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Opencv Canny边缘检测 滞后阈值

Canny 边缘检测：第三步——滞后阈值

在这里我们进行 Canny 边缘检测的最后一步。

在这里我们将通过设置高阈值（HT：high threshold）和低阈值（LT：low threshold）来将梯度幅值二值化。

  1. 如果梯度幅值edge(x,y)大于高阈值的话，令edge(x,y)=255；
  2. 如果梯度幅值edge(x,y)小于低阈值的话，令edge(x,y)=0；
  3. 如果梯度幅值edge(x,y)介于高阈值和低阈值之间并且周围8邻域内有比高阈值高的像素点存在，令edge(x,y)=255；

在这里，我们使高阈值为100，低阈值为20。顺便说一句，阈值的大小需要边看结果边调整。

上面的算法就是Canny边缘检测算法了。
python实现：

import cv2
import numpy as np
import matplotlib.pyplot as plt

def Canny(img):

    # Gray scale
    def BGR2GRAY(img):
        b = img[:, :, 0].copy()
        g = img[:, :, 1].copy()
        r = img[:, :, 2].copy()

        # Gray scale
        out = 0.2126 * r + 0.7152 * g + 0.0722 * b
        out = out.astype(np.uint8)

        return out


    # Gaussian filter for grayscale
    def gaussian_filter(img, K_size=3, sigma=1.3):

        if len(img.shape) == 3:
            H, W, C = img.shape
            gray = False
        else:
            img = np.expand_dims(img, axis=-1)
            H, W, C = img.shape
            gray = True

        ## Zero padding
        pad = K_size // 2
        out = np.zeros([H + pad * 2, W + pad * 2, C], dtype=np.float)
        out[pad : pad + H, pad : pad + W] = img.copy().astype(np.float)

        ## prepare Kernel
        K = np.zeros((K_size, K_size), dtype=np.float)
        for x in range(-pad, -pad + K_size):
            for y in range(-pad, -pad + K_size):
                K[y + pad, x + pad] = np.exp( - (x ** 2 + y ** 2) / (2 * sigma * sigma))
        #K /= (sigma * np.sqrt(2 * np.pi))
        K /= (2 * np.pi * sigma * sigma)
        K /= K.sum()

        tmp = out.copy()

        # filtering
        for y in range(H):
            for x in range(W):
                for c in range(C):
                    out[pad + y, pad + x, c] = np.sum(K * tmp[y : y + K_size, x : x + K_size, c])

        out = np.clip(out, 0, 255)
        out = out[pad : pad + H, pad : pad + W]
        out = out.astype(np.uint8)

        if gray:
            out = out[..., 0]

        return out


    # sobel filter
    def sobel_filter(img, K_size=3):
        if len(img.shape) == 3:
            H, W, C = img.shape
        else:
            H, W = img.shape

        # Zero padding
        pad = K_size // 2
        out = np.zeros((H + pad * 2, W + pad * 2), dtype=np.float)
        out[pad : pad + H, pad : pad + W] = img.copy().astype(np.float)
        tmp = out.copy()

        out_v = out.copy()
        out_h = out.copy()

        ## Sobel vertical
        Kv = [[1., 2., 1.],[0., 0., 0.], [-1., -2., -1.]]
        ## Sobel horizontal
        Kh = [[1., 0., -1.],[2., 0., -2.],[1., 0., -1.]]

        # filtering
        for y in range(H):
            for x in range(W):
                out_v[pad + y, pad + x] = np.sum(Kv * (tmp[y : y + K_size, x : x + K_size]))
                out_h[pad + y, pad + x] = np.sum(Kh * (tmp[y : y + K_size, x : x + K_size]))

        out_v = np.clip(out_v, 0, 255)
        out_h = np.clip(out_h, 0, 255)

        out_v = out_v[pad : pad + H, pad : pad + W]
        out_v = out_v.astype(np.uint8)
        out_h = out_h[pad : pad + H, pad : pad + W]
        out_h = out_h.astype(np.uint8)

        return out_v, out_h


    def get_edge_angle(fx, fy):
        # get edge strength
        edge = np.sqrt(np.power(fx.astype(np.float32), 2) + np.power(fy.astype(np.float32), 2))
        edge = np.clip(edge, 0, 255)

        fx = np.maximum(fx, 1e-10)
        #fx[np.abs(fx) <= 1e-5] = 1e-5

        # get edge angle
        angle = np.arctan(fy / fx)

        return edge, angle


    def angle_quantization(angle):
        angle = angle / np.pi * 180
        angle[angle < -22.5] = 180 + angle[angle < -22.5]
        _angle = np.zeros_like(angle, dtype=np.uint8)
        _angle[np.where(angle <= 22.5)] = 0
        _angle[np.where((angle > 22.5) & (angle <= 67.5))] = 45
        _angle[np.where((angle > 67.5) & (angle <= 112.5))] = 90
        _angle[np.where((angle > 112.5) & (angle <= 157.5))] = 135

        return _angle


    def non_maximum_suppression(angle, edge):
        H, W = angle.shape
        _edge = edge.copy()

        for y in range(H):
            for x in range(W):
                    if angle[y, x] == 0:
                            dx1, dy1, dx2, dy2 = -1, 0, 1, 0
                    elif angle[y, x] == 45:
                            dx1, dy1, dx2, dy2 = -1, 1, 1, -1
                    elif angle[y, x] == 90:
                            dx1, dy1, dx2, dy2 = 0, -1, 0, 1
                    elif angle[y, x] == 135:
                            dx1, dy1, dx2, dy2 = -1, -1, 1, 1
                    if x == 0:
                            dx1 = max(dx1, 0)
                            dx2 = max(dx2, 0)
                    if x == W-1:
                            dx1 = min(dx1, 0)
                            dx2 = min(dx2, 0)
                    if y == 0:
                            dy1 = max(dy1, 0)
                            dy2 = max(dy2, 0)
                    if y == H-1:
                            dy1 = min(dy1, 0)
                            dy2 = min(dy2, 0)
                    if max(max(edge[y, x], edge[y + dy1, x + dx1]), edge[y + dy2, x + dx2]) != edge[y, x]:
                            _edge[y, x] = 0

        return _edge

    def hysterisis(edge, HT=100, LT=30):
        H, W = edge.shape

        # Histeresis threshold
        edge[edge >= HT] = 255
        edge[edge <= LT] = 0

        _edge = np.zeros((H + 2, W + 2), dtype=np.float32)
        _edge[1 : H + 1, 1 : W + 1] = edge

        ## 8 - Nearest neighbor
        nn = np.array(((1., 1., 1.), (1., 0., 1.), (1., 1., 1.)), dtype=np.float32)

        for y in range(1, H+2):
                for x in range(1, W+2):
                        if _edge[y, x] < LT or _edge[y, x] > HT:
                                continue
                        if np.max(_edge[y-1:y+2, x-1:x+2] * nn) >= HT:
                                _edge[y, x] = 255
                        else:
                                _edge[y, x] = 0

        edge = _edge[1:H+1, 1:W+1]

        return edge

    # grayscale
    gray = BGR2GRAY(img)

    # gaussian filtering
    gaussian = gaussian_filter(gray, K_size=5, sigma=1.4)

    # sobel filtering
    fy, fx = sobel_filter(gaussian, K_size=3)

    # get edge strength, angle
    edge, angle = get_edge_angle(fx, fy)

    # angle quantization
    angle = angle_quantization(angle)

    # non maximum suppression
    edge = non_maximum_suppression(angle, edge)

    # hysterisis threshold
    out = hysterisis(edge, 50, 20)

    return out


# Read image
img = cv2.imread("imori.jpg").astype(np.float32)

# Canny
edge = Canny(img)

out = edge.astype(np.uint8)

# Save result
cv2.imwrite("out.jpg", out)
cv2.imshow("result", out)
cv2.waitKey(0)
cv2.destroyAllWindows()

c++实现：

#include <opencv2/core.hpp>
#include <opencv2/highgui.hpp>
#include <iostream>
#include <math.h>


// RGB to Gray scale
cv::Mat BGR2GRAY(cv::Mat img){
  // get height and width
  int height = img.rows;
  int width = img.cols;
  int channel = img.channels();

  // prepare output
  cv::Mat out = cv::Mat::zeros(height, width, CV_8UC1);

  // BGR -> Gray
  for (int y = 0; y < height; y++){
    for (int x = 0; x < width; x++){
      out.at<uchar>(y, x) = (int)((float)img.at<cv::Vec3b>(y, x)[0] * 0.0722 + \
                  (float)img.at<cv::Vec3b>(y, x)[1] * 0.7152 + \
                  (float)img.at<cv::Vec3b>(y, x)[2] * 0.2126);
    }
  }
  return out;
}

float clip(float value, float min, float max){
  return fmin(fmax(value, 0), 255);
}

// gaussian filter
cv::Mat gaussian_filter(cv::Mat img, double sigma, int kernel_size){
  int height = img.rows;
  int width = img.cols;
  int channel = img.channels();

  // prepare output
  cv::Mat out = cv::Mat::zeros(height, width, CV_8UC3);
  if (channel == 1) {
    out = cv::Mat::zeros(height, width, CV_8UC1);
  }

  // prepare kernel
  int pad = floor(kernel_size / 2);
  int _x = 0, _y = 0;
  double kernel_sum = 0;

  // get gaussian kernel
  float kernel[kernel_size][kernel_size];

  for (int y = 0; y < kernel_size; y++){
    for (int x = 0; x < kernel_size; x++){
      _y = y - pad;
      _x = x - pad; 
      kernel[y][x] = 1 / (2 * M_PI * sigma * sigma) * exp( - (_x * _x + _y * _y) / (2 * sigma * sigma));
      kernel_sum += kernel[y][x];
    }
  }

  for (int y = 0; y < kernel_size; y++){
    for (int x = 0; x < kernel_size; x++){
      kernel[y][x] /= kernel_sum;
    }
  }

  // filtering
  double v = 0;

  for (int y = 0; y < height; y++){
    for (int x = 0; x < width; x++){
      // for BGR
      if (channel == 3){
        for (int c = 0; c < channel; c++){
          v = 0;
          for (int dy = -pad; dy < pad + 1; dy++){
            for (int dx = -pad; dx < pad + 1; dx++){
              if (((x + dx) >= 0) && ((y + dy) >= 0) && ((x + dx) < width) && ((y + dy) < height)){
                v += (double)img.at<cv::Vec3b>(y + dy, x + dx)[c] * kernel[dy + pad][dx + pad];
              }
            }
          }
          out.at<cv::Vec3b>(y, x)[c] = (uchar)clip(v, 0, 255);
        }
      } else {
        // for Gray
        v = 0;
        for (int dy = -pad; dy < pad + 1; dy++){
          for (int dx = -pad; dx < pad + 1; dx++){
            if (((x + dx) >= 0) && ((y + dy) >= 0) && ((x + dx) < width) && ((y + dy) < height)){
              v += (double)img.at<uchar>(y + dy, x + dx) * kernel[dy + pad][dx + pad];
            }
          }
        }
        out.at<uchar>(y, x) = (uchar)clip(v, 0, 255);
      }
    }
  }
  return out;
}

// Sobel filter
cv::Mat sobel_filter(cv::Mat img, int kernel_size, bool horizontal){
  int height = img.rows;
  int width = img.cols;
  int channel = img.channels();

  // prepare output
  cv::Mat out = cv::Mat::zeros(height, width, CV_8UC1);

  // prepare kernel
  double kernel[kernel_size][kernel_size] = {{1, 2, 1}, {0, 0, 0}, {-1, -2, -1}};

  if (horizontal){
    kernel[0][1] = 0;
    kernel[0][2] = -1;
    kernel[1][0] = 2;
    kernel[1][2] = -2;
    kernel[2][0] = 1;
    kernel[2][1] = 0;
  }

  int pad = floor(kernel_size / 2);

  double v = 0;

  // filtering  
  for (int y = 0; y < height; y++){
    for (int x = 0; x < width; x++){
      v = 0;
      for (int dy = -pad; dy < pad + 1; dy++){
        for (int dx = -pad; dx < pad + 1; dx++){
          if (((y + dy) >= 0) && (( x + dx) >= 0) && ((y + dy) < height) && ((x + dx) < width)){
            v += (double)img.at<uchar>(y + dy, x + dx) * kernel[dy + pad][dx + pad];
          }
        }
      }
      out.at<uchar>(y, x) = (uchar)clip(v, 0, 255);
    }
  }
  return out;
}

// get edge
cv::Mat get_edge(cv::Mat fx, cv::Mat fy){
  // get height and width
  int height = fx.rows;
  int width = fx.cols;

  // prepare output
  cv::Mat out = cv::Mat::zeros(height, width, CV_8UC1);

  double _fx, _fy;

  for(int y = 0; y < height; y++){
    for(int x = 0; x < width; x++){
      _fx = (double)fx.at<uchar>(y, x);
      _fy = (double)fy.at<uchar>(y, x);

      out.at<uchar>(y, x) = (uchar)clip(sqrt(_fx * _fx + _fy * _fy), 0, 255);
    }
  }

  return out;
}

// get angle
cv::Mat get_angle(cv::Mat fx, cv::Mat fy){
  // get height and width
  int height = fx.rows;
  int width = fx.cols;

  // prepare output
  cv::Mat out = cv::Mat::zeros(height, width, CV_8UC1);

  double _fx, _fy;
  double angle;

  for(int y = 0; y < height; y++){
    for(int x = 0; x < width; x++){
      _fx = fmax((double)fx.at<uchar>(y, x), 0.000001);
      _fy = (double)fy.at<uchar>(y, x);

      angle = atan2(_fy, _fx);
      angle = angle / M_PI * 180;

      if(angle < -22.5){
        angle = 180 + angle;
      } else if (angle >= 157.5) {
        angle = angle - 180;
      }

      //std::cout << angle << " " ;

      // quantization
      if (angle <= 22.5){
        out.at<uchar>(y, x) = 0;
      } else if (angle <= 67.5){
        out.at<uchar>(y, x) = 45;
      } else if (angle <= 112.5){
        out.at<uchar>(y, x) = 90;
      } else {
        out.at<uchar>(y, x) = 135;
      }
    }
  }

  return out;
}


// non maximum suppression
cv::Mat non_maximum_suppression(cv::Mat angle, cv::Mat edge){
  int height = angle.rows;
  int width = angle.cols;
  int channel = angle.channels();

  int dx1, dx2, dy1, dy2;
  int now_angle;

  // prepare output
  cv::Mat _edge = cv::Mat::zeros(height, width, CV_8UC1);

  for (int y = 0; y < height; y++){
    for (int x = 0; x < width; x++){
      now_angle = angle.at<uchar>(y, x);
      // angle condition
      if (now_angle == 0){
        dx1 = -1;
        dy1 = 0;
        dx2 = 1;
        dy2 = 0;
      } else if(now_angle == 45) {
        dx1 = -1;
        dy1 = 1;
        dx2 = 1;
        dy2 = -1;
      } else if(now_angle == 90){
        dx1 = 0;
        dy1 = -1;
        dx2 = 0;
        dy2 = 1;
      } else {
        dx1 = -1;
        dy1 = -1;
        dx2 = 1;
        dy2 = 1;
      }

      if (x == 0){
        dx1 = fmax(dx1, 0);
        dx2 = fmax(dx2, 0);
      }
      if (x == (width - 1)){
        dx1 = fmin(dx1, 0);
        dx2 = fmin(dx2, 0);
      }
      if (y == 0){
        dy1 = fmax(dy1, 0);
        dy2 = fmax(dy2, 0);
      }
      if (y == (height - 1)){
        dy1 = fmin(dy1, 0);
        dy2 = fmin(dy2, 0);
      }

      // if pixel is max among adjuscent pixels, pixel is kept
      if (fmax(fmax(edge.at<uchar>(y, x), edge.at<uchar>(y + dy1, x + dx1)), edge.at<uchar>(y + dy2, x + dx2)) == edge.at<uchar>(y, x)) {
        _edge.at<uchar>(y, x) = edge.at<uchar>(y, x);
      }
    }
  }

  return _edge;
}

// histerisis
cv::Mat histerisis(cv::Mat edge, int HT, int LT){
  int height = edge.rows;
  int width = edge.cols;
  int channle = edge.channels();

  // prepare output
  cv::Mat _edge = cv::Mat::zeros(height, width, CV_8UC1);

  int now_pixel;

  for (int y = 0; y < height; y++){
    for (int x = 0; x < width; x++){
      // get pixel
      now_pixel = edge.at<uchar>(y, x);

      // if pixel >= HT
      if (now_pixel >= HT){
        _edge.at<uchar>(y, x) = 255;
      } 
      // if LT < pixel < HT
      else if (now_pixel > LT) {
        for (int dy = -1; dy < 2; dy++){
          for (int dx = -1; dx < 2; dx++){
            // if 8 nearest neighbor pixel >= HT
            if (edge.at<uchar>(fmin(fmax(y + dy, 0), 255), fmin(fmax(x + dx, 0), 255)) >= HT){
              _edge.at<uchar>(y, x) = 255;
            }
          }
        }
      }
    }
  }
  return _edge;
}


// Canny
cv::Mat Canny(cv::Mat img){
  // BGR -> Gray
  cv::Mat gray = BGR2GRAY(img);

  // gaussian filter
  cv::Mat gaussian = gaussian_filter(gray, 1.4, 5);

  // sobel filter (vertical)
  cv::Mat fy = sobel_filter(gaussian, 3, false);

  // sobel filter (horizontal)
  cv::Mat fx = sobel_filter(gaussian, 3, true);

  // get edge
  cv::Mat edge = get_edge(fx, fy);

  // get angle
  cv::Mat angle = get_angle(fx, fy);

  // edge non-maximum suppression
  edge = non_maximum_suppression(angle, edge);

  // histerisis
  edge = histerisis(edge, 50, 20);

  return edge;
}

int main(int argc, const char* argv[]){
  // read image
  cv::Mat img = cv::imread("imori.jpg", cv::IMREAD_COLOR);

  // Canny
  cv::Mat edge = Canny(img);

  //cv::imwrite("out.jpg", out);
  cv::imshow("answer(edge)", edge);
  cv::waitKey(0);
  cv::destroyAllWindows();

  return 0;
}

输入：

Opencv Canny边缘检测 滞后阈值

输出：

Opencv Canny边缘检测 滞后阈值

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