Image warping (using opencv findHomography, warpPerspective)

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

https://www.youtube.com/watch?v=UszvePGFuMQ

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