org.openimaj.math.geometry.transforms

Enum HomographyRefinement

java.lang.Object

java.lang.Enum<HomographyRefinement>

org.openimaj.math.geometry.transforms.HomographyRefinement

All Implemented Interfaces:

Serializable, Comparable<HomographyRefinement>

@Reference(type=Book,
           author={"Hartley, R.~I.","Zisserman, A."},
           title="Multiple View Geometry in Computer Vision",
           year="2004",
           edition="Second",
           publisher="Cambridge University Press, ISBN: 0521540518")
public enum HomographyRefinement
extends Enum<HomographyRefinement>

Refinement of homographies estimates using non-linear optimisation (Levenberg-Marquardt) under different geometric distance/error assumptions.

Author:

Jonathon Hare (jsh2@ecs.soton.ac.uk)

Enum Constant Summary

Enum Constants

Enum Constant and Description
NONE Don't perform any refinement and just return the initial input matrix
SINGLE_IMAGE_TRANSFER The points in the first image are projected by the homography matrix to produce new estimates of the second image points from which the residuals are computed and minimised by the optimiser.
SINGLE_IMAGE_TRANSFER_INVERSE The points in the second image are projected by the inverse homography matrix to produce new estimates of the first image points from which the residuals are computed and minimised by the optimiser.
SYMMETRIC_TRANSFER The points in the first image are projected by the homography matrix to produce new estimates of the second image points and the second image point projected by the inverse homography to produce estimates of the first.

Method Summary

Modifier and Type	Method and Description
abstract double	computeError(Jama.Matrix h, List<? extends IndependentPair<? extends Point2d,? extends Point2d>> data) Compute the error value being optimised between the two point sets.
protected abstract org.apache.commons.math3.analysis.MultivariateMatrixFunction	getJacobianFunction(List<? extends IndependentPair<? extends Point2d,? extends Point2d>> data)
protected abstract org.apache.commons.math3.analysis.MultivariateVectorFunction	getValueFunction(List<? extends IndependentPair<? extends Point2d,? extends Point2d>> data)
abstract Jama.Matrix	refine(Jama.Matrix initial, List<? extends IndependentPair<? extends Point2d,? extends Point2d>> data) Refine an initial guess at the homography that takes the first points in data to the second using non-linear Levenberg Marquardt optimisation.
static HomographyRefinement	valueOf(String name) Returns the enum constant of this type with the specified name.
static HomographyRefinement[]	values() Returns an array containing the constants of this enum type, in the order they are declared.

Methods inherited from class java.lang.Enum

clone, compareTo, equals, finalize, getDeclaringClass, hashCode, name, ordinal, toString, valueOf

Methods inherited from class java.lang.Object

getClass, notify, notifyAll, wait, wait, wait

Enum Constant Detail

NONE

public static final HomographyRefinement NONE

Don't perform any refinement and just return the initial input matrix

SINGLE_IMAGE_TRANSFER

public static final HomographyRefinement SINGLE_IMAGE_TRANSFER

The points in the first image are projected by the homography matrix to produce new estimates of the second image points from which the residuals are computed and minimised by the optimiser. The assumption is that there is only noise in the second image, and that the first image is noise free.

Value and analytic Jacobian implementations auto-generated from Matlab using the following:

 
 syms h0 h1 h2 h3 h4 h5 h6 h7 h8 real
 syms X1 Y1 real
 Mi = [X1 Y1 1]';
 H1 = [h0 h1 h2];
 H2 = [h3 h4 h5];
 H3 = [h6 h7 h8];
 mihat = (1 / (H3*Mi)) * [H1*Mi; H2*Mi];
 J = jacobian(mihat, [h0,h1,h2,h3,h4,h5,h6,h7,h8]);
 ccode(mihat, 'file', 'singleImageTransfer_value.c')
 ccode(J, 'file', 'singleImageTransfer_jacobian.c')
 
 

SINGLE_IMAGE_TRANSFER_INVERSE

public static final HomographyRefinement SINGLE_IMAGE_TRANSFER_INVERSE

The points in the second image are projected by the inverse homography matrix to produce new estimates of the first image points from which the residuals are computed and minimised by the optimiser. Technically, the optimiser optimises the inverse of the initial homography and then inverts the result. The assumption is that there is only noise in the first image.

SYMMETRIC_TRANSFER

public static final HomographyRefinement SYMMETRIC_TRANSFER

The points in the first image are projected by the homography matrix to produce new estimates of the second image points and the second image point projected by the inverse homography to produce estimates of the first. Residuals are computed from both point sets and minimised by the optimiser.

Value and analytic Jacobian implementations auto-generated from Matlab using the following:

 
 syms h0 h1 h2 h3 h4 h5 h6 h7 h8 real
 syms X1 Y1 X2 Y2 real
 M1 = [X1 Y1 1]';
 M2 = [X2 Y2 1]';
 H = [h0 h1 h2; h3 h4 h5; h6 h7 h8];
 Hi = inv(H);
 H1 = H(1,:);
 H2 = H(2,:);
 H3 = H(3,:);
 H1i = Hi(1,:);
 H2i = Hi(2,:);
 H3i = Hi(3,:);
 mihat = [(1 / (H3i*M2)) * [H1i*M2; H2i*M2]; (1 / (H3*M1)) * [H1*M1; H2*M1]];
 J = jacobian(mihat, [h0,h1,h2,h3,h4,h5,h6,h7,h8]);
 ccode(mihat, 'file', 'symImageTransfer_value.c')
 ccode(J, 'file', 'symImageTransfer_jacobian.c')
 
 
 

Method Detail

values

public static HomographyRefinement[] values()

Returns an array containing the constants of this enum type, in the order they are declared. This method may be used to iterate over the constants as follows:

for (HomographyRefinement c : HomographyRefinement.values())
    System.out.println(c);

Returns:

an array containing the constants of this enum type, in the order they are declared

valueOf

public static HomographyRefinement valueOf(String name)

Returns the enum constant of this type with the specified name. The string must match exactly an identifier used to declare an enum constant in this type. (Extraneous whitespace characters are not permitted.)

Parameters:

name - the name of the enum constant to be returned.

Returns:

the enum constant with the specified name

Throws:

IllegalArgumentException - if this enum type has no constant with the specified name

NullPointerException - if the argument is null

getValueFunction

protected abstract org.apache.commons.math3.analysis.MultivariateVectorFunction getValueFunction(List<? extends IndependentPair<? extends Point2d,? extends Point2d>> data)

getJacobianFunction

protected abstract org.apache.commons.math3.analysis.MultivariateMatrixFunction getJacobianFunction(List<? extends IndependentPair<? extends Point2d,? extends Point2d>> data)

computeError

public abstract double computeError(Jama.Matrix h,
                                    List<? extends IndependentPair<? extends Point2d,? extends Point2d>> data)

Compute the error value being optimised between the two point sets. Actual computation depends on the specific HomographyRefinement method in use.

Parameters:

h - the homography

data - the data point-pairs

Returns:

the error value

refine

public abstract Jama.Matrix refine(Jama.Matrix initial,
                                   List<? extends IndependentPair<? extends Point2d,? extends Point2d>> data)

Refine an initial guess at the homography that takes the first points in data to the second using non-linear Levenberg Marquardt optimisation. The initial guess would normally be computed using the direct linear transform (TransformUtilities.homographyMatrixNorm(List)).

Parameters:

initial - the initial estimate (probably from the DLT technique)

data - the pairs of data points

Returns:

the optimised estimate