Module imagingbook.common
Package imagingbook.common.geometry.mappings.nonlinear

Class BilinearMapping2D

java.lang.Object
imagingbook.common.geometry.mappings.nonlinear.BilinearMapping2D
All Implemented Interfaces:
Mapping2D, Cloneable
public class BilinearMapping2D extends Object implements Mapping2D

This class represents a bilinear transformation in 2D with 8 parameters a0, ..., a3, b0, ..., b3 of the form 

 x' = a0 * x + a1 * y + a2 * x * y + a3
 y' = b0 * x + b1 * y + b2 * x * y + b3

Note that this is a non-linear transformation because of the mixed term x * y. See Secs. 21.1.5 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
    Modifier and Type
    Field
    Description
    final double
    a0
     
    final double
    a1
     
    final double
    a2
     
    final double
    a3
     
    final double
    b0
     
    final double
    b1
     
    final double
    b2
     
    final double
    b3
     

  • Constructor Summary

    Constructors
    Constructor
    Description
    BilinearMapping2D(double a0, double a1, double a2, double a3, double b0, double b1, double b2, double b3)
     

  • Method Summary

    Modifier and Type
    Method
    Description
    Pnt2d
    applyTo(Pnt2d pnt)
    Applies this mapping to a single 2D point.
    static BilinearMapping2D
    fromPoints(Pnt2d[] P, Pnt2d[] Q)
    Calculates and returns the bilinear mapping M between two point sets P, Q, with 4 points each, such that q_i = M(p_i).
    String
    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

  • Field Details

    • a0

      public final double a0

    • a1

      public final double a1

    • a2

      public final double a2

    • a3

      public final double a3

    • b0

      public final double b0

    • b1

      public final double b1

    • b2

      public final double b2

    • b3

      public final double b3

  • Constructor Details

    • BilinearMapping2D

      public BilinearMapping2D(double a0, double a1, double a2, double a3, double b0, double b1, double b2, double b3)

  • Method Details

    • fromPoints

      public static BilinearMapping2D fromPoints(Pnt2d[] P, Pnt2d[] Q)
      Calculates and returns the bilinear mapping M between two point sets P, Q, with 4 points each, such that q_i = M(p_i). The inverse mapping is obtained by simply swapping the two point sets.
      Parameters:
      P - the first point sequence
      Q - the second point sequence
      Returns:
      a new bilinear mapping

    • applyTo

      public Pnt2d applyTo(Pnt2d pnt)
      Description copied from interface: Mapping2D
      Applies this mapping to a single 2D point.
      Specified by:
      applyTo in interface Mapping2D
      Parameters:
      pnt - the original point
      Returns:
      the transformed point

    • toString

      public String toString()
      Overrides:
      toString in class Object