opencv笔记（三十四）——线性分段

刺骨的言语ヽ痛彻心扉 2021-11-01 06:22 354阅读 0赞

线性分段方法的难点在于分段点的选取，对于目标与背景灰度值差异明显的，可以采用生成灰度直方图，然后人工选点的方式，也可以采用统计灰度值的算法来自动计算分段点，如下:

当待处理图片目标和背景灰度值的对比度比较低时，线性分段分段点的选取主要采用“最小误差法”【1】选取，。

最小误差法是KITTLER1984年在MINIMUM ERROR THRESHOLDING文章中提出的一种基于直方图的阈值分割方法，简称KITTLER算法。其思想：假设灰度图像由目标和背景组成，且目标和背景满足一混合高斯分布，计算目标和背景的均值、方差，根据最小分类误差思想得到的最小误差目标函数，取目标函数最小时的阈值即为最佳阈值。按此阈值将图像分割为二值图像【2】。

算法过程【3】：

![watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzM3NzY0MTI5_size_16_color_FFFFFF_t_70][]

![20190810190223893.png][]

### 1、计算目标和背景的均值、方差。 ###

![watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzM3NzY0MTI5_size_16_color_FFFFFF_t_70 1][]

###   2、根据最小分类误差思想得到最小误差目标函数。 ###

![20190810190329329.png][]

### 3、取使目标函数最小值为阈值。 ###

![20190810190420830.png][]

最小误差法参考代码（matlab）：

I = imread('rice.bmp');
    MAXD = 100000;
    imag = imag(:,:,1);
    [counts, x] = imhist(imag);  % counts are the histogram. x is the intensity level.
    GradeI = length(x);   % the resolusion of the intensity. i.e. 256 for uint8.
    J_t = zeros(GradeI, 1);  % criterion function
    prob = counts ./ sum(counts);  % Probability distribution
    meanT = x' * prob;  % Total mean level of the picture
    % Initialization
    w0 = prob(1);   % Probability of the first class
    miuK = 0;   % First-order cumulative moments of the histogram up to the kth level.
    J_t(1) = MAXD; 
    n = GradeI-1;
    for i = 1 : n
        w0 = w0 + prob(i+1);
        miuK = miuK + i * prob(i+1);  % first-order cumulative moment
        if (w0 == 0) || (w0 == 1)
            J_t(i+1) = MAXD;    % T = i
        else
            miu1 = miuK / w0;
            miu2 = (meanT-miuK) / (1-w0);
            var1 = (((0 : i)'-miu1).^2)' * prob(1 : i+1);
            var1 = var1 / w0;  % variance
            var2 = (((i+1 : n)'-miu2).^2)' * prob(i+2 : n+1);
            var2 = var2 / (1-w0);
            if var1 > 0 && var2 > 0   % in case of var1=0 or var2 =0
                J_t(i+1) = 1+2*w0 * log(var1)+2*(1-w0) * log(var2)-2*w0*log(w0)-2*(1-w0)*log(1-w0);
            else
                J_t(i+1) = MAXD;
            end
        end
    end
    minJ = min(J_t);
    index = find(J_t == minJ);
    th = mean(index);
    th = (th-1)/n
    imagBW = im2bw(imag, th);
    figure, imshow(I_bw);

线性分段代码：(人工选取分段点）

#include <iostream>
    #include <opencv2\highgui\highgui.hpp>
    
    using namespace std;
    using namespace cv;
    
    
    int main()
    {
    	Mat image;
    	image = imread("E:\\QT text\\blood vessel processing\\xianxingfenduan\\image\\11.bmp");
    
    	if (!image.data)
    	{
    		cout << "image read is error!" << endl;
    		return 0;
    	}
    	imshow("原图", image);
    
    	//将图像转换为灰度图
    	Mat Image_Gray;
    	cvtColor(image, Image_Gray, CV_RGB2GRAY);
    
    
    	//线性分段
    	Mat Image = Image_Gray.clone();
    	int c = 1;
    	int d = 150;
    	int data_max = 0, data_min = 255;
    	int nl = Image.rows; //行
    	int nc = Image.cols * Image.channels(); //列
    	//不带c，d版本，不起作用
    	if (Image.isContinuous()) //检测图像是否连续,当图像连通时，我们就可以把图像完全展开，看成是一行.具体介绍看https://blog.csdn.net/kaka_36/article/details/18553679
    	{
    		nc = nc * nl;
    		nl = 1;
    	}
    	int i, j;
    	uchar *data;
    	for (j = 0; j < nl; j++)
    	{
    		data = Image.ptr<uchar>(j);
    		for (i = 0; i < nc; i++)  //遍历找出这一副图像中的最大值点和最小值点，从而确定两个拐点
    		{
    			if (data[i] > data_max)        
    				data_max = data[i];
    			if (data[i] < data_min)        
    				data_min = data[i];
    		}
    	}
    	int temp = data_max - data_min;//目标区域灰度
    	for (j = 0; j < nl; j++)
    	{
    		data = Image.ptr<uchar>(j);
    		for (i = 0; i < nc; i++)
    		{
    			data[i] = (data[i] - data_min) * 255 / temp;
    		}
    	}
    	namedWindow("Process Image");
    	imshow("Process Image", Image);
    	//imwrite("E:\\QT text\\blood vessel processing\\xianxingfenduan\\image\\b,a=[0,255]结果.jpg", Image);
    
    	//带c、d版本，效果不好
    	/*uchar *cc = Image.data;
    	for (int i = 0; i < nl; ++i) {
    		for (int j = 0; j < nc; ++j) {
    			int val = *cc;
    			if (data_min > val) data_min = val;
    			if (data_max < val) data_max = val;
    			cc++;
    		}
    	}
    	cc = Image.data;
    	float k = float(d - c) / (data_max - data_min);
    	//CString c1; c1.Format(_T("a=%d,b=%d,c=%d,d=%d,k=%.2f\n"), a,b,c,d,k);MessageBox(c1); 
    	for (int i = 0; i < nl; ++i) 
    	{
    		for (int j = 0; j < nc; ++j) 
    		{
    			int val = *cc;
    			int s = (int)(k*(val - data_min) + c);
    			//int s = (int)((val - data_min)*255 / k);
    			*cc = s;
    			cc++;
    		}
    	}
    	imshow("线性分段", Image);
    	//imwrite("E:\\QT text\\blood vessel processing\\xianxingfenduan\\image\\方法二结果.jpg", Image);*/
    
    	waitKey(0);
    	return 0;
    }

--------------------

参考：

【1】基于分段线性变换的图像增强

【2】图像阈值分割（二值化）：[https://blog.csdn.net/wrightman/article/details/39204265][https_blog.csdn.net_wrightman_article_details_39204265]

【3】二维直线最小误差阈值分割法：[http://www.docin.com/p-860488440.html][http_www.docin.com_p-860488440.html]

[watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzM3NzY0MTI5_size_16_color_FFFFFF_t_70]: /images/20211101/9e1e4e131bd642b9862a7ae757956224.png
[20190810190223893.png]: /images/20211101/1f515e8c47ba43c78ec52db0943d3444.png
[watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzM3NzY0MTI5_size_16_color_FFFFFF_t_70 1]: /images/20211101/b84d6cebe620427596ee041feeb9c96a.png
[20190810190329329.png]: /images/20211101/fb1beef9c05a438b803719bbe47cd7f9.png
[20190810190420830.png]: /images/20211101/81490cf8d4e740cfa2b3654ef1fc0716.png
[https_blog.csdn.net_wrightman_article_details_39204265]: https://blog.csdn.net/wrightman/article/details/39204265
[http_www.docin.com_p-860488440.html]: http://www.docin.com/p-860488440.html