affine3d

3-D affine geometric transformation

Description

An affine3d object stores information about a 3-D affine geometric transformation and enables forward and inverse transformations.

Creation

You can create an affine3d object using the following methods:

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

• randomAffine3d — Creates a randomized 3-D affine transformation

• The affine3d function described here

Syntax

tform = affine3d

tform = affine3d(A)

Description

tform = affine3d creates an affine3d object with default property settings that correspond to the identity transformation.

tform = affine3d(A) sets the property T with a valid affine transformation defined by nonsingular matrix A.

Properties

T — Forward 3-D affine transformation

nonsingular 4-by-4 numeric matrix

Forward 3-D affine transformation, specified as a nonsingular 4-by-4 numeric matrix.

The matrix T uses the convention:

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

where T has the form:

 [a b c 0;
  d e f 0;
  g h i 0;
  j k l 1];

The default of T is the identity transformation.

Data Types: double | single

Dimensionality — Describes the dimensionality of the geometric transformation

3

Describes the dimensionality of the geometric transformation for both input and output points, specified as the value 3.

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 3-D Affine Transformation Object for Anisotropic Scaling

Create an affine3d object that scales a 3-D image by a different factor in each dimension.

Sx = 1.2;
Sy = 1.6;
Sz = 2.4;
tform = affine3d([Sx 0 0 0; 0 Sy 0 0; 0 0 Sz 0; 0 0 0 1])

tform = 
  affine3d with properties:

                 T: [4x4 double]
    Dimensionality: 3

Load a 3-D volume into the workspace.

load('mri');
D = squeeze(D);

Apply the geometric transformation to the image using imwarp.

B = imwarp(D,tform);

Visualize an axial slice through the center of each volume to see the effect of scale translation. Note that the center slice of the transformed volume has a different index than the center slice of the original volume because of the scaling in the z-dimension.

figure
imshowpair(D(:,:,14),B(:,:,33),'montage');

The original image is on the left, and the transformed image is on the right. The transformed image is scaled more in the vertical direction than in the horizontal direction, as expected since Sy is larger than Sx.

Extended Capabilities

C/C++ Code Generation

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

Usage notes and limitations:

• affine3d 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.

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