How do I apply a linear translation to my image using the Image Processing Toolbox 3.0 (R12)?

How do I apply a linear translation to my image using the Image Processing Toolbox 3.0 (R12)?

I have the x and y coordinates of a linear translation that I would like to apply to my image. How do I go about making the calculations?

Answer 1

[MathWorks Support Team]

The following is an example that applies a linear translation to an image. It uses functions from the Image Processing Toolbox 3.0 (R12) and higher.

I = checkerboard; % Load initial figure

tx = 5; % Integer translation along the horizontal component
ty = 3; % Integer translation along the vertical component

% Transform image
t                  = maketform('affine',[1 0 ; 0 1; tx ty]);
bounds        = findbounds(t,[1 1; size(I)]);
bounds(1,:) = [1 1];
J                  = imtransform(I,t,'XData',bounds(:,2)','YData',bounds(:,1)');

figure, imshow(J) % Display transformed image

The behavior when the translation is a non-integer value is more complicated since the image may be resampled. Depending on the interpolation scheme, i.e., the INTERP argument of IMTRANSFORM, the size of the image may increase by 1 in either or both dimensions.

For more information, please see the documentation on MAKETFORM, FINDBOUNDS, and IMTRANSFORM. Pay particular attention to the 'XData' and 'YData' parameters available for IMTRANSFORM.

Without specifying the 'XData' and 'YData' parameters, the output image will look as if no transformation was applied to it. The following extended example describes how MATLAB applies the transformation in more detail by studying the results of a sample image:

First we define the image and the transformation structure:

a = [1 1 1; 2 2 2; 3 3 3];
TRANSLATION = [1 0 0; 0 1 0; 1 0 1];     % Translate positive 1 unit in the x-direction
tform = maketform('affine',TRANSLATION);

In order to see the positive 1 translation in the x-direction reflected in the appearance of the output, you can explicitly tell IMTRANSFORM to use a range in the output space starting at 1 in x. The documentation for IMTRANSFORM describes these under the 'XData' and 'YData' parameters.

For example,

b = imtransform(a,tform,'XData',[1 5],'YData',[1 5])

gives the output

b =

0     1     1     1     0
0     2     2     2     0
0     3     3     3     0
0     0     0     0     0
0     0     0     0     0,

or

b = imtransform(a,tform,'XData',[1 3],'YData',[1 3])

gives the output

b =
0     1     1
0     2     2
0     3     3

preserving the original input size but losing data.

Therefore, you must choose the right parameter values depending on your application.

Please note that MATLAB 6.0 (R12) was originally shipped with the Image Processing Toolbox 2.2.2 (R12). However, owners of this release are eligible to download the Image Processing Toolbox 3.0 (R12). You can start the process of downloading this product at the following URL:

http://www.mathworks.com/web_downloads/

Alternatively, you can receive help for obtaining this version by contacting Customer Service