Opencv日常之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⎤⎦⎥
H = \begin{bmatrix}
h00&h01 & h02 \\
h10& h11 & h12\\
h20& h21& h22
\end{bmatrix}

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);

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);
}

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);

}

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;
}

结果：