Opencv中Homography

1. 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 image    vector<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 Homography    Mat h = findHomography(pts_src, pts_dst);    // Output image    Mat im_out;    // Warp source image to destination based on homography    warpPerspective(im_src, im_out, h, im_dst.size());    // Display images    imshow("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 3/4    Size 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 event    Mat 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 event    setMouseCallback("Image", mouseHandler, &data);    waitKey(0);    // Calculate the homography    Mat h = findHomography(data.points, pts_dst);    // Warp source image to destination    warpPerspective(im_src, im_dst, h, size);    // Show image    imshow("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 image    Mat im_dst = imread("times-square.jpg");    // Set data for mouse handler    Mat im_temp = im_dst.clone();    userdata data;    data.im = im_temp;    //show the image    imshow("Image", im_temp);    cout << "Click on four corners of a billboard and then press ENTER" << endl;    //set the callback function for any mouse event    setMouseCallback("Image", mouseHandler, &data);    waitKey(0);    // Calculate Homography between source and destination points    Mat h = findHomography(pts_src, data.points);    // Warp source image    warpPerspective(im_src, im_temp, h, im_temp.size());    // Extract four points from mouse data    Point 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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结果：