【OpenCV】Canny 邊緣檢測
阿新 • • 發佈:2019-01-29
Canny 邊緣檢測演算法
1986年,JOHN CANNY 提出一個很好的邊緣檢測演算法,被稱為Canny編邊緣檢測器[1]。
Canny邊緣檢測根據對信噪比與定位乘積進行測度,得到最優化逼近運算元,也就是Canny運算元。類似與 LoG 邊緣檢測方法,也屬於先平滑後求導數的方法。
使用Canny邊緣檢測器,圖象邊緣檢測必須滿足兩個條件:
- 能有效地抑制噪聲;
- 必須儘量精確確定邊緣的位置。
演算法大致流程:
1、求影象與高斯平滑濾波器卷積:
2、使用一階有限差分計算偏導數的兩個陣列P與Q:
3、幅值和方位角:
4、非極大值抑制(NMS ) :細化幅值影象中的屋脊帶,即只保留幅值區域性變化最大的點。
將梯度角的變化範圍減小到圓周的四個扇區之一,方向角和幅值分別為:
非極大值抑制通過抑制梯度線上所有非屋脊峰值的幅值來細化M[i,j],中的梯度幅值屋脊.這一演算法首先將梯度角θ[i,j]的變化範圍減小到圓周的四個扇區之一,如下圖所示:
5、取閾值
-
將低於閾值的所有值賦零,得到影象的邊緣陣列
- 閾值τ取得太低->假邊緣
- 閾值τ取得太高->部分輪廊丟失
- 選用兩個閾值: 更有效的閾值方案.
相關程式碼
Canny演算法實現:
- 用高斯濾波器平滑影象(在呼叫Canny之前自己用blur平滑)
- 用一階偏導的有限差分來計算梯度的幅值和方向.
- 對梯度幅值應用非極大值抑制 .
- 用雙閾值演算法檢測和連線邊緣.
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() 呼叫介面(C++):
void Canny(InputArray image, OutputArray edges, double threshold1, double threshold2,
int apertureSize=3, bool L2gradient=false )
實踐示例
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;
}
原圖:
邊緣檢測效果圖:
(從左到右lowThread分別為0、50、100)
參考文獻:
[1] Canny. A Computational Approach to Edge Detection, IEEE Trans. on Pattern Analysis and Machine Intelligence, 8(6), pp. 679-698 (1986).
[1] Canny. A Computational Approach to Edge Detection, IEEE Trans. on Pattern Analysis and Machine Intelligence, 8(6), pp. 679-698 (1986).