2D射影儿何和变换——柱面投影，图像拼接柱面投影

引入二维空间(以下简称2D) 的射影变换

这些变换发生在用透视摄像机对平面摄像的时候.

该章偏重于入门介绍并为三维空间(以下简称3D) 几何铺路.

大多数的概念在2D 中比3D 中更容易理解和可视化. 

本章介绍射影变换，包括它的特殊悄况:仿射和相似变换; 

并把注意力主要集中在从透视图像中恢复仿射性质(例如平行钱)和度量性质(例如线之间的角度) .

// mapcyl.cpp : Defines the entry point for the console application.
//

#include "stdafx.h"
#include <opencv/cv.h>
#include <opencv/highgui.h>

cv::Point2f convert_pt(cv::Point2f point,int w,int h)
{
	//center the point at 0,0
	cv::Point2f pc(point.x-w/2,point.y-h/2);

	//these are your free parameters
	//negative focal length since we are rear projecting
	float f = -w/2;
	float r = w;

	float omega = w/2;
	float z0 = f - sqrt(r*r-omega*omega);
	
	float zc = (2*z0+sqrt(4*z0*z0-4*(pc.x*pc.x/(f*f)+1)*(z0*z0-r*r)))/(2* (pc.x*pc.x/(f*f)+1)); 
	
	cv::Point2f final_point(pc.x*zc/f,pc.y*zc/f);
	final_point.x += w/2;
	final_point.y += h/2;
	
	return final_point;
}

int _tmain(int argc, _TCHAR* argv[])
{
	cv::Mat imgMat = cv::imread("lena.jpg", CV_LOAD_IMAGE_GRAYSCALE);
	cv::copyMakeBorder(imgMat, imgMat, 175, 175, 175, 175, cv::BORDER_CONSTANT);  
	
	cv::namedWindow("Original",CV_WINDOW_AUTOSIZE);
	cv::imshow("Original", imgMat);
	cv::waitKey(0);

	cv::Mat destImgMat(imgMat.size(), CV_8U);

	for(int y = 0; y < imgMat.rows; y++)
	{
		for(int x = 0; x < imgMat.cols; x++)
		{
			cv::Point2f current_pos(x,y);

			current_pos = convert_pt(current_pos, imgMat.cols, imgMat.rows);

			cv::Point2i top_left((int)current_pos.x,(int)current_pos.y); //top left because of integer rounding

			//make sure the point is actually inside the original image
			if(top_left.x < 0 || top_left.x > imgMat.cols-2 || top_left.y < 0 || top_left.y > imgMat.rows-2)
			{
				continue;
			}

			//bilinear interpolation
			float dx = current_pos.x-top_left.x;
			float dy = current_pos.y-top_left.y;

			float weight_tl = (1.0 - dx) * (1.0 - dy);
			float weight_tr = (dx)       * (1.0 - dy);
			float weight_bl = (1.0 - dx) * (dy);
			float weight_br = (dx)       * (dy);

			uchar value = weight_tl * imgMat.at<uchar>(top_left) +
			weight_tr * imgMat.at<uchar>(top_left.y,top_left.x+1) +
			weight_bl * imgMat.at<uchar>(top_left.y+1,top_left.x) +
			weight_br * imgMat.at<uchar>(top_left.y+1,top_left.x+1);

			destImgMat.at<uchar>(y,x) = value;
		}
	}
	
	cv::namedWindow("Cylindrical",CV_WINDOW_AUTOSIZE);
	cv::imshow("Cylindrical",destImgMat);
	cv::waitKey(0);
	
	cv::imwrite( "cyl_lena.jpg", destImgMat );

    return 0;
}

结果：

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