将全帧鱼眼转换为数学等值矩形

Question

我想将全帧鱼眼图像转换为等矩形，因此我可以将其用于全景拼接。我为此使用了Hugin和libpano，并且它们工作正常。以下图片已被hugin转换。我想知道可以实现这种或类似转换的数学方程式。

原始图片

转换的图像

Answer 1

使用该link作为参考我已成功转化的靠近所产生的一个HUGIN图像。它仍然需要亚像素采样以获得更好的图像质量

#include <iostream> 
#include <sstream> 
#include <time.h> 
#include <stdio.h> 
#include <opencv2/core/core.hpp> 
#include <opencv2/imgproc/imgproc.hpp> 
#include <opencv2/calib3d/calib3d.hpp> 
#include <opencv2/highgui/highgui.hpp> 
using namespace std; 
using namespace cv; 
#define PI 3.1415926536 
Point2f getInputPoint(int x, int y,int srcwidth, int srcheight) 
{ 
    Point2f pfish; 
    float theta,phi,r; 
    Point3f psph; 
    //float FOV = PI; 
    float FOV =(float)PI/180 * 150; 
    float FOV2 = (float)PI/180 * 120;; 
    float width = srcwidth; 
    float height = srcheight; 
    theta = PI * (x/width - 0.5); // -pi to pi 
    phi = PI * (y/height - 0.5); // -pi/2 to pi/2 
    psph.x = cos(phi) * sin(theta); 
    psph.y = cos(phi) * cos(theta); 
    psph.z = sin(phi); 
    theta = atan2(psph.z,psph.x); 
    phi = atan2(sqrt(psph.x*psph.x+psph.z*psph.z),psph.y); 
    r = width * phi/FOV; 
    float r2 = height * phi/FOV2; 
    pfish.x = 0.5 * width + r * cos(theta); 
    pfish.y = 0.5 * height + r2 * sin(theta); 
    return pfish; 
} 
int main(int argc, char **argv) 
{ 
    if(argc< 3) 
     return 0; 
    Mat orignalImage = imread(argv[1]); 
    if(orignalImage.empty()) 
    { 
     cout<<"Empty image\n"; 
     return 0; 
    } 
    Mat outImage(orignalImage.rows,orignalImage.cols,CV_8UC3); 
     //getInputPoint(0,5,10,10); 
    namedWindow("result",CV_WINDOW_NORMAL); 
    for(int i=0; i<outImage.cols; i++) 
    { 
     for(int j=0; j<outImage.rows; j++) 
     { 

      Point2f inP = getInputPoint(i,j,orignalImage.cols,orignalImage.rows); 
      //cout<<"in "<<i<<","<<j<<endl; 
      //cout<<"out "<<inP.x<<","<<inP.y<<endl; 
      Point inP2((int)inP.x,(int)inP.y); 
      if(inP2.x >= orignalImage.cols || inP2.y >= orignalImage.rows) 
       continue; 
      if(inP2.x < 0 || inP2.y < 0) 
       continue; 
      Vec3b color = orignalImage.at<Vec3b>(inP2); 
      outImage.at<Vec3b>(Point(i,j)) = color; 

     } 
    } 

    imshow("result",outImage); 
    imwrite(argv[2],outImage); 


}