affinetform2d

2-D affine geometric transformation

Since R2022b. Recommended over affine2d.

Description

An affinetform2d object stores information about a 2-D affine geometric transformation and enables forward and inverse transformations.

Creation

You can create an affinetform2d object in these ways:

• imregtform — Estimate a geometric transformation that maps a moving image to a fixed image using similarity optimization.

• imregcorr — Estimate a geometric transformation that maps a moving image to a fixed image using phase correlation.

• fitgeotform2d — Estimate a geometric transformation that maps pairs of control points between two images.

• randomAffine2d — Create a randomized 2-D affine transformation.

• The affinetform2d function described here.

Syntax

tform = affinetform2d

tform = affinetform2d(affineMat)

tform = affinetform2d(tformIn)

Description

tform = affinetform2d creates an affinetform2d object that performs an identity transformation.

tform = affinetform2d(affineMat) creates an affinetform2d object from the specified 2-D affine transformation matrix, affineMat.

tform = affinetform2d(tformIn) creates an affinetform2d object from another geometric transformation object, tformIn, that represents a valid 2-D affine geometric transformation.

Input Arguments

affineMat — Forward 2-D affine transformation

3-by-3 identity matrix (default) | 3-by-3 numeric matrix | 2-by-3 numeric matrix

Forward 2-D affine transformation, specified as a 3-by-3 numeric matrix. You can also specify affineMat as a 2-by-3 numeric matrix. In this case, the object concatenates the row vector [0 0 1] to the end of the matrix, forming a 3-by-3 matrix.

A valid 2-D affine transformation A has the form:

$${\rm A}=\left[\begin{array}{ccc}a& b& c\\ d& e& f\\ 0& 0& 1\end{array}\right]$$

This argument sets the A property.

Data Types: double | single

tformIn — Affine 2-D geometric transformation

affinetform2d object | rigidtform2d object | simtform2d object | transltform2d object | projtform2d object

Affine 2-D geometric transformation, specified as an affinetform2d object, rigidtform2d object, simtform2d object, transltform2d object, or projtform2d object.

Output Arguments

tform — Affine 2-D geometric transformation

affinetform2d object

Affine 2-D geometric transformation, returned as an affinetform2d object.

Properties

A — Forward 2-D affine transformation

3-by-3 identity matrix (default) | 3-by-3 numeric matrix

Forward 2-D affine transformation, specified as a 3-by-3 numeric matrix. The default value of A is the identity matrix.

The matrix A transforms the point (u, v) in the input coordinate space to the point (x, y) in the output coordinate space using the convention:

$$\left[\begin{array}{c}x\\ y\\ 1\end{array}\right]={\rm A}\times \left[\begin{array}{c}u\\ v\\ 1\end{array}\right]$$

For an affine transformation, A has the form:

$${\rm A}=\left[\begin{array}{ccc}a& b& c\\ d& e& f\\ 0& 0& 1\end{array}\right]$$

Data Types: double | single

Dimensionality — Dimensionality of geometric transformation

Read-only: 2 (default)

This property is read-only.

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

Object Functions

invert	Invert geometric transformation
outputLimits	Find output spatial limits given input spatial limits
transformPointsForward	Apply forward geometric transformation
transformPointsInverse	Apply inverse geometric transformation

Examples

Create 2-D Affine Transformation

Define a 3-by-3 geometric transformation matrix. This example specifies a matrix for an affine transformation consisting of vertical shear and horizontal stretch.

A = [2 0 0; 0.33 1 0; 0 0 1];

Create an affinetform2d object from the transformation matrix.

tform = affinetform2d(A)

tform = 
  affinetform2d with properties:

    Dimensionality: 2

                 A: [2.0000         0         0
                     0.3300    1.0000         0
                          0         0    1.0000]

Read and display an image.

I = imread("pout.tif");
imshow(I)

Apply the geometric transformation to the image, and display the result.

J = imwarp(I,tform);
imshow(J)

Extended Capabilities

C/C++ Code Generation

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

Usage notes and limitations:

• affinetform2d supports the generation of C and C++ code (requires MATLAB^® Coder™). For more information, see Code Generation for Image Processing.

• When generating code, you can only specify singular objects. Arrays of objects are not supported.

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 affine2d

Starting in R2022b, most Image Processing Toolbox™ functions create and perform geometric transformations using the premultiply convention. The affinetform2d object stores information about 2-D affine geometric transformations in a format consistent with the premultiply convention.

The affine2d object is not recommended because it uses the postmultiply convention. Although there are no plans to remove the affine2d object at this time, you can streamline your geometric transformation workflows by switching to the affinetform2d object. For more information, see Migrate Geometric Transformations to Premultiply Convention.