Opencv 膨胀

将imori.jpg大津二值化之后，进行两次形态学膨胀处理。

在形态学处理的过程中，二值化图像中白色（255）的部分向4-近邻（上下左右）膨胀或收缩一格 。

反复进行膨胀和收缩操作，可以消除独立存在的白色像素点（见问题四十九：开操作）；或者连接白色像素点（见问题五十：闭操作）。

形态学处理中的膨胀算法如下。对于待操作的像素I(x,y)=0，I(x, y-1)，I(x-1, y)，I(x+1, y)，I(x, y+1)中不论哪一个为255，令I(x,y)=255。

换句话说，如果将上面的操作执行两次，则可以扩大两格。

在实际进行形态学处理的时候，待操作的像素4-近邻与矩阵\left[\begin{matrix}0&1&0\\1&0&1\\0&1&0\end{matrix}\right]相乘，结果大于255的话，将中心像素设为255

python实现：

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


# 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

# Otsu Binalization
def otsu_binarization(img, th=128):
    H, W = img.shape
    out = img.copy()

    max_sigma = 0
    max_t = 0

    # determine threshold
    for _t in range(1, 255):
        v0 = out[np.where(out < _t)]
        m0 = np.mean(v0) if len(v0) > 0 else 0.
        w0 = len(v0) / (H * W)
        v1 = out[np.where(out >= _t)]
        m1 = np.mean(v1) if len(v1) > 0 else 0.
        w1 = len(v1) / (H * W)
        sigma = w0 * w1 * ((m0 - m1) ** 2)
        if sigma > max_sigma:
            max_sigma = sigma
            max_t = _t

    # Binarization
    print("threshold >>", max_t)
    th = max_t
    out[out < th] = 0
    out[out >= th] = 255

    return out


# Morphology Erode
def Morphology_Erode(img, Dil_time=1):
    H, W = img.shape

    # kernel
    MF = np.array(((0, 1, 0),
                (1, 0, 1),
                (0, 1, 0)), dtype=np.int)

    # each dilate time
    out = img.copy()
    for i in range(Dil_time):
        tmp = np.pad(out, (1, 1), 'edge')
        for y in range(1, H+1):
            for x in range(1, W+1):
                if np.sum(MF * tmp[y-1:y+2, x-1:x+2]) >= 255:
                    out[y-1, x-1] = 255

    return out

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


# Grayscale
gray = BGR2GRAY(img)

# Otsu's binarization
otsu = otsu_binarization(gray)

# Morphology - dilate
out = Morphology_Erode(otsu, Dil_time=2)

# 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>

// 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;
}

// Gray -> Binary
cv::Mat Binarize_Otsu(cv::Mat gray){
  int width = gray.cols;
  int height = gray.rows;

  // determine threshold
  double w0 = 0, w1 = 0;
  double m0 = 0, m1 = 0;
  double max_sb = 0, sb = 0;
  int th = 0;
  int val;

  // Get threshold
  for (int t = 0; t < 255; t++){
    w0 = 0;
    w1 = 0;
    m0 = 0;
    m1 = 0;
    for (int y = 0; y < height; y++){
      for (int x = 0; x < width; x++){
        val = (int)(gray.at<uchar>(y, x));

        if (val < t){
          w0++;
          m0 += val;
        } else {
          w1++;
          m1 += val;
        }
      }
    }

    m0 /= w0;
    m1 /= w1;
    w0 /= (height * width);
    w1 /= (height * width);
    sb = w0 * w1 * pow((m0 - m1), 2);

    if(sb > max_sb){
      max_sb = sb;
      th = t;
    }
  }

  std::cout << "threshold:" << th << std::endl;

  // 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++){
      // Binarize
      if (gray.at<uchar>(y, x) > th){
        out.at<uchar>(y, x) = 255;
      } else {
        out.at<uchar>(y, x) = 0;
      }

    }
  }

  return out;
}

// Morphology Erode
cv::Mat Morphology_Erode(cv::Mat img, int Erode_time){
  int height = img.cols;
  int width = img.rows;

  // output image
  cv::Mat tmp_img;
  cv::Mat out = img.clone();

  // for erode time
  for (int i = 0; i < Erode_time; i++){
    tmp_img = out.clone();

    // each pixel
    for (int y = 0; y < height; y++){
      for (int x = 0; x < width; x++){
        // check left pixel
        if ((x > 0) && (tmp_img.at<uchar>(y, x - 1) == 255)){
          out.at<uchar>(y, x) = 255;
          continue;
        } 

        // check up pixel
        if ((y > 0) && (tmp_img.at<uchar>(y - 1, x) == 255)){
          out.at<uchar>(y, x) = 255;
          continue;
        }

        // check right pixel
        if ((x < width - 1) && (tmp_img.at<uchar>(y, x + 1) == 255)){
          out.at<uchar>(y, x) = 255;
          continue;
        }

        // check left pixel
        if ((y < height - 1) && (tmp_img.at<uchar>(y + 1, x) == 255)){
          out.at<uchar>(y, x) = 255;
          continue;
        }
      }
    }
  }

  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);

  // Gray -> Binary
  cv::Mat bin = Binarize_Otsu(gray);

  // Morphology Erode
  cv::Mat out = Morphology_Erode(bin, 2);

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

  return 0;
}

输入：

大津二值化：

输出：