fig 1. Left: set 4 points (Left Top, Right Top, Right Bottom, Left Bottom), right:warped image to (0,0) (300,0), (300,300), (0,300)
Firstly, we have to know Homography matrix for image warping.
A homography matrix is that the converting matrix can transform from A plane to B plane in 3D space.
See more detail about Homography in here
http://en.wikipedia.org/wiki/Homography_%28computer_vision%29
So, as the above equation, H matrix convert A matrix to B matrix.
In here, A is left, B is right 4 points in fig 1.
In OpenCV function, findHomography function gives H matrix.
Input parameter is findHomography(A, B). Do not confuse.
After get H matrix, we can warp image using various transform functions in opencv.
In this example, I use warpPerspective function, because rectangle shape is a trapezoidal model.
Input parameter is warpPerspective(Origin_mage, warped_image, H, cv::Size(cols, rows));
see the test video of this example source code in here
In source code, actually to get homography and warping part is 88 ~ 108 lines.
And 109~142 lines are the part for calculated value confirm.
Left code is for interface and selection point ordering.
About interface and 4 points ordering refer to this page
http://study.marearts.com/2015/03/any-4-points-odering-by-lefttop.html
#include < opencv2\opencv.hpp> #include < string> #include < stdio.h> #ifdef _DEBUG #pragma comment(lib, "opencv_core249d.lib") #pragma comment(lib, "opencv_imgproc249d.lib") //MAT processing #pragma comment(lib, "opencv_highgui249d.lib") #pragma comment(lib, "opencv_calib3d249d.lib") #else #pragma comment(lib, "opencv_core249.lib") #pragma comment(lib, "opencv_highgui249.lib") #pragma comment(lib, "opencv_calib3d249.lib") #endif using namespace std; using namespace cv; static void onMouse( int event, int x, int y, int, void* ); Point2f roi4point[4]={0,}; int roiIndex=0; bool oksign = false; Point2f MinDistFind(float x, float y, Point2f* inPoints); void PointOrderbyConner(Point2f* inPoints, int w, int h ); int main() { //image loading //char fileName[100] = "./road-ahead.jpg"; char fileName[100] = "./chess.jpg"; //origin Mat GetImg = imread( fileName ); //copy for drawing Mat RoiImg; //window namedWindow( "set roi by 4 points", 0 ); //mouse callback setMouseCallback( "set roi by 4 points", onMouse, 0 ); //point selection until 4 points setting while(1) { if(oksign == true) //right button click break; //draw point RoiImg = GetImg.clone(); for(int i=0; i< roiIndex; ++i) circle(RoiImg, roi4point[i], 5,CV_RGB(255,0,255),5); imshow("set roi by 4 points", RoiImg); waitKey(10); } printf("points ordered by LT, RT, RB, LB \n"); PointOrderbyConner(roi4point, GetImg.size().width, GetImg.size().height); for(int i=0; i< 4; ++i) { printf("[%d] (%.2lf, %.2lf) \n",i, roi4point[i].x, roi4point[i].y ); } //drwaring RoiImg = GetImg.clone(); string TestStr[4]={"LT","RT","RB","LB"}; putText(RoiImg, TestStr[0].c_str(), roi4point[0], CV_FONT_NORMAL, 1, Scalar(0,0,255),3); circle(RoiImg, roi4point[0], 3,CV_RGB(0,0,255)); int i; for(i=1; i< roiIndex; ++i) { line(RoiImg, roi4point[i-1], roi4point[i], CV_RGB(255,0,0),1 ); circle(RoiImg, roi4point[i], 1,CV_RGB(0,0,255),3); putText(RoiImg, TestStr[i].c_str(), roi4point[i], CV_FONT_NORMAL, 1, Scalar(0,0,255),3); } line(RoiImg, roi4point[0], roi4point[i-1], CV_RGB(255,0,0),1 ); imshow("set roi by 4 points2", RoiImg); //prepare to get homography matrix vector< Point2f> P1; //clicked positions vector< Point2f> P2(4); //user setting positions for(int i=0; i< 4; ++i) P1.push_back( roi4point[i] ); //user setting position P2[0].x = 0; P2[0].y = 0; P2[1].x = 300; P2[1].y = 0; P2[2].x = 300; P2[2].y = 300; P2[3].x = 0; P2[3].y = 300; //get homography Mat H = findHomography(P1, P2); //warping Mat warped_image; warpPerspective(GetImg, warped_image, H,cv::Size(GetImg.cols, GetImg.rows)); rectangle(warped_image, Point(0,0), Point(300,300), CV_RGB(255,0,0) ); imshow("warped_image", warped_image); /////////////////////////// //calculation confirm cout << "h" << endl << H << endl; cout << "size rows and cols " << H.rows << " " << H.cols << endl; Mat A(3,4,CV_64F); //3xN, P1 Mat B(3,4,CV_64F); //3xN, P2 //B = H*A (P2 = h(P1)) for(int i=0; i< 4; ++i) { A.at< double>(0,i) = P1[i].x; A.at< double>(1,i) = P1[i].y; A.at< double>(2,i) = 1; B.at< double>(0,i) = P2[i].x; B.at< double>(1,i) = P2[i].y; B.at< double>(2,i) = 1; } cout << "a" << endl << A << endl; cout << "b" << endl << B << endl; Mat HA = H*A; for(int i=0; i< 4; ++i) { HA.at< double>(0,i) /= HA.at< double>(2,i); HA.at< double>(1,i) /= HA.at< double>(2,i); HA.at< double>(2,i) /= HA.at< double>(2,i); } cout << "HA" << endl << HA << endl; waitKey(0); } void PointOrderbyConner(Point2f* inPoints, int w, int h ) { vector< pair< float, float> > s_point; for(int i=0; i< 4; ++i) s_point.push_back( make_pair(inPoints[i].x, inPoints[i].y) ); //sort sort(s_point.begin(), s_point.end(), [](const pair< float, float>& A, const pair< float, float>& B){ return A.second < B.second; } ); if( s_point[0].first < s_point[1].first ) { inPoints[0].x = s_point[0].first; inPoints[0].y = s_point[0].second; inPoints[1].x = s_point[1].first; inPoints[1].y = s_point[1].second; }else{ inPoints[0].x = s_point[1].first; inPoints[0].y = s_point[1].second; inPoints[1].x = s_point[0].first; inPoints[1].y = s_point[0].second; } if( s_point[2].first > s_point[3].first ) { inPoints[2].x = s_point[2].first; inPoints[2].y = s_point[2].second; inPoints[3].x = s_point[3].first; inPoints[3].y = s_point[3].second; }else{ inPoints[2].x = s_point[3].first; inPoints[2].y = s_point[3].second; inPoints[3].x = s_point[2].first; inPoints[3].y = s_point[2].second; } } static void onMouse( int event, int x, int y, int, void* ) { if( event == CV_EVENT_LBUTTONDOWN && oksign==false) { //4 point select if(roiIndex>=4) { roiIndex=0; for(int i=0; i< 4; ++i) roi4point[i].x = roi4point[i].y =0; } roi4point[roiIndex].x = x; roi4point[roiIndex].y = y; //point coordinate print printf("-(%..2lf,%.2lf), 2:(%.2lf,%.2lf), 3:(%.2lf,%.2lf), 4:(%.2lf,%.2lf)\n", roi4point[0].x, roi4point[0].y,roi4point[1].x, roi4point[1].y,roi4point[2].x, roi4point[2].y,roi4point[3].x, roi4point[3].y ); roiIndex++; } if(event == CV_EVENT_RBUTTONDOWN) { //set point. if(roiIndex == 4) { oksign = true; printf("Warping Start!!!\n"); } } }
This is matlab source code for confirm.
x1 is clicked 4 point in opencv(I did value copy into matlab), matlabH is calculated by homography2d function. (refer to peter homepage for this function detail http://www.csse.uwa.edu.au/~pk/Research/MatlabFns/index.html)
x2 is calculate exactly when matlabH*x1.
I try in opencv with same values of x1, x2.
opencvH is calculated value from opencv source code.
Value is slightly different. Because scaling, OpenCV H and Matlab H will be same when (3,3) value will be divided by equal to 1.
clc; clear all; x1 =[259 126 1; 566 222 1; 400 473 1; 33 305 1]'; x2 =[0 0 1; 300 0 1; 300 300 1; 0 300 1]'; matlabH = homography2d(x1, x2) matlab_X2= matlabH*x1; matlab_X2(:,1) = matlab_X2(:,1)/matlab_X2(3,1); matlab_X2(:,2) = matlab_X2(:,2)/matlab_X2(3,2); matlab_X2(:,3) = matlab_X2(:,3)/matlab_X2(3,3); matlab_X2(:,4) = matlab_X2(:,4)/matlab_X2(3,4); matlab_X2 opencvH = [1.021877004679779, 1.290191078534245, -427.2302201073777; -0.6109166533338892, 1.953660547640664, -87.93381578924605; 5.540800373074552e-006, 0.002051557898988468, 1] opencv_x2 = opencvH * x1; opencv_x2(:,1) = opencv_x2(:,1)/opencv_x2(3,1); opencv_x2(:,2) = opencv_x2(:,2)/opencv_x2(3,2); opencv_x2(:,3) = opencv_x2(:,3)/opencv_x2(3,3); opencv_x2(:,4) = opencv_x2(:,4)/opencv_x2(3,4); opencv_x2
