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

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.
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()
{
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

```
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