Hi,
An affine transformation is described in mathematical form as:
Here, [x y] are the transformed coordinates while [w z] are the original coordinates. The T matrix (also called the Transformation matrix is stored in T.tdata.T. In the example that you have provided, this transformation matrix (stored in T.tdata.T) is such that it maps each row of U to the corresponding row of X. The U and X arguments are each 3-by-2 and define the corners of input and output triangles. For example:
U = [11 11;21 11; 21 21];
X = [51 51;61 51;61 61];
tform2 = maketform('affine',U,X);
>> tform2.tdata.T
ans =
1 0 0
0 1 0
40 40 1
Now if you check:
>> [U [1;1;1]]*tform2.tdata.T
ans =
51 51 1
61 51 1
61 61 1
which is just [X [1;1;1]]. I hope this helps.
Screenshot taken from:Digital Image Processing Using MATLAB, 2e
