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Fit geometric transformation to control point pairs


  • tform = fitgeotrans(movingPoints,fixedPoints,transformationType)
  • tform = fitgeotrans(movingPoints,fixedPoints,'polynomial',degree)
  • tform = fitgeotrans(movingPoints,fixedPoints,'pwl')
  • tform = fitgeotrans(movingPoints,fixedPoints,'lwm',n)



tform = fitgeotrans(movingPoints,fixedPoints,transformationType) takes the pairs of control points, movingPoints and fixedPoints, and uses them to infer the geometric transformation, specified by transformationType.

tform = fitgeotrans(movingPoints,fixedPoints,'polynomial',degree) fits an images.geotrans.PolynomialTransformation2D object to control point pairs movingPoints and fixedPoints. Specify the degree of the polynomial transformation degree, which can be 2, 3, or 4.

tform = fitgeotrans(movingPoints,fixedPoints,'pwl') fits an images.geotrans.PiecewiseLinearTransformation2D object to control point pairs movingPoints and fixedPoints. This transformation maps control points by breaking up the plane into local piecewise-linear regions in which a different affine transformation maps control points in each local region.

tform = fitgeotrans(movingPoints,fixedPoints,'lwm',n) fits an images.geotrans.LocalWeightedMeanTransformation2D object to control point pairs movingPoints and fixedPoints. The local weighted mean transformation creates a mapping, by inferring a polynomial at each control point using neighboring control points. The mapping at any location depends on a weighted average of these polynomials. The n closest points are used to infer a second degree polynomial transformation for each control point pair.

Code Generation support: Yes.

MATLAB Function Block support: Yes.


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This example shows how to create a geometric transformation that can be used to align two images.

Create a checkerboard image and rotate it to create a misaligned image.

I = checkerboard;
J = imrotate(I,30);

Define some control points on the fixed image (the checkerboard) and moving image (the rotated checkerboard). You can define points interactively using the Control Point Selection tool.

fixedPoints  = [11 11; 41 71];
movingPoints = [14 44; 70 81];

Create a geometric transformation that can be used to align the two images, returned as an affine2d geometric transformation object.

tform = fitgeotrans(movingPoints,fixedPoints,'NonreflectiveSimilarity')
tform = 

  affine2d with properties:

                 T: [3×3 double]
    Dimensionality: 2

Use the tform estimate to resample the rotated image to register it with the fixed image. The regions of color (green and magenta) in the false color overlay image indicate error in the registration due to lack of precise correspondence in the control points.

Jregistered = imwarp(J,tform,'OutputView',imref2d(size(I)));
falsecolorOverlay = imfuse(I,Jregistered);

Recover angle and scale of the transformation by checking how a unit vector parallel to the x-axis is rotated and stretched.

u = [0 1];
v = [0 0];
[x, y] = transformPointsForward(tform, u, v);
dx = x(2) - x(1);
dy = y(2) - y(1);
angle = (180/pi) * atan2(dy, dx)
scale = 1 / sqrt(dx^2 + dy^2)
angle =


scale =


Input Arguments

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X and Y coordinates of control points in the image you want to transform, specified as an m-by-2 double matrix.

Example: fixedPoints = [11 11; 41 71];

Data Types: double

X and Y coordinates of control points in the base image, specified as an m-by-2 double matrix.

Example: movingPoints = [14 44; 70 81];

Data Types: double

Type of transformation, specified as one of the following:

'affine'Affine transformation
'nonreflectivesimilarity'Nonreflective similarity
'projective'Projective transformation

Example: tform = fitgeotrans(movingPoints,fixedPoints,'nonreflectivesimilarity');

Data Types: char

Degree of the polynomial, specified as the integer 2, 3, or 4.

Data Types: double

Number of points to use in local weighted mean calculation, specified as a numeric value. n can be as small as 6, but making n small risks generating ill-conditioned polynomials

Data Types: double

Output Arguments

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Transformation, specified as a transformation object. The type of object depends on the transformation type. For example, if you specify the transformation type 'affine', tform is an affine2d object. If you specify 'pwl', tform is an image.geotrans.PiecewiseLinearTransformation2d object.

More About

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Code Generation

This function supports the generation of C code using MATLAB® Coder™. For more information, see Code Generation for Image Processing.

When generating code, the transformationType argument must be a compile-time constant and only the following transformation types are supported: 'nonreflectivesimilarity', 'similarity', 'affine', and'projective'.

MATLAB Function Block

You can use this function in the MATLAB Function Block in Simulink.


[1] Goshtasby, Ardeshir, "Piecewise linear mapping functions for image registration," Pattern Recognition, Vol. 19, 1986, pp. 459-466.

[2] Goshtasby, Ardeshir, "Image registration by local approximation methods," Image and Vision Computing, Vol. 6, 1988, pp. 255-261.

Introduced in R2013b

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