affine2d

2-D affine geometric transformation

Description

An affine2d object stores information about a 2-D affine geometric transformation and enables forward and inverse transformations.

Creation

You can create an affine2d object using the following methods:

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

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

• fitgeotrans — Estimates a geometric transformation that maps pairs of control points between two images

• randomAffine2d — Creates a randomized 2-D affine transformation

• The affine2d function described here

Syntax

tform = affine2d

tform = affine2d(A)

Description

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

tform = affine2d(A) sets the property T with a valid affine transformation defined by nonsingular matrix A.

Properties

T — Forward 2-D affine transformation

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 the geometric transformation

2

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 transformation is rigid transformation
isSimilarity	Determine if transformation is similarity transformation
isTranslation	Determine if 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 Object for Rotation

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:

    Dimensionality: 2
                 T: [3x3 double]

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).

figure
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:

    Dimensionality: 2
                 T: [3x3 double]

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.