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Opencv Canny边缘检测 边缘细化

Canny边缘检测：第二步——边缘细化

在这里我们完成Canny边缘检测的第三步。

我们从在前面的文章中求出的边缘梯度进行非极大值抑制，来对边缘进行细化。

非极大值抑制是对除去非极大值以外的值的操作的总称（这个术语在其它的任务中也经常出现）。

在这里，我们比较我们我们所关注的地方梯度的法线方向邻接的三个像素点的梯度幅值，如果该点的梯度值不比其它两个像素大，那么这个地方的值设置为0。

也就是说，我们在注意梯度幅值\text{edge}(x,y)的时候，可以根据下式由梯度方向\text{angle}(x,y)来变换\text{edge}(x,y)：

  • $$\text{angle}(x,y) = 0$$

    如果在$$\text{edge}(x,y)$$、$$\text{edge}(x-1,y)$$、$$\text{edge}(x+1,y)$$中$$\text{edge}(x,y)$$不是最大的，那么$$\text{edge}(x,y)=0$$；

  • $$\text{angle}(x,y) = 45$$

    如果在$$\text{edge}(x,y)$$、$$\text{edge}(x-1,y)$$、$$\text{edge}(x+1,y)$$中$$\text{edge}(x,y)$$不是最大的，那么$$\text{edge}(x,y)=0$$；

  • $$\text{angle}(x,y) = 90$$

    如果在$$\text{edge}(x,y)$$、$$\text{edge}(x-1,y)$$、$$\text{edge}(x+1,y)$$中$$\text{edge}(x,y)$$不是最大的，那么$$\text{edge}(x,y)=0$$；

  • $$\text{angle}(x,y) = 135$$

    如果在$$\text{edge}(x,y)$$、$$\text{edge}(x-1,y)$$、$$\text{edge}(x+1,y)$$中$$\text{edge}(x,y)$$不是最大的，那么$$\text{edge}(x,y)=0$$；

python实现：

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

def Canny_step2(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
        else:
            img = np.expand_dims(img, axis=-1)
            H, W, C = img.shape

        ## 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 ** 2)))
        #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)
        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].astype(np.uint8)
        out_h = out_h[pad: pad + H, pad: pad + W].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-5)
        #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

    # 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)

    return edge, angle


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

# Canny (step2)
edge, angle = Canny_step2(img)

edge = edge.astype(np.uint8)
angle = angle.astype(np.uint8)

# Save result
cv2.imwrite("out.jpg", edge)
cv2.imshow("result", edge)
cv2.imwrite("out2.jpg", angle)
cv2.imshow("result2", angle)
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;
}


// Canny step 2
int Canny_step2(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);

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

  return 0;
}

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

  // Canny step 2
  Canny_step2(img);

  return 0;
}

输入：

Opencv Canny边缘检测 边缘细化

输出：

Opencv Canny边缘检测 边缘细化

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