How to compute Homography for Triangle and Hexagon? - c++

Question

I'm computing Homography for different shapes i.e (QUAD, HEXAGON, TRIANGLE). This logic is working fine for QUAD but not working for Hexagon or triangle. Looks like there is a problem with my matrix calculation logic. Can you pls review?
Here is my code:
#import <Foundation/Foundation.h>
#import "EigenWrapper.h"
#import <Eigen/Dense>
#implementation EigenWrapper
constexpr double W = 800;
constexpr double H = 800;
constexpr size_t NQUAD = 4;
constexpr size_t NTRI = 3;
constexpr size_t NHEX = 6;
Eigen::Matrix3d Homography;
//QUAD
Eigen::Matrix<double,2,NQUAD> DSTQUAD;
Eigen::Matrix<double,2*NQUAD,9> AQUAD;
Eigen::Matrix<double,2,NQUAD> SRCQUAD;
//Triangle
Eigen::Matrix<double,2,NTRI> DSTTRI;
Eigen::Matrix<double,2*NTRI,9> ATRI;
Eigen::Matrix<double,2,NTRI> SRCTRI;
//HEXA
Eigen::Matrix<double,2,NHEX> DSTHEX;
Eigen::Matrix<double,2*NHEX,9> AHEX;
Eigen::Matrix<double,2,NHEX> SRCHEX;
- (instancetype)initEigenWrapper:(size_t)sides {
return self;
}
+ (double*)eigenGetHomogprahyMatrix :(double)topLeftX : (double)topLeftY :(double)topRightX :(double)topRightY :(double)bottomLeftX :(double)bottomLeftY :(double)bottomRightX :(double)bottomRightY {
SRCQUAD <<
0, W, 0, W,
0, 0, H, H;
DSTQUAD <<
topLeftX, topRightX, bottomLeftX, bottomRightX,
topLeftY, topRightY,bottomLeftY, bottomRightY;
AQUAD.setZero();
for (size_t i = 0; i < NQUAD; i++) {
const double x_ = DSTQUAD(0,i), y_ = DSTQUAD(1,i);
const double x = SRCQUAD(0,i), y = SRCQUAD(1,i);
AQUAD(2*i,0) = AQUAD(2*i+1,3) = x_;
AQUAD(2*i,1) = AQUAD(2*i+1,4) = y_;
AQUAD(2*i,2) = AQUAD(2*i+1,5) = 1;
AQUAD(2*i,6) = -x*x_;
AQUAD(2*i,7) = -x*y_;
AQUAD(2*i,8) = -x;
AQUAD(2*i+1,6) = -y*x_;
AQUAD(2*i+1,7) = -y*y_;
AQUAD(2*i+1,8) = -y;
}
Eigen::JacobiSVD<Eigen::Matrix<double,2*NQUAD,9>> svd(AQUAD, Eigen::ComputeFullV);
Eigen::Matrix<double,9,1> h = svd.matrixV().col(8);
Homography <<
h(0), h(1), h(2),
h(3), h(4), h(5),
h(6), h(7), h(8);
for (int i = 0; i < 10; i++) {
printf("\n: %f", Homography.array().data()[i]);
}
return Homography.array().data();
}
+ (double *)eigenGetHomogprahyTriangle :(double)middleX :(double)middleY :(double)bottomLeftX :(double)bottomLeftY :(double)bottomRightX :(double)bottomRightY {
SRCTRI <<
0, W, W/2,
H, H, 0;
DSTTRI <<
bottomLeftX, bottomRightX, middleX,
bottomLeftY, bottomRightY, middleY;
ATRI.setZero();
for (size_t i = 0; i < NTRI; i++) {
const double x_ = DSTTRI(0,i), y_ = DSTTRI(1,i);
const double x = SRCTRI(0,i), y = SRCTRI(1,i);
ATRI(2*i,0) = ATRI(2*i+1,3) = x_;
ATRI(2*i,1) = ATRI(2*i+1,4) = y_;
ATRI(2*i,2) = ATRI(2*i+1,5) = 1;
ATRI(2*i,6) = -x*x_;
ATRI(2*i,7) = -x*y_;
ATRI(2*i,8) = -x;
ATRI(2*i+1,6) = -y*x_;
ATRI(2*i+1,7) = -y*y_;
ATRI(2*i+1,8) = -y;
}
Eigen::JacobiSVD<Eigen::Matrix<double,2*NTRI,9>> svd(ATRI, Eigen::ComputeFullV);
Eigen::Matrix<double,9,1> h = svd.matrixV().col(8);
Homography <<
h(0), h(1), h(2),
h(3), h(4), h(5),
h(6), h(7), h(8);
for (int i = 0; i < 10; i++) {
printf("\n: %f", Homography.array().data()[i]);
}
return Homography.array().data();
}
+ (double *)eigenGetHomogprahyMatrixHexa:(double)topLeftX :(double)topLeftY :(double)topRightX :(double)topRightY :(double)middleLeftX :(double)middleLeftY :(double)middleRightX :(double)middleRightY :(double)bottomLeftX :(double)bottomLeftY :(double)bottomRightX :(double)bottomRightY {
SRCHEX <<
0, W, W/2, 0, W, W,
0, 0, H/2, H, H, H/2;
DSTHEX <<
topLeftX, topRightX, middleLeftX,bottomLeftX, bottomRightX, middleRightX,
topLeftY, topRightY, middleLeftY, bottomLeftY, bottomRightY, middleRightY;
AHEX.setZero();
for (size_t i = 0; i < NHEX; i++) {
const double x_ = DSTHEX(0,i), y_ = DSTHEX(1,i);
const double x = SRCHEX(0,i), y = SRCHEX(1,i);
AHEX(2*i,0) = AHEX(2*i+1,3) = x_;
AHEX(2*i,1) = AHEX(2*i+1,4) = y_;
AHEX(2*i,2) = AHEX(2*i+1,5) = 1;
AHEX(2*i,6) = -x*x_;
AHEX(2*i,7) = -x*y_;
AHEX(2*i,8) = -x;
AHEX(2*i+1,6) = -y*x_;
AHEX(2*i+1,7) = -y*y_;
AHEX(2*i+1,8) = -y;
}
Eigen::JacobiSVD<Eigen::Matrix<double,2*NHEX,9>> svd(AHEX, Eigen::ComputeFullV);
Eigen::Matrix<double,9,1> h = svd.matrixV().col(8);
Homography <<
h(0), h(1), h(2),
h(3), h(4), h(5),
h(6), h(7), h(8);
for (int i = 0; i < 10; i++) {
printf("\n: %f", Homography.array().data()[i]);
}
return Homography.array().data();
}
#end
After computing homogrphy, I'm just wrapping the texture image with OpenCV. I'm also want to change the background of the out image from black to transparent.
cv::Mat sourceImage = imread("texture.png", cv::IMREAD_COLOR);
for (int i=0; i<9; i++) {
printf(":- %.7f", homographyMatrix[i]);
}
cv::Matx33d H(homographyMatrix[0], homographyMatrix[3], homographyMatrix[6],
homographyMatrix[1], homographyMatrix[4], homographyMatrix[7],
homographyMatrix[2], homographyMatrix[5], homographyMatrix[8]);
cv::Mat destImage;
cv::warpPerspective(sourceImage, destImage, H, cv::Size(width,height),
cv::INTER_LINEAR | cv::WARP_INVERSE_MAP);
UIImage * deImage = MatToUIImage(destImage);
Here is the outPut for Hexagon
Here is the outPut for Triangle
Thanks