3D Rotation around generic axis

I want to rotate an image around a the y axis using Matlab, I expect to have a 3 dimensional matrix as output and each plane of the matrix should contain a small strip of the image.

I insert my image in a 3D array and then I apply the transformation matrix using affine3d and imwarp commands.

This is an example:

c = cos(theta); s=sin(theta);
ux =0; uy=1; uz=0;
tx =0; ty=0; tz=0;
tt = [(1-c)*ux^2+c (1-c)*ux*uy-s*uz (1-c)*ux*uz+s*uy tx;...
(1-c)*ux*uy+s*uz (1-c)*uy^2+c (1-c)*uy*uz-s*ux ty;...
(1-c)*ux*uz-s*uy (1-c)*uy*uz+s*ux (1-c)*uz^2+c tz; 0 0 0 1];
tform = affine3d(tt);
R = imref3d(size(image));
imrot = imwarp(image,R,tform);

In this way I get a rotation around the origin axis, but I want the rotation around the centre of the image so I change the value of ty.

 ty=128

But affine3d wants only [0 0 0 1] as last column. Is there a way to rotate using these commands or do I have to find another way?

Answer 1

[Alex Taylor]

The Image Processing Toolbox uses a different convention for the transformation matrix than the one you are expecting. This is discussed here:

http://blogs.mathworks.com/steve/2006/02/07/spatial-transformations-affine/

The form used by IPT is:

[A B C 0;...
 D E F 0;...
 G H I 0;...
 Tx Ty Tz 1];

In other words, its the transpose of what you are expecting.

Answer 2

[Matt J]

In addition to what Alex said, changing the translation parameters to the location of the image center is not equivalent to making that the center of rotation. You can use this tool

http://www.mathworks.com/matlabcentral/fileexchange/30864-3d-rotation-about-shifted-axis

to get the R,t data for a rotation about the axis you want. Then feed [R,t].' to maketform.