Documentation

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.

Description

example

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

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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

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

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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

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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