Main Content

geometricTransform3d

3-D geometric transformation object

Description

A geometricTransform3d object defines a custom 3-D geometric transformation using point-wise mapping functions.

Creation

Description

example

tform = geometricTransform3d(inverseFcn) creates a geometricTransform3d object and sets the value of inverse mapping function property, InverseFcn to inverseFcn.

tform = geometricTransform3d(inverseFcn,forwardFcn) also sets the value of forward mapping function property, ForwardFcn to forwardFcn.

Properties

expand all

Inverse mapping function, specified as a function handle. The function must accept and return coordinates as an n-by-3 numeric matrix representing the packed (x,y,z) coordinates of n points.

For more information about function handles, see Create Function Handle.

Example: ifcn = @(xyz) [xyz(:,1).^2,xyz(:,2).^2,xyz(:,3).^2];

Forward mapping function, specified as a function handle. The function must accept and return coordinates as an n-by-3 numeric matrix representing the packed (x,y,z) coordinates of n points.

For more information about function handles, see Create Function Handle.

Example: ffcn = @(xyz) [sqrt(xyz(:,1)),sqrt(xyz(:,2)),sqrt(xyz(:,3))];

Object Functions

outputLimitsFind output spatial limits given input spatial limits
transformPointsForwardApply forward geometric transformation
transformPointsInverseApply inverse geometric transformation

Examples

collapse all

Specify the packed (x,y,z) coordinates of five input points. The packed coordinates are stored as a 5-by-3 matrix, where the first, second, and third columns contain the x-, y-, and z- coordinates,respectively.

XYZ = [5 25 20;10 5 25;15 10 5;20 15 10;25 20 15];

Define an inverse mapping function that accepts and returns points in packed (x,y,z) format.

inverseFcn = @(c) [c(:,1)+c(:,2),c(:,1)-c(:,2),c(:,3).^2];

Create a 3-D geometric transformation object, tform, that stores this inverse mapping function.

tform = geometricTransform3d(inverseFcn)
tform = 
  geometricTransform3d with properties:

        InverseFcn: @(c)[c(:,1)+c(:,2),c(:,1)-c(:,2),c(:,3).^2]
        ForwardFcn: []
    Dimensionality: 3

Apply the inverse transformation of this 3-D geometric transformation to the input points.

UVW = transformPointsInverse(tform,XYZ)
UVW = 5×3

    30   -20   400
    15     5   625
    25     5    25
    35     5   100
    45     5   225

Specify the x-, y- and the z-coordinate vectors of five points to transform.

x = [3 5 7 9 11];
y = [2 4 6 8 10];
z = [5 9 13 17 21];

Define the inverse and forward mapping functions that accept and return points in packed (x,y,z) format.

inverseFcn = @(c)[c(:,1).^2,c(:,2).^2,c(:,3).^2];
forwardFcn = @(c)[sqrt(c(:,1)),sqrt(c(:,2)),sqrt(c(:,3))];

Create a 3-D geometric transformation object, tform, that stores these inverse and forward mapping functions.

tform = geometricTransform3d(inverseFcn,forwardFcn)
tform = 
  geometricTransform3d with properties:

        InverseFcn: @(c)[c(:,1).^2,c(:,2).^2,c(:,3).^2]
        ForwardFcn: @(c)[sqrt(c(:,1)),sqrt(c(:,2)),sqrt(c(:,3))]
    Dimensionality: 3

Apply the inverse transformation of this 3-D geometric transformation to the input points.

[u,v,w] = transformPointsInverse(tform,x,y,z)
u = 1×5

     9    25    49    81   121

v = 1×5

     4    16    36    64   100

w = 1×5

    25    81   169   289   441

Apply the forward geometric transform to the transformed points u, v, and w.

[x,y,z] = transformPointsForward(tform,u,v,w)
x = 1×5

     3     5     7     9    11

y = 1×5

     2     4     6     8    10

z = 1×5

     5     9    13    17    21

Define an inverse mapping function that performs reflection about horizontal axis. The function must accept and return packed (x,y,z) coordinates, where the first, second, and third columns contain the x-, y-, and z-coordinates, respectively.

inverseFcn = @(xyz)[xyz(:,1),-xyz(:,2),xyz(:,3)];

Create a 3-D geometric transformation object, tform, that stores this inverse mapping function.

tform = geometricTransform3d(inverseFcn)
tform = 
  geometricTransform3d with properties:

        InverseFcn: @(xyz)[xyz(:,1),-xyz(:,2),xyz(:,3)]
        ForwardFcn: []
    Dimensionality: 3

Load and display an MRI volume to be transformed.

s = load('mri');
mriVolume = squeeze(s.D);

Use imwarp to apply the inverse geometric transform to the input MRI volume.

[mriVolumeTransformed] = imwarp(mriVolume,tform,'nearest','SmoothEdges',true);

Display the image slices from the input MRI volume as montage.

montage(mriVolume,'Size',[4 8],'BackgroundColor','w')
title('Image Slices from 3-D MRI','FontSize',14)

Display the image slices from the transformed MRI volume as a montage. The transformed image slices are the reflection of the input image slices across the x-axis.

montage(mriVolumeTransformed,'Size',[4 8],'BackgroundColor','w')
title('Image Slices from Inverse Geometric Transformation of 3-D MRI','FontSize',14)

Version History

Introduced in R2018b