Opencv Sobel滤波器

使用3\times3的Sobel滤波器来进行滤波吧。

Sobel滤波器可以提取特定方向（纵向或横向）的边缘，滤波器按下式定义：

纵向：
K=\left[
\begin{matrix}
1&2&1\\
0&0&0\\
-1&-2&-1
\end{matrix}
\right]
横向：
K=\left[
\begin{matrix}
1&0&-1\\
2&0&-2\\
1&0&-1
\end{matrix}
\right]

python实现：

import cv2
import numpy as np

# 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


# sobel filter
def sobel_filter(img, K_size=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), dtype=np.float)
    out[pad: pad + H, pad: pad + W] = gray.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

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

# grayscale
gray = BGR2GRAY(img)

# sobel filtering
out_v, out_h = sobel_filter(gray, K_size=3)

# Save result
cv2.imwrite("out_v.jpg", out_v)
cv2.imshow("result_v", out_v)
while cv2.waitKey(100) != 27:# loop if not get ESC
    if cv2.getWindowProperty('result_v',cv2.WND_PROP_VISIBLE) <= 0:
        break
cv2.destroyWindow('result_v')

cv2.imwrite("out_h.jpg", out_h)
cv2.imshow("result_h", out_h)
# loop if not get ESC or click x
while cv2.waitKey(100) != 27:
    if cv2.getWindowProperty('result_h',cv2.WND_PROP_VISIBLE) <= 0:
        break
cv2.destroyWindow('result_h')
cv2.destroyAllWindows()

C++：

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


// BGR -> Gray
cv::Mat BGR2GRAY(cv::Mat img){
  // get height and width
  int width = img.cols;
  int height = img.rows;

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

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

  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 += img.at<uchar>(y + dy, x + dx) * kernel[dy + pad][dx + pad];
          }
        }
      }
      v = fmax(v, 0);
      v = fmin(v, 255);
      out.at<uchar>(y, x) = (uchar)v;
    }
  }
  return out;
}

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

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

  // sobel filter (vertical)
  cv::Mat out_v = sobel_filter(gray, 3, false);

  // sobel filter (horizontal)
  cv::Mat out_h = sobel_filter(gray, 3, true);

  //cv::imwrite("out.jpg", out);
  cv::imshow("answer (vertical)", out_v);
  cv::imshow("answer (horizontal)", out_h);
  cv::waitKey(0);
  cv::destroyAllWindows();

  return 0;
}

输入：

纵向输出：

横向输出：