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 0,0cv::Point2f pc(point.x-w/2,point.y-h/2);//these are your free parameters//negative focal length since we are rear projectingfloat 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 imageif(top_left.x < 0 || top_left.x > imgMat.cols-2 || top_left.y < 0 || top_left.y > imgMat.rows-2){continue;}//bilinear interpolationfloat 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;
}

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