PiecewiseLinearTransformation2D

2-D piecewise linear geometric transformation

Description

A PiecewiseLinearTransformation2D object encapsulates a 2-D piecewise linear geometric transformation.

Creation

You can create a PiecewiseLinearTransformation2D object using the following methods:

• The fitgeotrans function, which estimates a geometric transformation that maps pairs of control points between two images.

• The images.geotrans.PiecewiseLinearTransformation2D function described here. This function creates a PiecewiseLinearTransformation2D object using coordinates of fixed points and moving points.

Syntax

tform = images.geotrans.PiecewiseLinearTransformation2D(movingPoints,fixedPoints)

Description

tform = images.geotrans.PiecewiseLinearTransformation2D(movingPoints,fixedPoints) creates a PiecewiseLinearTransformation2D object given control point coordinates in movingPoints and fixedPoints, which define matched control points in the moving and fixed images, respectively.

Input Arguments

movingPoints — x- and y-coordinates of control points in the moving image

m-by-2 matrix

x- and y-coordinates of control points in the moving image, specified as an m-by-2 matrix. The number of control points m must be greater than or equal to n.

Data Types: double | single

fixedPoints — x- and y-coordinates of control points in the fixed image

m-by-2 matrix

x- and y-coordinates of control points in the fixed image, specified as an m-by-2 matrix. The number of control points m must be greater than or equal to n.

Data Types: double | single

Properties

Dimensionality — Dimensionality of the geometric transformation

2

Dimensionality of the geometric transformation for both input and output points, specified as the value 2.

Object Functions

outputLimits	Find output spatial limits given input spatial limits
transformPointsInverse	Apply inverse geometric transformation

Examples

Fit Set of Control Points Related by Affine Transformation

Fit a piecewise linear transformation to a set of fixed and moving control points that are actually related by a single global affine2d transformation across the domain.

Create a 2D affine transformation.

theta = 10;
tformAffine = affine2d([cosd(theta) -sind(theta) 0; sind(theta) cosd(theta) 0; 0 0 1])

tformAffine = 

  affine2d with properties:

                 T: [3x3 double]
    Dimensionality: 2

Arbitrarily choose 6 pairs of control points.

fixedPoints = [10 20; 10 5; 2 3; 0 5; -5 3; -10 -20];

Apply forward geometric transformation to map fixed points to obtain effect of fixed and moving points that are related by some geometric transformation.

movingPoints = transformPointsForward(tformAffine,fixedPoints)

movingPoints =

   13.3210   17.9597
   10.7163    3.1876
    2.4906    2.6071
    0.8682    4.9240
   -4.4031    3.8227
  -13.3210  -17.9597

Estimate piecewise linear transformation that maps movingPoints to fixedPoints.

tformPiecewiseLinear = images.geotrans.PiecewiseLinearTransformation2D(movingPoints,fixedPoints)

tformPiecewiseLinear = 

  PiecewiseLinearTransformation2D with properties:

    Dimensionality: 2

Verify the fit of the PiecewiseLinearTransformation2D object at the control points.

movingPointsComputed = transformPointsInverse(tformPiecewiseLinear,fixedPoints);
 
errorInFit = hypot(movingPointsComputed(:,1)-movingPoints(:,1),...
                   movingPointsComputed(:,2)-movingPoints(:,2))

errorInFit =

   1.0e-15 *

         0
         0
    0.4441
         0
         0
         0