = 0;
        }
        else
            memset(_norm-1, 0, /* cn* */mapstep*sizeof(int));
		
        // at the very beginning we do not have a complete ring
        // buffer of 3 magnitude rows for non-maxima suppression
        if (i == 0)
            continue;

        uchar* _map = map + mapstep*i + 1;
        _map[-1] = _map[src.cols] = 1;

        int* _mag = mag_buf[1] + 1; // take the central row
        ptrdiff_t magstep1 = mag_buf[2] - mag_buf[1];
        ptrdiff_t magstep2 = mag_buf[0] - mag_buf[1];

        const short* _x = dx.ptr<short>(i-1);
        const short* _y = dy.ptr<short>(i-1);

        if ((stack_top - stack_bottom) + src.cols > maxsize)
        {
            int sz = (int)(stack_top - stack_bottom);
            maxsize = maxsize * 3/2;
            stack.resize(maxsize);
            stack_bottom = &stack[0];
            stack_top = stack_bottom + sz;
        }

        int prev_flag = 0;
        for (int j = 0; j < src.cols; j++)
        {
            #define CANNY_SHIFT 15
            const int TG22 = (int)(0.4142135623730950488016887242097*(1<<CANNY_SHIFT) + 0.5);

            int m = _mag[j];

            if (m > low)
            {
                int xs = _x[j];
                int ys = _y[j];
                int x = std::abs(xs);
                int y = std::abs(ys) << CANNY_SHIFT;

                int tg22x = x * TG22;

                if (y < tg22x)
                {
                    if (m > _mag[j-1] && m >= _mag[j+1]) goto __ocv_canny_push;
                }
                else
                {
                    int tg67x = tg22x + (x << (CANNY_SHIFT+1));
                    if (y > tg67x)
                    {
                        if (m > _mag[j+magstep2] && m >= _mag[j+magstep1]) goto __ocv_canny_push;
                    }
                    else
                    {
                        int s = (xs ^ ys) < 0 ? -1 : 1;
                        if (m > _mag[j+magstep2-s] && m > _mag[j+magstep1+s]) goto __ocv_canny_push;
                    }
                }
            }
            prev_flag = 0;
            _map[j] = uchar(1);
            continue;
__ocv_canny_push:
            if (!prev_flag && m > high && _map[j-mapstep] != 2)
            {
                CANNY_PUSH(_map + j);
                prev_flag = 1;
            }
            else
                _map[j] = 0;
        }

        // scroll the ring buffer
        _mag = mag_buf[0];
        mag_buf[0] = mag_buf[1];
        mag_buf[1] = mag_buf[2];
        mag_buf[2] = _mag;
    }

    // now track the edges (hysteresis thresholding)
    while (stack_top > stack_bottom)
    {
        uchar* m;
        if ((stack_top - stack_bottom) + 8 > maxsize)
        {
            int sz = (int)(stack_top - stack_bottom);
            maxsize = maxsize * 3/2;
            stack.resize(maxsize);
            stack_bottom = &stack[0];
            stack_top = stack_bottom + sz;
        }

        CANNY_POP(m);

        if (!m[-1])         CANNY_PUSH(m - 1);
        if (!m[1])          CANNY_PUSH(m + 1);
        if (!m[-mapstep-1]) CANNY_PUSH(m - mapstep - 1);
        if (!m[-mapstep])   CANNY_PUSH(m - mapstep);
        if (!m[-mapstep+1]) CANNY_PUSH(m - mapstep + 1);
        if (!m[mapstep-1])  CANNY_PUSH(m + mapstep - 1);
        if (!m[mapstep])    CANNY_PUSH(m + mapstep);
        if (!m[mapstep+1])  CANNY_PUSH(m + mapstep + 1);
    }

    // the final pass, form the final image
    const uchar* pmap = map + mapstep + 1;
    uchar* pdst = dst.ptr();
    for (int i = 0; i < src.rows; i++, pmap += mapstep, pdst += dst.step)
    {
        for (int j = 0; j < src.cols; j++)
            pdst[j] = (uchar)-(pmap[j] >> 1);
    }
}

Canny() 调用接口（C++）：

void Canny(InputArray image, OutputArray edges, double threshold1, double threshold2, 
                   int apertureSize=3, bool L2gradient=false )

实践示例

Mat src, src_gray;
Mat dst, detected_edges;
int edgeThresh = 1;
int lowThreshold;
int const max_lowThreshold = 100;
int ratio = 3;
int kernel_size = 3;
char* window_name = "Edge Map";

void CannyThreshold(int, void*)
{
    /// Reduce noise with a kernel 3x3
    blur( src_gray, detected_edges, Size(3,3) );
    /// Canny detector
    Canny( detected_edges, detected_edges, lowThreshold, lowThreshold*ratio, kernel_size );
    dst = Scalar::all(0);
    src.copyTo( dst, detected_edges);
    imshow( window_name, dst );
}

int main( )
{
  src = imread( "images\\happycat.png" );
  if( !src.data )
    { return -1; }
  dst.create( src.size(), src.type() );
  cvtColor( src, src_gray, CV_BGR2GRAY );
  namedWindow( window_name, CV_WINDOW_AUTOSIZE );
  createTrackbar( "Min Threshold:", window_name, &lowThreshold, max_lowThreshold, CannyThreshold );
  CannyThreshold(0, 0);
  waitKey(0);
  return 0;
}

原图：