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2-D piecewise linear geometric transformation


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


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.



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


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

Object Functions

outputLimitsFind output spatial limits given input spatial limits
transformPointsInverseApply inverse geometric transformation


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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),...
errorInFit =

   1.0e-15 *


Version History

Introduced in R2013b