Homography

什么是Homography 
在图1中有两张书的平面图，两张图分别有四个相对位置相同的点，Homography就是一个变换（3*3矩阵），将一张图中的点映射到另一张图中对应的点 

因为Homography是一个3*3矩阵，所以可以写成 

H=⎡⎣⎢h00h10h20h01h11h21h02h12h22⎤⎦⎥

两张图间的H映射关系就可以表示成 

Homography应用：图像对齐

上面公式得出的H ，对于图一中的所有点都是正确的，换句话说，可以用H将第一个图中的点映射到第二张图。

如何得到一个Homography

要得到两张图片的H,就必须至少知道4个相同对应位置的点，opencv中可以利用findHomography正确得到

// pts_src and pts_dst are vectors of points in source // and destination images. They are of type vector<Point2f>. // We need at least 4 corresponding points.Mat h = findHomography(pts_src, pts_dst);// The calculated homography can be used to warp // the source image to destination. im_src and im_dst are // of type Mat. Size is the size (width,height) of im_dst. warpPerspective(im_src, im_dst, h, size);

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OpenCV C++ Homography的一个简单例子：

#include "opencv2/opencv.hpp" using namespace cv; using namespace std; int main( int argc, char** argv) { // Read source image.Mat im_src = imread("book2.jpg");// Four corners of the book in source imagevector<Point2f> pts_src;pts_src.push_back(Point2f(141, 131));pts_src.push_back(Point2f(480, 159));pts_src.push_back(Point2f(493, 630));pts_src.push_back(Point2f(64, 601));// Read destination image.Mat im_dst = imread("book1.jpg");// Four corners of the book in destination image.vector<Point2f> pts_dst;pts_dst.push_back(Point2f(318, 256));pts_dst.push_back(Point2f(534, 372));pts_dst.push_back(Point2f(316, 670));pts_dst.push_back(Point2f(73, 473));// Calculate HomographyMat h = findHomography(pts_src, pts_dst);// Output imageMat im_out;// Warp source image to destination based on homographywarpPerspective(im_src, im_out, h, im_dst.size());// Display imagesimshow("Source Image", im_src);imshow("Destination Image", im_dst);imshow("Warped Source Image", im_out);waitKey(0); }

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Homography应用：图像矫正

假设你有一张如下所示的图片 

你想点击图中书的四个顶点，然后得到正放的书： 

该如何做？ 
利用Homography可以做到这点。 
1.首先获取书本四个顶点的坐标 pts_src 
2.然后我们需要知道书本的宽高比，此书的宽高比是3/4,所以可使输出图像的size 为300*400，就可设其四个点的坐标为（0,0），（299,0），（299,399），（0,399）保存在pts_dst中 
3.通过pts_src和pts_dst 获取homography 
4.对原图应用homography 得到输出

#include <opencv2/opencv.hpp> using namespace cv; using namespace std;struct userdata{Mat im;vector<Point2f> points; };void mouseHandler(int event, int x, int y, int flags, void* data_ptr) {if ( event == EVENT_LBUTTONDOWN ){userdata *data = ((userdata *) data_ptr);circle(data->im, Point(x,y),3,Scalar(0,0,255), 5, CV_AA);imshow("Image", data->im);if (data->points.size() < 4){data->points.push_back(Point2f(x,y));}} } void main() {// Read source image.Mat im_src = imread("book1.jpg");// Destination image. The aspect ratio of the book is 3/4Size size(300,400);Mat im_dst = Mat::zeros(size,CV_8UC3);// Create a vector of destination points.vector<Point2f> pts_dst;pts_dst.push_back(Point2f(0,0));pts_dst.push_back(Point2f(size.width - 1, 0));pts_dst.push_back(Point2f(size.width - 1, size.height -1));pts_dst.push_back(Point2f(0, size.height - 1 ));// Set data for mouse eventMat im_temp = im_src.clone();userdata data;data.im = im_temp;cout << "Click on the four corners of the book -- top left first and" << endl<< "bottom left last -- and then hit ENTER" << endl;// Show image and wait for 4 clicks. imshow("Image", im_temp);// Set the callback function for any mouse eventsetMouseCallback("Image", mouseHandler, &data);waitKey(0);// Calculate the homographyMat h = findHomography(data.points, pts_dst);// Warp source image to destinationwarpPerspective(im_src, im_dst, h, size);// Show imageimshow("Image", im_dst);waitKey(0); }

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Homography应用：虚拟广告牌

在足球或者棒球体育直播中，经常可以看到球场旁边有虚拟广告，并且还会根据地区，国家的不同播放不同的广告，这是如何做到的？ 
看完此篇博客，你应该就能知道如何实现了。原理跟前一个差不多，这里直接上代码

#include <opencv2/opencv.hpp> using namespace cv; using namespace std; struct userdata{Mat im;vector<Point2f> points; };void mouseHandler(int event, int x, int y, int flags, void* data_ptr) {if ( event == EVENT_LBUTTONDOWN ){userdata *data = ((userdata *) data_ptr);circle(data->im, Point(x,y),3,Scalar(0,255,255), 5, CV_AA);imshow("Image", data->im);if (data->points.size() < 4){data->points.push_back(Point2f(x,y));}} } int main( int argc, char** argv) {// Read in the image.Mat im_src = imread("first-image.jpg");Size size = im_src.size();// Create a vector of points.vector<Point2f> pts_src;pts_src.push_back(Point2f(0,0));pts_src.push_back(Point2f(size.width - 1, 0));pts_src.push_back(Point2f(size.width - 1, size.height -1));pts_src.push_back(Point2f(0, size.height - 1 ));// Destination imageMat im_dst = imread("times-square.jpg");// Set data for mouse handlerMat im_temp = im_dst.clone();userdata data;data.im = im_temp;//show the imageimshow("Image", im_temp);cout << "Click on four corners of a billboard and then press ENTER" << endl;//set the callback function for any mouse eventsetMouseCallback("Image", mouseHandler, &data);waitKey(0);// Calculate Homography between source and destination pointsMat h = findHomography(pts_src, data.points);// Warp source imagewarpPerspective(im_src, im_temp, h, im_temp.size());// Extract four points from mouse dataPoint pts_dst[4];for( int i = 0; i < 4; i++){pts_dst[i] = data.points[i];}// Black out polygonal area in destination image.fillConvexPoly(im_dst, pts_dst, 4, Scalar(0), CV_AA);// Add warped source image to destination image.im_dst = im_dst + im_temp;// Display image.imshow("Image", im_dst);waitKey(0);return 0; }

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总结

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