OpenCV图像处理学习二十一，直方图比较方法

一.直方图比较

直方图比较是对输入的两张图像进行计算得到直方图H1与H2，归一化到相同的尺度空间，然后可以通过计算H1与H2的之间的距离得到两个直方图的相似程度（每张图像都有唯一的直方图与之对应），进而比较图像本身的相似程度。Opencv提供的比较方法有四种：

Correlation 相关性比较

Chi-Square 卡方比较

Intersection 十字交叉性

Bhattacharyya distance 巴氏距离。

（1）直方图比较方法-相关性计算(CV_COMP_CORREL)

             d(h1,h2)=∑I(H1(I)−H¯1)(H2(I)−H¯2)∑I(H1(I)−H¯1)2∑I(H2(I)−H2¯)2" role="presentation" style="position: relative;">d(h1,h2)=∑I(H1(I)−H¯1)(H2(I)−H¯2)∑I(H1(I)−H¯1)2∑I(H2(I)−H2¯)2√$d\left(h_1,h_2\right)=\frac{\sum _I\left(H_1\left(I\right)-{\overline{H}}_1\right)\left(H_2\left(I\right)-{\overline{H}}_2\right)}{\sqrt{\sum _I{\left(H_1\left(I\right)-{\overline{H}}_1\right)}^2\sum _I{\left(H_2\left(I\right)-\overline{H_2}\right)}^2}}$

其中：                       

其中N是直方图的BIN个数，是均值。

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（2）直方图比较方法-相关性计算(CV_COMP_CORREL)

             d(h1,h2)=∑I(H1(I)−H¯2)2H1(I)" role="presentation" style="position: relative;">d(h1,h2)=∑I(H1(I)−H¯2)2H1(I)$d\left(h_1,h_2\right)=\sum _I^{}\frac{{\left(H_1\left(I\right)-{\overline{H}}_2\right)}^2}{H_{1\left(I\right)}}$

H1,H2分别表示两个图像的直方图数据

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(3)直方图比较方法-十字交叉性计算(CV_COMP_INTERSECT)

            d(h1,h2)=∑Imin(H1(I),H2(I))" role="presentation" style="position: relative;">d(h1,h2)=∑Imin(H1(I),H2(I))$d\left(h_1,h_2\right)=\sum _I^{}min\left(H_1\left(I\right),H_2\left(I\right)\right)$

H1,H2分别表示两个图像的直方图数据

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(4)直方图比较方法-巴氏距离计算(CV_COMP_BHATTACHARYYA )

         d(h1,h2)=1−1H¯1H¯2N2∑jH1(I)H2(I)" role="presentation" style="position: relative;">d(h1,h2)=1−1H¯1H¯2N2√∑jH1(I)H2(I)−−−−−−−−−−√−−−−−−−−−−−−−−−−−−−−−−−−−√$d\left(h_1,h_2\right)=\sqrt{1-\frac{1}{\sqrt{{\overline{H}}_1{\overline{H}}_2{N}^2}}\sum _j^{}\sqrt{H_1\left(I\right)H_2\left(I\right)}}$

H1,H2分别表示两个图像的直方图数据,

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二.图像直方图比较方法

• 加载原图像
• 将图像色彩空间由BGR三通道转换为HSV空间（由于直方图对亮度和灰度比较敏感，色彩空间转换就是突出这两个因素尽量去除其他因素）
• 计算直方图进行归一化处理，归一化到0到1之间，调用calcHist和normalize
• 直方图比较，使用上述四种方法之一，调用compareHist

直方图比较API函数接口

#API接口
double compareHist(InputArray h1,InputArray H2,int method)
//参数说明：
第一个参数InputArray类型 h1,直方图数据
第二个参数InputArray类型 h2,直方图数据
第三个参数int类型 method比较方法，上述四种方法之一
 
返回值：采用上述四中方法之一计算后的两个直方图相关系数

关于 int method 的取值：

enum HistCompMethods {
    HISTCMP_CORREL        = 0,    //相关性比较
    HISTCMP_CHISQR        = 1,    //卡方比较
    HISTCMP_INTERSECT     = 2,    //十字交叉性
    HISTCMP_BHATTACHARYYA = 3,    //巴氏距离
    HISTCMP_HELLINGER     = HISTCMP_BHATTACHARYYA, 
    HISTCMP_CHISQR_ALT    = 4,    //替代卡方：通常用于纹理比较。
    HISTCMP_KL_DIV        = 5     //KL散度
};

不同直方图相关性比较方法的特点：

Correlation相关性比较（CV_COMP_CORREL）值越大，相关度越高，最大值为1，最小值为0，越接近1越相似
Chi-Square卡方比较(CV_COMP_CHISQR) 值越小，相关度越高，最大值无上界，最小值0，越接近0越相似
Intersection十字交叉性（CV_COMP_INTERSECT）对于相似度比较，值越大，表明相关度越高，最大值无上界；完美匹配为1，完全不匹配为0；
Bhattacharyya distance巴氏距离(CV_COMP_BHATTACHARYYA)值越小，相关度越高，最大值为1，最小值为0，越接近1越相似

=========================================================================

代码实现

#include"stdafx.h"
#include <opencv2/opencv.hpp>
#include <iostream>
#include <math.h>
 
using namespace std;
using namespace cv;
 
string convertToString(double d);
int main(int argc, char** argv) {
	Mat base, test1, test2;          //RGB图像
	Mat hsvbase, hsvtest1, hsvtest2; //HSV图像
	base = imread("F:/photo/zx.jpg");
	if (!base.data) {
		printf("could not load image...\n");
		return -1;
	}
	test1 = imread("F:/photo/a.jpg");
	test2 = imread("F:/photo/c.jpg");
	//转化为HSV图像
	cvtColor(base, hsvbase, COLOR_BGR2HSV);
	cvtColor(test1, hsvtest1, COLOR_BGR2HSV);
	cvtColor(test2, hsvtest2, COLOR_BGR2HSV);
 
	int h_bins = 50; int s_bins = 60;
	int histSize[] = { h_bins, s_bins };
	// hue varies from 0 to 179, saturation from 0 to 255     
	float h_ranges[] = { 0, 180 };
	float s_ranges[] = { 0, 256 };
	const float* ranges[] = { h_ranges, s_ranges };
	// Use the o-th and 1-st channels     
	int channels[] = { 0, 1 };
	MatND hist_base;
	MatND hist_test1;
	MatND hist_test2;
 
	calcHist(&hsvbase, 1, channels, Mat(), hist_base, 2, histSize, ranges, true, false);
	normalize(hist_base, hist_base, 0, 1, NORM_MINMAX, -1, Mat());
 
	calcHist(&hsvtest1, 1, channels, Mat(), hist_test1, 2, histSize, ranges, true, false);
	normalize(hist_test1, hist_test1, 0, 1, NORM_MINMAX, -1, Mat());
 
	calcHist(&hsvtest2, 1, channels, Mat(), hist_test2, 2, histSize, ranges, true, false);
	normalize(hist_test2, hist_test2, 0, 1, NORM_MINMAX, -1, Mat());
 
	double basebase = compareHist(hist_base, hist_base, 2);//zx
	double basetest1 = compareHist(hist_base, hist_test1,2);//zx and a
	double basetest2 = compareHist(hist_base, hist_test2, 2);//zx and c
	double tes1test2 = compareHist(hist_test1, hist_test2, 2);//a and c
	printf("test1 compare with test2 correlation value :%f", tes1test2);
 
	Mat test12;
	test2.copyTo(test12);
	putText(base, convertToString(basebase), Point(50, 50), FONT_HERSHEY_COMPLEX, 1, Scalar(0, 0, 255), 2, LINE_AA);  //zx
	putText(test1, convertToString(basetest1), Point(50, 50), FONT_HERSHEY_COMPLEX, 1, Scalar(0, 0, 255), 2, LINE_AA);//zx and a
	putText(test2, convertToString(basetest2), Point(50, 50), FONT_HERSHEY_COMPLEX, 1, Scalar(0, 0, 255), 2, LINE_AA);//zx and c
	putText(test12, convertToString(tes1test2), Point(50, 50), FONT_HERSHEY_COMPLEX, 1, Scalar(0, 0, 255), 2, LINE_AA);//a and c
 
	namedWindow("base", 0);
	resizeWindow("base", base.cols / 2, base.rows / 2);
	namedWindow("test1", 0);
	resizeWindow("test1", test1.cols / 2, test1.rows / 2);
	namedWindow("test2", 0);
	resizeWindow("test2", test2.cols / 2, test2.rows / 2);
 
	imshow("base", base);
	imshow("test1", test1);
	imshow("test2", test2);
	imshow("test12", test12);
 
	waitKey(0);
	return 0;
}
 
string convertToString(double d) {
	ostringstream os;
	if (os << d)
		return os.str();
	return "invalid conversion";
}

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图像处理效果

代码中，车道线图片base自行十字交叉性比较，basebase = 36.8538，数值越大，图像相关性程度越高 

base图片与test1图片进行十字交叉性比较，test1base = 9.55181，数值较小，图像相识度较低

下面图像是test1图像与test2图像直方图对比，test2base = 7.98399，相识度较小