boofcv.alg.geo.h

Class HomographyLinear4

java.lang.Object

boofcv.alg.geo.h.HomographyLinear4

public class HomographyLinear4
extends Object

Using linear algebra it computes a planar homography matrix using for or more points. Typically used as an initial estimate for a non-linear optimization.

The algorithm works by solving the equation below:
hat(x₂)*H*x₁ = 0
where hat(x) is the skew symmetric cross product matrix. To solve this equation is is reformatted into A*H^s=0 using the Kronecker product and the null space solved for.

Primarily based on chapter 4 in, "Multiple View Geometry in Computer Vision" 2nd Ed. but uses normalization from "An Invitation to 3-D Vision" 2004.

Author:

Peter Abeles

Field Summary

Fields

Modifier and Type	Field and Description
protected org.ejml.data.DenseMatrix64F	A
protected org.ejml.data.DenseMatrix64F	N1
protected org.ejml.data.DenseMatrix64F	N2
protected org.ejml.factory.SingularValueDecomposition<org.ejml.data.DenseMatrix64F>	svd

Constructor Summary

Constructors

Constructor and Description
HomographyLinear4(boolean normalizeInput) Configure homography calculation

Method Summary

Methods

Modifier and Type	Method and Description
protected boolean	computeH(org.ejml.data.DenseMatrix64F A, org.ejml.data.DenseMatrix64F H) Computes the SVD of A and extracts the homography matrix from its null space
protected void	createA(List<AssociatedPair> points, org.ejml.data.DenseMatrix64F A) Compute the 'A' matrix used to solve for H from un-normalized points.
protected void	createANormalized(List<AssociatedPair> points, org.ejml.data.DenseMatrix64F A) Compute the 'A' matrix used to solve for H from normalized points.
boolean	process(List<AssociatedPair> points, org.ejml.data.DenseMatrix64F foundH) Computes the homography matrix given a set of observed points in two images.
protected void	undoNormalizationH(org.ejml.data.DenseMatrix64F M, org.ejml.data.DenseMatrix64F N1, org.ejml.data.DenseMatrix64F N2) Undoes normalization for a homography matrix.

Methods inherited from class java.lang.Object

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

Field Detail

A

protected org.ejml.data.DenseMatrix64F A

svd

protected org.ejml.factory.SingularValueDecomposition<org.ejml.data.DenseMatrix64F> svd

N1

protected org.ejml.data.DenseMatrix64F N1

N2

protected org.ejml.data.DenseMatrix64F N2

Constructor Detail

HomographyLinear4

public HomographyLinear4(boolean normalizeInput)

Configure homography calculation

Parameters:

normalizeInput - Should image coordinate be normalized? Needed when coordinates are in units of pixels.

Method Detail

process

public boolean process(List<AssociatedPair> points,
              org.ejml.data.DenseMatrix64F foundH)

Computes the homography matrix given a set of observed points in two images. A set of AssociatedPair is passed in. The computed homography 'H' is found such that the attributes 'keyLoc' and 'currLoc' in AssociatedPair refers to x1 and x2, respectively, in the equation below:
x₂ = H*x₁

Parameters:

points - A set of observed image points that are generated from a planar object. Minimum of 4 pairs required.

foundH - Output: Storage for the found solution. 3x3 matrix.

Returns:

true if the calculation was a success.

computeH

protected boolean computeH(org.ejml.data.DenseMatrix64F A,
               org.ejml.data.DenseMatrix64F H)

Computes the SVD of A and extracts the homography matrix from its null space

undoNormalizationH

protected void undoNormalizationH(org.ejml.data.DenseMatrix64F M,
                      org.ejml.data.DenseMatrix64F N1,
                      org.ejml.data.DenseMatrix64F N2)

Undoes normalization for a homography matrix.

createANormalized

protected void createANormalized(List<AssociatedPair> points,
                     org.ejml.data.DenseMatrix64F A)

Compute the 'A' matrix used to solve for H from normalized points.

createA

protected void createA(List<AssociatedPair> points,
           org.ejml.data.DenseMatrix64F A)

Compute the 'A' matrix used to solve for H from un-normalized points.