fitgeotform2d

Fit 2-D geometric transformation to control point pairs

Since R2022b

Syntax

tform = fitgeotform2d(movingPoints,fixedPoints,tformType)

tform = fitgeotform2d(movingPoints,fixedPoints,"polynomial",degree)

tform = fitgeotform2d(movingPoints,fixedPoints,"pwl")

tform = fitgeotform2d(movingPoints,fixedPoints,"lwm",n)

Description

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

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

Create Similarity Geometric Transformation from Control Point Pairs

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

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

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)

Input Arguments

movingPoints — Control points in moving image

m-by-2 matrix

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

fixedPoints — Control points in fixed image

m-by-2 matrix

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

tformType — Type of linear transformation

"similarity" | "reflectivesimilarity" | "affine" | "projective"

Type of linear transformation, specified as "similarity", "reflectivesimilarity", "affine", or "projective".

Data Types: char | string

degree — Degree of polynomial

2 | 3 | 4

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

n — Number of points to use in local weighted mean calculation

positive integer

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

tform — Geometric transformation

geometric transformation object

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

Transformation Types

The table lists the transformation types supported by fitgeotform2d in order of complexity.

Transformation Type	Description	Minimum Number of Control Point Pairs	Example
"similarity"	Use this transformation when shapes in the moving image are unchanged, but the image is distorted by some combination of translation, rotation, and isotropic scaling. Straight lines remain straight, and parallel lines are still parallel.	2
"reflectivesimilarity"	Same as "similarity", with the addition of optional reflection.	3
"affine"	Use this transformation when shapes in the moving image exhibit shearing or anisotropic scaling. Straight lines remain straight, and parallel lines remain parallel, but rectangles become parallelograms.	3
"projective"	Use this transformation when the scene appears tilted. Straight lines remain straight, but parallel lines converge toward a vanishing point.	4
"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)
"pwl"	Use this transformation (piecewise linear) when parts of the image appear distorted differently from each other.	4
"lwm"	Use this transformation (local weighted mean) when the distortion varies locally and piecewise linear is not sufficient.	6 (12 recommended)

The first five transformations, "similarity", "reflectivesimilarity", "affine", "projective", and "polynomial", are global transformations. In these transformations, a single mathematical expression applies to an entire image. The last two transformations, "pwl" (piecewise linear) and "lwm" (local weighted mean), are local transformations. In these transformations, different mathematical expressions apply to different regions within an image. When exploring how different transformations affect the images you are working with, try the global transformations first. If these transformations are not satisfactory, try the local transformations: the piecewise linear transformation first, and then the local weighted mean transformation.

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

C/C++ Code Generation

Generate C and C++ code using MATLAB® Coder™.

Usage notes and limitations:

• fitgeotform2d supports the generation of C code (requires MATLAB^® Coder™). For more information, see Code Generation for Image Processing.

• The tformType argument must be a compile-time constant.

• Only these transformation types are supported: "similarity", "reflectivesimilarity", "affine", and "projective".

GPU Code Generation

Generate CUDA® code for NVIDIA® GPUs using GPU Coder™.

Usage notes and limitations:

• The tformType argument must be a compile-time constant.

• Only these transformation types are supported: "similarity", "reflectivesimilarity", "affine", and "projective".

Thread-Based Environment

Run code in the background using MATLAB® backgroundPool or accelerate code with Parallel Computing Toolbox™ ThreadPool.

This function fully supports thread-based environments. For more information, see Run MATLAB Functions in Thread-Based Environment.

Version History

Introduced in R2022b

R2022b: Recommended over fitgeotrans

Starting in R2022b, most Image Processing Toolbox™ functions create and perform geometric transformations using the premultiply convention. However, the fitgeotrans function estimates geometric transformations using the old 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.

fitgeotform2d and fitgeotrans have different values of the tformType argument for these two transformation types:

• The "similarity" transformation type for the fitgeotform2d function is equivalent to the "nonreflectivesimilarity" transformation type for the fitgeotrans function. The "similarity" type supports translation, rotation, and scaling.

• The "reflectivesimilarity" transformation type for the fitgeotform2d function is equivalent to the "similarity" transformation type for the fitgeotrans function. The "reflectivesimilarity" transformation type supports translation, rotation, scaling, and reflection.