图像处理中常用的坐标系转换

我会带着你远行 2022-09-05 06:09 213阅读 0赞

# 共有四种坐标系 #

![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L21hb19odWlfZmVp_size_16_color_FFFFFF_t_70]

### 世界坐标系——>相机坐标系 ###

![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L21hb19odWlfZmVp_size_16_color_FFFFFF_t_70 1]  
\[Xc,Yc,Zc\]T表示相机坐标，\[Xw,Yw,Zw，1\]T表示归物体所在的世界坐标。R表示旋转矩阵，T表示平移矩阵。

### 相机坐标系——>图像坐标系 ###

![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L21hb19odWlfZmVp_size_16_color_FFFFFF_t_70 2]

### 图像坐标系——>像素坐标系 ###

![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L21hb19odWlfZmVp_size_16_color_FFFFFF_t_70 3]  
通过相机标定，我们可以获取相机的内参数和外参数矩阵  
内参数矩阵：  
[https://www.cnblogs.com/wangguchangqing/p/8126333.html][https_www.cnblogs.com_wangguchangqing_p_8126333.html]

其中Fx=f*dx，Fy=f*dy，u0=cx，v0=cy。

综合上述，则总公式如下：  
![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L21hb19odWlfZmVp_size_16_color_FFFFFF_t_70 4]

## 转换代码 ##

/***************************************************************************************** 1、激光雷达映射图像 *****************************************************************************************/
    #include<opencv2/opencv.hpp>
    #include <iostream> 
    #include <fstream> 
    #include <stdlib.h> //srand()和rand()函数 
    #include <time.h> //time()函数 
    #include <opencv2/core/core.hpp> 
    #include <opencv2/highgui/highgui.hpp> 
    #include <opencv2/imgproc/imgproc.hpp> 
    #include <opencv2/objdetect/objdetect.hpp> 
    #include <opencv2/ml/ml.hpp> 
    #include<opencv2\opencv.hpp>
    #include <opencv2\imgproc\types_c.h>
    #include<windows.h>
    using namespace std;
    using namespace cv;
    using namespace ml;
    
    //double R[] = 
    //{ 
    //-0.000946327557628447 , 0.00924509852185524, 0.999956815376281,
    //-0.999910170350762 , 0.0133606413543068, -0.00106980919429913,
    //-0.0133699548714382 , -0.999868001996225, 0.00923162449479668
    //};
    
    double R[] =
    { 
    	-0.000946327557628447 ,  -0.999910170350762, -0.0133699548714382,
    	0.00924509852185524    ,  0.0133606413543068, -0.999868001996225,
    	0.999956815376281   ,  -0.00106980919429913,   0.00923162449479668
    };
    
    double T[] =
    { 
    	0.106387638682809, - 0.0655453193303612, - 0.0423556338963880
    };
    
    
    int main()
    { 
    	//double Xw = 0;
    	//double Yw = 0;
    	//double Zw = 0;
    	double Xw = 1.16;
    	double Yw = 1.18;
    	double Zw = 0.253;
    
    	double Xw1 = 1.52;
    	double Yw1 = 0.274;
    	double Zw1 = -0.433;
    
    	double Xw2 = 1.51;
    	double Yw2 = 0.274;
    	double Zw2 = -0.346;
    
    	/*8月20日*/
    	double Xw3 = 5.12;
    	double Yw3 = 1.94;
    	double Zw3 = 1.26;
    
    	double Xw4 = 5.62;
    	double Yw4 = 1.3;
    	double Zw4 = 1.32;
    
    
    	double Xc = 0;
    	double Yc = 0;
    	double Zc = 0;
    
    	double Xc1 = 0;
    	double Yc1 = 0;
    	double Zc1 = 0;
    
    	double Xc2 = 0;
    	double Yc2 = 0;
    	double Zc2 = 0;
    
    	double Xc3 = 0;
    	double Yc3 = 0;
    	double Zc3 = 0;
    
    
    	double Xc4 = 0;
    	double Yc4 = 0;
    	double Zc4 = 0;
    
    	double Fx = 901.542952546068;
    	double Fy = 899.822262198022 ;
    	double Cx = 1014.57219246244;
    	double Cy = 431.675147682217;
    	double u = 0;
    	double v = 0;
    	double u1 = 0;
    	double v1 = 0;	
    	double u2 = 0;
    	double v2 = 0;
    	printf("R[0]=%f R[1]=%f R[2]=%f \n R[3]=%f R[4]=%f R[5]=%f \n R[6]=%f R[7]=%f R[8]=%f\n", 
    		R[0], R[1], R[2],R[3],R[4],R[5], R[6], R[7], R[8]);
    
    
    	//1、世界坐标系——>相机坐标系
    	Xc = Xw*R[0] + Yw*R[1] + Zw*R[2] + T[0];
    	Yc = Xw*R[3] + Yw*R[4] + Zw*R[5] + T[1];
    	Zc = Xw*R[6] + Yw*R[7] + Zw*R[8] + T[2];
    
    	Xc1 = Xw1*R[0] + Yw1*R[1] + Zw1*R[2] + T[0];
    	Yc1 = Xw1*R[3] + Yw1*R[4] + Zw1*R[5] + T[1];
    	Zc1 = Xw1*R[6] + Yw1*R[7] + Zw1*R[8] + T[2];
    
    	Xc2 = Xw2*R[0] + Yw2*R[1] + Zw2*R[2] + T[0];
    	Yc2= Xw2*R[3] + Yw2*R[4] + Zw2*R[5] + T[1];
    	Zc2 = Xw2*R[6] + Yw2*R[7] + Zw2*R[8] + T[2];
    
    	Xc3 = Xw3*R[0] + Yw3*R[1] + Zw3*R[2] + T[0];
    	Yc3 = Xw3*R[3] + Yw3*R[4] + Zw3*R[5] + T[1];
    	Zc3 = Xw3*R[6] + Yw3*R[7] + Zw3*R[8] + T[2];
    
    	Xc4 = Xw4*R[0] + Yw4*R[1] + Zw4*R[2] + T[0];
    	Yc4 = Xw4*R[3] + Yw4*R[4] + Zw4*R[5] + T[1];
    	Zc4 = Xw4*R[6] + Yw4*R[7] + Zw4*R[8] + T[2];
    
    
    	//2、相机坐标系——>图像坐标系——>像素坐标系
    
    	u = Fx*Xc / Zc + Cx;
    	v=  Fy*Yc / Zc + Cy;
    	printf("u=%f\n", u);
    	printf("v=%f\n", v);
    
    	u1 = Fx*Xc1 / Zc1 + Cx;
    	v1 = Fy*Yc1 / Zc1 + Cy;
    	printf("u1=%f\n", u1);
    	printf("v1=%f\n", v1);
    
    	u2 = Fx*Xc2 / Zc2 + Cx;
    	v2 = Fy*Yc2 / Zc2 + Cy;
    	printf("u2=%f\n", u2);
    	printf("v2=%f\n", v2);
    
    	double u3 = Fx*Xc3 / Zc3 + Cx;
    	double v3 = Fy*Yc3 / Zc3 + Cy;
    	printf("u2=%f\n", u2);
    	printf("v2=%f\n", v2);
    
    	double u4 = Fx*Xc4 / Zc4 + Cx;
    	double v4 = Fy*Yc4 / Zc4 + Cy;
    	printf("u4=%f\n", u4);
    	printf("v4=%f\n", v4);
    
    
    	Mat srcImage0 = imread("2.png");//读取图片 
    
    	resize(srcImage0, srcImage0, Size(1920,1080), 0, 0, INTER_LINEAR);
    	if (srcImage0.empty())
    	{ 
    		printf("[ALG ERROR][函数:%s][行号:%d],图片未正常读取，请检查输入路径十分正确 \n", __FUNCTION__, __LINE__, 1);
    	}
    	//circle(srcImage0, Point(u,v), 10, Scalar(0, 255, 0), -1); 
    	//circle(srcImage0, Point(u1, v1), 10, Scalar(0, 255, 0), -1); 
    	//circle(srcImage0, Point(u2, v2), 10, Scalar(0, 255, 0), -1); 
    	
    	circle(srcImage0, Point(u3, v3), 10, Scalar(0, 0, 255), -1); 
    	circle(srcImage0, Point(u4, v4), 10, Scalar(0, 0, 255), -1);
    
    	namedWindow("srcImage0", 0);
    	imshow("srcImage0", srcImage0);
    	waitKey(200);
    
    
    
    
    	
    	return 0;
    }

# 相关转换代码 #

[https://blog.csdn.net/guyuealian/article/details/104184551][https_blog.csdn.net_guyuealian_article_details_104184551]

参考：  
[https://blog.csdn.net/weizhangyjs/article/details/81020177][https_blog.csdn.net_weizhangyjs_article_details_81020177]  
[https://blog.csdn.net/baidu\_38172402/article/details/81949447][https_blog.csdn.net_baidu_38172402_article_details_81949447]  
[https://www.cnblogs.com/wangguchangqing/p/8126333.html][https_www.cnblogs.com_wangguchangqing_p_8126333.html]  
[https://blog.csdn.net/yangdashi888/article/details/51356385][https_blog.csdn.net_yangdashi888_article_details_51356385]

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[watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L21hb19odWlfZmVp_size_16_color_FFFFFF_t_70 2]: /images/20220829/31dd612b7c0142af8fc94506cb4b7fa3.png
[watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L21hb19odWlfZmVp_size_16_color_FFFFFF_t_70 3]: /images/20220829/040ba475d2fe428882b47fd2cc51fcda.png
[https_www.cnblogs.com_wangguchangqing_p_8126333.html]: https://www.cnblogs.com/wangguchangqing/p/8126333.html
[watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L21hb19odWlfZmVp_size_16_color_FFFFFF_t_70 4]: /images/20220829/782fb6c78a904bf7a37bc51d1df9b22e.png
[https_blog.csdn.net_guyuealian_article_details_104184551]: https://blog.csdn.net/guyuealian/article/details/104184551
[https_blog.csdn.net_weizhangyjs_article_details_81020177]: https://blog.csdn.net/weizhangyjs/article/details/81020177
[https_blog.csdn.net_baidu_38172402_article_details_81949447]: https://blog.csdn.net/baidu_38172402/article/details/81949447
[https_blog.csdn.net_yangdashi888_article_details_51356385]: https://blog.csdn.net/yangdashi888/article/details/51356385