ScaramuzzaOCamCalib 鱼眼镜头定标，计算像素位置与光线入射角的关系

Question

 ###### 问题描述
在使用ScaramuzzaOCamCalib 鱼眼镜头的matlab程序对图像进行标定后，使用标定后参数以及cam2world函数进行反投影，并计算三维坐标系下的天顶角。发现角度超出相机视场范围，不明白是为什么。

 ###### 棋盘格图片来自官网提供的 190°鱼眼相机拍摄的棋盘格。以下是官网提供给的cam2world函数测试用例

/*
    测试用例：
    VMRImage0.jpg    calib_results.txt
*/

#include"ocam_functions.h"
#include<fstream>

void cam2world_test(double point3D[3], double point2D[2], struct ocam_model *myocam_model)
{
    double *pol = myocam_model->pol;
    double xc = (myocam_model->xc);
    double yc = (myocam_model->yc);
    double c = (myocam_model->c);
    double d = (myocam_model->d);
    double e = (myocam_model->e);
    int length_pol = (myocam_model->length_pol);
    double invdet = 1 / (c - d * e); // 1/det(A), where A = [c,d;e,1] as in the Matlab file

    double xp = invdet * ((point2D[0] - xc) - d * (point2D[1] - yc));
    double yp = invdet * (-e * (point2D[0] - xc) + c * (point2D[1] - yc));

    double r = sqrt(xp*xp + yp * yp); //distance [pixels] of  the point from the image center
    double r_temp = r;
    double zp = pol[0];
    double r_i = 1;
    int i;

    for (i = 1; i < length_pol; i++)
    {
        r_i *= r;
        zp += r_i * pol[i];
    }

    //normalize to unit norm
    double invnorm = 1 / sqrt(xp*xp + yp * yp + zp * zp);

    point3D[0] = invnorm * xp;
    point3D[1] = invnorm * yp;
    point3D[2] = invnorm * zp;
    double z = point3D[2];
    double theta = atan(sqrt(point3D[0] * point3D[0] + point3D[1] * point3D[1]) / point3D[2])*90;
    //cout << r << "\t" << theta << endl;
    //if (r_temp > 290) {
        int a = point2D[0];
        int b = point2D[1];
        ofstream ofs;
        ofs.open("test.txt", ios::app); //不指定地址的时候，会把文件和当前cpp文件放在一起
        ofs << point2D[0] << "\t" << point2D[1] << "\t"  << r << "\t" << theta << endl;
        ofs.close();
    //}
}

int main() {
    struct ocam_model o;
    //get_ocam_model(&o, "./calib_results_fisheye.txt");
    get_ocam_model(&o, "./calib_results.txt");  //获取标定文件

    //IplImage *src1 = cvLoadImage("./undistorted_perspective.jpg");
    IplImage *src1 = cvLoadImage("./Fisheye190deg1.jpg"); 
    //IplImage *src1 = cvLoadImage("./VMRImage0.jpg"); //获取图像
    CvMat* mapx_persp = cvCreateMat(src1->height, src1->width, CV_32FC1);
    int width = mapx_persp->cols; //New width
    int height = mapx_persp->rows;//New height   //获取像素数
    for (int i = 0; i < height; i += 1) {
        //for (int j = 0; j < width; j += 10) {
            double point2D[2] = { i,375 };
            //double point2D[2] = { 0,0 };
            double point3D[3] = { 0 ,0 ,0 };
            cam2world_test(point3D, point2D, &o);
        //}
    }

    return 0;
}

 ###### 190°视场的相机，按照 double theta = atan(sqrt(point3D[0] * point3D[0] + point3D[1] * point3D[1]) / point3D[2])*90; 这个方式计算，最终theta值应该在0-95°之间，但我实际计算出来是在0-104°之间。  

Answer 1

【鱼眼镜头6】[鱼眼畸变模型]：统一相机模型标定
https://blog.csdn.net/djfjkj52/article/details/122014468