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fitgeotrans

(Not recommended) Fit geometric transformation to control point pairs

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fitgeotrans is not recommended. Use the fitgeotform2d function instead. For more information, see Version History.

Syntax

tform = fitgeotrans(movingPoints,fixedPoints,tformType)
tform = fitgeotrans(movingPoints,fixedPoints,"polynomial",degree)
tform = fitgeotrans(movingPoints,fixedPoints,"pwl")
tform = fitgeotrans(movingPoints,fixedPoints,"lwm",n)

Description

tform = fitgeotrans(movingPoints,fixedPoints,tformType) fits a linear geometric transformation of type tformType to control point pairs movingPoints and fixedPoints.

example

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

tform = fitgeotrans(movingPoints,fixedPoints,"pwl") fits a PiecewiseLinearTransformation2D object to control point pairs movingPoints and fixedPoints. This transformation creates a Delaunay triangulation of the fixed control points, and maps moving control points to the corresponding fixed control points. A different affine transformation maps control points in each local region. The mapping is continuous across the control points, but is not continuously differentiable.

tform = fitgeotrans(movingPoints,fixedPoints,"lwm",n) fits a 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.

Examples

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Open Live Script

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

I = checkerboard(40);
J = imrotate(I,30);
imshowpair(I,J,"montage")

Figure contains an axes object. The hidden axes object contains an object of type image.

Define some matching 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 = [41 41; 281 161];
movingPoints = [56 175; 324 160];

Create an affine geometric transformation that can be used to align the two images.

tform = fitgeotform2d(movingPoints,fixedPoints,"similarity");

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. This error comes from a lack of precise correspondence in the control points.

Jregistered = imwarp(J,tform,OutputView=imref2d(size(I)));
imshowpair(I,Jregistered)

Figure contains an axes object. The hidden axes object contains an object of type image.

Input Arguments

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Control points in the moving image, specified as an m-by-2 matrix. Each row specifies the (x, y) coordinate of a control point.

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

Data Types: double | single

Control points in the fixed image, specified as an m-by-2 matrix. Each row specifies the (x, y) coordinate of a control point.

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

Data Types: double | single

Type of linear transformation, specified as "nonreflectivesimilarity", "similarity", "affine", or "projective". For more information, see Transformation Types.

Data Types: char | string

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

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64

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

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64

Output Arguments

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Transformation, returned as a geometric transformation object. The type of object depends on the transformation type.

Transformation Type

Geometric Transformation Object
"nonreflectivesimilarity"affine2d
"similarity"affine2d
"affine"affine2d
"projective"projective2d
"polynomial"PolynomialTransformation2D
"pwl"PiecewiseLinearTransformation2D
"lwm"LocalWeightedMeanTransformation2D

More About

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Transformation Types

The table lists all the transformation types supported by fitgeotrans in order of complexity.

Transformation Type

DescriptionMinimum Number of Control Point PairsExample
"nonreflectivesimilarity"Use this transformation when shapes in the moving image are unchanged, but the image is distorted by some combination of translation, rotation, and scaling. Straight lines remain straight, and parallel lines are still parallel. 2

Original and transformed checkerboard image. The transformed image appears rotated 45 degrees counter-clockwise.

"similarity"Same as "nonreflectivesimilarity" with the addition of optional reflection.3

Original and transformed checkerboard image. The transformed image appears rotated 45 degrees counter-clockwise and reflected along its vertical axis.

"affine"Use this transformation when shapes in the moving image exhibit shearing. Straight lines remain straight, and parallel lines remain parallel, but rectangles become parallelograms.3

Original and transformed checkerboard image. The transformed image appears sheared in the horizontal direction.

"projective"Use this transformation when the scene appears tilted. Straight lines remain straight, but parallel lines converge toward a vanishing point.4

Original and transformed checkerboard image. The transformed image appears tilted out of plane of the image.

"polynomial"Use this transformation when objects in the image are curved. The higher the order of the polynomial, the better the fit, but the result can contain more curves than the fixed image.

6 (order 2)

10 (order 3)

15 (order 4)

Original and transformed checkerboard image. The transformed image appears curved.

"pwl"Use this transformation (piecewise linear) when parts of the image appear distorted differently.4

Original and transformed checkerboard image. The right side of the transformed image appears stretched horizontally.

"lwm"Use this transformation (local weighted mean) when the distortion varies locally and piecewise linear is not sufficient. 6 (12 recommended)

Original and transformed checkerboard image. The transformed image appears nonuniformly stretched.

References

[1] Goshtasby, Ardeshir. “Piecewise Linear Mapping Functions for Image Registration.” Pattern Recognition 19, no. 6 (January 1986): 459–66. https://doi.org/10.1016/0031-3203(86)90044-0.

[2] Goshtasby, Ardeshir. “Image Registration by Local Approximation Methods.” Image and Vision Computing 6, no. 4 (November 1988): 255–61. https://doi.org/10.1016/0262-8856(88)90016-9.

Extended Capabilities

Version History

Introduced in R2013b

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R2022b: Not recommended

Starting in R2022b, most Image Processing Toolbox™ functions create and perform geometric transformations using the premultiply convention. However, the fitgeotrans function estimates linear geometric transformations using the postmultiply convention. Although there are no plans to remove fitgeotrans at this time, you can streamline your geometric transformation workflows by switching to the fitgeotform2d function, which supports the premultiply convention. For more information, see Migrate Geometric Transformations to Premultiply Convention.

To update your code, change instances of the function name fitgeotrans to fitgeotform2d. You must also change the value of tformType for these two transformation types:

  • Replace "nonreflectivesimilarity" with "similarity". The "similarity" transformation type supports translation, rotation, and scaling, and it does not support reflection.

  • Replace "similarity" with "reflectivesimilarity". The "reflectivesimilarity" transformation supports translation, rotation, scaling, and reflection.

You do not need to change the other arguments.

Discouraged UsageRecommended Replacement

This example estimates a 2-D affine transformation from three control point pairs using the fitgeotrans function.

mp = [14.5 44.6; 31.8 34.8; 44.4 96.9];
fp = [10.5 10.5; 30.5 10.5; 10.5 70.5];
tform = fitgeotrans(mp,fp,"affine");

This example estimates a 2-D affine transformation from three control point pairs using the fitgeotform function.

mp = [14.5 44.6; 31.8 34.8; 44.4 96.9];
fp = [10.5 10.5; 30.5 10.5; 10.5 70.5];
tform = fitgeotform2d(mp,fp,"affine");

This example estimates a 2-D affine transformation consisting only of translation, rotation, and isotropic scaling.

mp = [14.5 44.6; 31.8 34.8; 44.4 96.9];
fp = [10.5 10.5; 30.5 10.5; 10.5 70.5];
tform = fitgeotrans(mp,fp,"nonreflectivesimilarity");

This example estimates a 2-D affine transformation consisting only of translation, rotation, and isotropic scaling.

mp = [14.5 44.6; 31.8 34.8; 44.4 96.9];
fp = [10.5 10.5; 30.5 10.5; 10.5 70.5];
tform = fitgeotform2d(mp,fp,"similarity");

This example estimates a 2-D affine transformation consisting only of translation, rotation, isotropic scaling, and reflection.

mp = [14.5 44.6; 31.8 34.8; 44.4 96.9];
fp = [10.5 10.5; 30.5 10.5; 10.5 70.5];
tform = fitgeotrans(mp,fp,"similarity");

This example estimates a 2-D affine transformation consisting only of translation, rotation, isotropic scaling, and reflection.

mp = [14.5 44.6; 31.8 34.8; 44.4 96.9];
fp = [10.5 10.5; 30.5 10.5; 10.5 70.5];
tform = fitgeotform2d(mp,fp,"reflectivesimilarity");

See Also

Topics