Main Content

fitgeotform2d

Fit 2-D geometric transformation to control point pairs

Since R2022b

Description

tform = fitgeotform2d(movingPoints,fixedPoints,tformType) fits a linear geometric transformation of type tformType to the control point pairs movingPoints and fixedPoints.

example

tform = fitgeotform2d(movingPoints,fixedPoints,"polynomial",degree) fits a polynomial transformation of degree degree to the control point pairs movingPoints and fixedPoints. Specify the degree of the polynomial transformation degree, which can be 2, 3, or 4.

tform = fitgeotform2d(movingPoints,fixedPoints,"pwl") fits a piecewise linear transformation to the 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 = fitgeotform2d(movingPoints,fixedPoints,"lwm",n) fits a local weighted mean transformation to the 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 function uses the n closest points to infer a second degree polynomial transformation for each control point pair.

Examples

collapse all

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 a similarity geometric transformation that you can use 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

collapse all

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

The transformation type impacts the minimum number of control point pairs. For example, a similarity transformation without reflection requires at least two control point pairs. A fourth order polynomial transformation requires at least 15 control point pairs. For more information, see Transformation Types.

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 "similarity", "reflectivesimilarity", "affine", or "projective".

Data Types: char | string

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

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

Output Arguments

collapse all

Geometric transformation, returned as a geometric transformation object as defined in the table.

Transformation Type

Geometric Transformation Object
"similarity"simtform2d
"reflectivesimilarity"affinetform2d
"affine"affinetform2d
"projective"projtform2d
"polynomial"PolynomialTransformation2D
"pwl"PiecewiseLinearTransformation2D
"lwm"LocalWeightedMeanTransformation2D

More About

collapse all

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

expand all

Version History

Introduced in R2022b

expand all