edu.umich.eecs.april.image

Class Homography33b

java.lang.Object

edu.umich.eecs.april.image.Homography33b

public class Homography33b
extends java.lang.Object

Compute 3x3 homography using Direct Linear Transform y = Hx (y = image coordinates in homogeneous coordinates, H = 3x3 homography matrix, x = homogeneous 2D world coordinates) For each point correspondence, constrain y x Hx = 0 (where x is cross product). This means that they have the same direction, and ignores scale factor. We rewrite this as Ah = 0, where h is the 9x1 column vector of the elements of H. Each point correspondence gives us 3 equations of rank 2. The solution h is the minimum right eigenvector of A, which we can obtain via SVD, USV' = A. h is the right-most column of V'. We will actually maintain A'A internally, which is 9x9 regardless of how many correspondences we're given, and has the same eigenvectors as A.

Field Summary

Fields

Modifier and Type	Field and Description
(package private) double[][]	A
java.util.ArrayList<double[]>	correspondences
(package private) double[][]	H
(package private) Normalize2D	normImage
(package private) Normalize2D	normWorld

Constructor Summary

Constructors

Constructor and Description
Homography33b()

Method Summary

Modifier and Type	Method and Description
void	addCorrespondence(double worldx, double worldy, double imagex, double imagey)
void	addCorrespondences(double[][] worldxy, double[][] imagexy)
(package private) double[][]	compute()
double[][]	getH()
static void	main(java.lang.String[] args)
double[]	project(double worldx, double worldy)

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Field Detail

A

double[][] A

H

double[][] H

correspondences

public java.util.ArrayList<double[]> correspondences

normWorld

Normalize2D normWorld

normImage

Normalize2D normImage

Constructor Detail

Homography33b

public Homography33b()

Method Detail

getH

public double[][] getH()

addCorrespondences

public void addCorrespondences(double[][] worldxy,
                               double[][] imagexy)

addCorrespondence

public void addCorrespondence(double worldx,
                              double worldy,
                              double imagex,
                              double imagey)

compute

double[][] compute()

project

public double[] project(double worldx,
                        double worldy)

main

public static void main(java.lang.String[] args)