Using homogeneous coordinates to rotate an image

Question

Currently, I have this code snippet, but it's a little bit slow:

% input image
input_matrix = imread('placa.bmp');
[rows cols] = size(input_matrix);
% rotation
degree = 30;
radians = (pi * degree) / 180; 
theta = radians;
% output matrix
t_matrix = input_matrix;
t_matrix(t_matrix == input_matrix) = NaN;
% transformation matrix
T = [cos(theta) -sin(theta) 0; sin(theta) cos(theta) 1; 0 0 1];
% loop over each input_matrix coordinate
for n = 1:numel(input_matrix)
 % current coordinate
 [x y] = ind2sub([rows cols], n);
 % transpose
 v = [x y 1]';
 % homogeneous coordinate
 v = T*v;
 % transponse again
 v = v';
 % only integer values
 a = floor(v(1));
 b = floor(v(2));
 if a > 0 && b > 0
 % replace in t_matrix
 t_matrix(a,b) = input_matrix(x,y);
 end
end
% get only a part of t_matrix
t_matrix = t_matrix(1:rows, 1:cols);
figure; imshow(input_matrix); % original image
figure; imshow(t_matrix)

How can I improve it?

Condition: keep using this matrix:

% transformation matrix
T = [cos(theta) -sin(theta) 0; sin(theta) cos(theta) 1; 0 0 1];

Answer 1

Rather than looping over all x and y values you could put them into a vector, that should speed things up considerably.

y=repmat(1:cols,rows,1)
x=repmat((1:rows)',cols,1)
M=[x(:) y(:) ones(rows*cols,1)];

Now you just need to multiply M or M' with T or T' and you have subsitituted that part of the code.

• Trevor Pilley: It would help if you posted an example along with an explanation instead.
• Dennis Jaheruddin: Added the improved code part