affine2d

(Not recommended) 2-D affine geometric transformation using postmultiply convention

affine2d is not recommended. Use the affinetform2d object instead. For more information, see Version History.

Description

An affine2d object stores information about a 2-D affine geometric transformation using the postmultiply convention, and enables forward and inverse transformations.

Creation

Syntax

tform = affine2d

tform = affine2d(t)

Description

tform = affine2d creates an affine2d object with default property settings that correspond to the identity transformation.

tform = affine2d(t) sets the property T as the specified 2-D affine transformation matrix t.

Properties

T — Forward 2-D affine transformation

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

Forward 2-D affine transformation, specified as a nonsingular 3-by-3 numeric matrix. The matrix T uses the convention:

[x y 1] = [u v 1] * T

where T has the form:

 [a b 0;
  c d 0;
  e f 1];

The default of T is the identity transformation.

Data Types: double | single

Dimensionality — Dimensionality of geometric transformation

2 (default)

This property is read-only.

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

Object Functions

invert	Invert geometric transformation
isRigid	Determine if geometric transformation is rigid transformation
isSimilarity	Determine if geometric transformation is similarity transformation
isTranslation	Determine if geometric transformation is pure translation
outputLimits	Find output spatial limits given input spatial limits
transformPointsForward	Apply forward geometric transformation
transformPointsInverse	Apply inverse geometric transformation

Examples

Define 2-D Affine Transformation from Transformation Matrix

Create an affine2d object that defines a 30 degree rotation in the counterclockwise direction around the origin.

theta = 30;
tform = affine2d([ ...
    cosd(theta) sind(theta) 0;...
    -sind(theta) cosd(theta) 0; ...
    0 0 1])

tform = 
  affine2d with properties:

                 T: [3x3 double]
    Dimensionality: 2

Apply the forward geometric transformation to a point (10,0).

[x,y] = transformPointsForward(tform,10,0)

x = 
8.6603

y = 
5

Validate the transformation by plotting the original point (in blue) and the transformed point (in red).

plot(10,0,'bo',x,y,'ro')
axis([0 12 0 12])
axis square

Transform Image Using 2-D Affine Transformation Object

Read an image into the workspace.

A = imread('pout.tif');

Create an affine2d object that defines an affine geometric transformation. This example combines vertical shear and horizontal stretch.

tform = affine2d([2 0.33 0; 0 1 0; 0 0 1])

tform = 
  affine2d with properties:

                 T: [3x3 double]
    Dimensionality: 2

Apply the geometric transformation to the image using imwarp.

B = imwarp(A,tform);

Display the resulting image.

figure
imshow(B);
axis on equal;

Extended Capabilities

C/C++ Code Generation

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

Usage notes and limitations:

• affine2d supports the generation of 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.

GPU Code Generation

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

Usage notes and limitations:

• 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 R2013a

R2022b: Not recommended

Starting in R2022b, most Image Processing Toolbox™ functions create and perform geometric transformations using the premultiply convention. Accordingly, 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, 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 affine2d to affinetform2d.

• Specify the transformation matrix as the transpose of the matrix T, where T is either the value of the T property of the affine2d object or the transformation matrix used to create the affine2d object.

Discouraged Usage	Recommended Replacement
This example creates an affine2d object from transformation matrix T in the postmultiply convention. T = [2 0.33 0; 0 1 0; 0 0 1]; tformPost = affine2d(T);	This example creates an affinetform2d object from the transpose of the transformation matrix T. T = [2 0.33 0; 0 1 0; 0 0 1]; tform = affinetform2d(T'); This example starts with an affine2d object called tformPost and creates an affinetform2d object from the transpose of the T property of tformPost. T = tformPost.T; tform = affinetform2d(T');

R2022b: Fewer functions create affine2d objects

You can no longer create an affine2d object using the imregtform, imregcorr, fitgeotrans, or randomAffine2d functions. These functions return 2-D affine transformations as an affinetform2d object, rigidtform2d object, simtform2d object, or transltform2d object.

R2021b: Support for thread-based environments

affine2d now supports thread-based environments.