Opencv大津二值化算法|极客教程

Opencv大津二值化算法，也被称作最大类间方差法，是一种可以自动确定二值化中阈值的算法，从类内方差和类间方差的比值计算得来：

小于阈值 t 的类记作 0，大于阈值 t 的类记作 1；
$$w0$$ 和 $$w1$$ 是被阈值 t 分开的两个类中的像素数占总像素数的比率（满足 w0+w1=1）；
$$S0^2$$, $$S1^2$$ 是这两个类中像素值的方差；
$$M0$4, $$M1$$ 是这两个类的像素值的平均值；

也就是说：

类内方差： $Sw^2 = w0 * S0^2 + w1 * S1^2$

类间方差： $Sb^2 = w0 * (M0 - Mt)^2 + w1 * (M1 - Mt)^2 = w0 * w1 * (M0 - M1) ^2$

图像所有像素的方差： $St^2 = Sw^2 + Sb^2 = (const)$

根据以上的式子，我们用以下的式子计算分离度：

分离度 $X = Sb^2 / Sw^2 = Sb^2 / (St^2 - Sb^2)$

也就是说：

$argmax_{t} X = argmax_{t} Sb^2$

换言之，如果使 $Sb^2 = w0 * w1 * (M0 - M1) ^2$ 最大，就可以得到最好的二值化阈值 t。

pyhton实现：

import cv2
import numpy as np

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

H, W, C = img.shape

# Grayscale
out = 0.2126 * img[..., 2] + 0.7152 * img[..., 1] + 0.0722 * img[..., 0]
out = out.astype(np.uint8)

# Determine threshold of Otsu's binarization
max_sigma = 0
max_t = 0

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

# 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>

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

  int width = img.rows;
  int height = img.cols;

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

  // gray
  int val = 0;
  for (int j = 0; j < height; j++){
    for (int i = 0; i < width; i++){
      val = (int)((float)img.at<cv::Vec3b>(j,i)[0] * 0.0722 + \
          (float)img.at<cv::Vec3b>(j,i)[1] * 0.7152 + \
          (float)img.at<cv::Vec3b>(j,i)[2] * 0.2126);
      out.at<uchar>(j,i) = (uchar)val;
    }
  }

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

  for (int t = 0; t < 255; t++){
    w0 = 0;
    w1 = 0;
    m0 = 0;
    m1 = 0;
    for (int j = 0; j < height; j++){
      for (int i = 0; i < width; i++){
    val = (int)(out.at<uchar>(j,i));

    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;
    }

  }

  // binalization
  for (int j = 0; j < height; j++){
    for (int i = 0; i < width; i++){
      val = (int)(out.at<uchar>(j,i));
      if (val < th){
    val = 0;
      } else {
    val = 255;
      }
      out.at<uchar>(j,i) = (uchar)val;
    }
  }

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

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

  return 0;

}

输入：

Opencv大津二值化算法