Module imagingbook.common

Package imagingbook.common.geometry.mappings.linear

Class ProjectiveMapping2D

java.lang.Object

imagingbook.common.geometry.mappings.linear.LinearMapping2D

imagingbook.common.geometry.mappings.linear.ProjectiveMapping2D

All Implemented Interfaces:

Inversion, Jacobian, Mapping2D, Cloneable

Direct Known Subclasses:

AffineMapping2D

public class ProjectiveMapping2D
extends LinearMapping2D
implements Jacobian

This class represents a projective transformation in 2D (also known as a "homography"). It can be specified uniquely by four pairs of corresponding points. It can be assumed that every instance of this class is indeed a projective mapping. See Secs. 21.1.4 and 21.3.1 of [1] for details.

[1] W. Burger, M.J. Burge, Digital Image Processing – An Algorithmic Introduction, 3rd ed, Springer (2022).

Field Summary

Fields inherited from class imagingbook.common.geometry.mappings.linear.LinearMapping2D

a00, a01, a02, a10, a11, a12, a20, a21, a22

Constructor Summary

Constructors

Constructor	Description
ProjectiveMapping2D()	Creates the identity mapping.
ProjectiveMapping2D(double[][] A)	Creates a projective mapping from a transformation matrix A, of arbitrary size.
ProjectiveMapping2D(double a00, double a01, double a02, double a10, double a11, double a12, double a20, double a21)	Creates a projective mapping from the specified matrix elements.
ProjectiveMapping2D(LinearMapping2D m)	Creates a projective mapping from any linear mapping.
ProjectiveMapping2D(ProjectiveMapping2D m)	Creates a projective mapping from an existing instance.

Method Summary

Modifier and Type	Method	Description
ProjectiveMapping2D	concat(ProjectiveMapping2D B)	Concatenates this mapping A with another linear mapping B and returns a new mapping C, such that C(x) = B(A(x)).
ProjectiveMapping2D	duplicate()	Returns a copy of this mapping.
static ProjectiveMapping2D	fromPoints(Pnt2d[] P, Pnt2d[] Q)	Creates a projective 2D mapping from two sequences of corresponding points.
ProjectiveMapping2D	getInverse()	Calculates and returns the inverse mapping.
double[][]	getJacobian(Pnt2d xy)	Returns the Jacobian matrix for this mapping, evaluated at the given 2D point.
static void	main(String[] args)	For testing only.

Methods inherited from class imagingbook.common.geometry.mappings.linear.LinearMapping2D

applyTo, concat, concatenate, getTransformationMatrix, normalize, toString

Methods inherited from class java.lang.Object

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

Methods inherited from interface imagingbook.common.geometry.mappings.Mapping2D

applyTo

Constructor Details

ProjectiveMapping2D

public ProjectiveMapping2D()

Creates the identity mapping.

ProjectiveMapping2D

public ProjectiveMapping2D(double[][] A)

Creates a projective mapping from a transformation matrix A, of arbitrary size. All relevant elements of A are inserted into actual 3x3 transformation matrix, except element (2,2) which is ignored and always set to 1 (to keep the transformation projective). If A is larger than 3 x 3, the remaining elements are ignored.

Parameters:

A - a transformation matrix of arbitrary size

ProjectiveMapping2D

public ProjectiveMapping2D(double a00,
 double a01,
 double a02,
 double a10,
 double a11,
 double a12,
 double a20,
 double a21)

Creates a projective mapping from the specified matrix elements.

Parameters:

a00 - matrix element A_00

a01 - matrix element A_01

a02 - matrix element A_02

a10 - matrix element A_10

a11 - matrix element A_11

a12 - matrix element A_12

a20 - matrix element A_20

a21 - matrix element A_21

ProjectiveMapping2D

public ProjectiveMapping2D(LinearMapping2D m)

Creates a projective mapping from any linear mapping. The transformation matrix gets normalized to a22 = 1.

Parameters:

m - a linear mapping

ProjectiveMapping2D

public ProjectiveMapping2D(ProjectiveMapping2D m)

Creates a projective mapping from an existing instance.

Parameters:

m - a projective mapping

Method Details

fromPoints

public static ProjectiveMapping2D fromPoints(Pnt2d[] P,
 Pnt2d[] Q)

Creates a projective 2D mapping from two sequences of corresponding points. If 4 point pairs are specified, the mapping is exact, otherwise a minimum least-squares fit is calculated.

Parameters:

P - the source points

Q - the target points

Returns:

a new projective mapping for the two point sets

concat

public ProjectiveMapping2D concat(ProjectiveMapping2D B)

Concatenates this mapping A with another linear mapping B and returns a new mapping C, such that C(x) = B(A(x)).

Parameters:

B - the second mapping

Returns:

the concatenated mapping

duplicate

public ProjectiveMapping2D duplicate()

Returns a copy of this mapping.

Overrides:

duplicate in class LinearMapping2D

Returns:

a new projective mapping

getInverse

public ProjectiveMapping2D getInverse()

Calculates and returns the inverse mapping. Note that the inverse A' of a projective transformation matrix A is again a linear transformation but its a'2' element is generally not 1. Scaling A' to A'' = A' / a22' yields a projective transformation that reverses A. While A * A' = I, the result of A * A'' is a scaled identity matrix.

Specified by:

getInverse in interface Inversion

Overrides:

getInverse in class LinearMapping2D

Returns:

the inverse projective transformation

getJacobian

public double[][] getJacobian(Pnt2d xy)

Description copied from interface: Jacobian

Returns the Jacobian matrix for this mapping, evaluated at the given 2D point. See Appendix Sec. D.1.1 of [1] for more details.

[1] W. Burger, M.J. Burge, Digital Image Processing – An Algorithmic Introduction, 3rd ed, Springer (2022).

Specified by:

getJacobian in interface Jacobian

Parameters:

xy - the 2D position to calculate the Jacobian for

Returns:

the Jacobian matrix

main

public static void main(String[] args)

For testing only.

Parameters:

args - ignored