Finding a pixel location after imrotate

Hello all,

I'm trying to find the location of a certain pixel after imrotate with crop. Let's say I have an image I of size = (679, 1024) and then I rotate it with imrotate(I, 10, 'crop') for 10 degrees. So here's the original image and the marked pixel:

And here's the rotate image and the marked pixel after rotation:

So the marked pixel at location (354, 32) is transfomred to the new location (303, 64). How do I find the new location only having the rotation angle (10) and the original location?

Answer 1

[Matt J]

Well, the center of the image in your example is at

c=[512.5;340];

and the rotation matrix expressing the rotation is

R=[cosd(10) +sind(10); -sind(10), cosd(10)]

The transformation of ij=[354; 32] is therefore

>> R*(ij-c)+c

ans =

  302.9243
   64.2024

[Amir Hossein Farzaneh]

Thank you so much for answering this; but when I use your snippets I get the answer as:

ans =

  270.3494
   36.8688

Also c should be:

   c=[339.5; 512]

right?

UPDATE:

I found out the bug: so here will be the solution:

c = [512; 339.5];
p = [354; 32];
R = [cosd(10) +sind(10); -sind(10), cosd(10)];
p_new = R*(p-c)+c

p_new =

  303.0036
   64.1080

Thank you so much for the help Matt

[Matt J]

You're quite welcome, but please Accept-click the answer if it has brought you to a solution.

[Amir Hossein Farzaneh]

I will do that! Will you edit your answer so everything is right if people refer to this thread in the future?

[Matt J]

I have fixed the problem with c, but the center is at c=[512.5, 340] because the first pixel is centered at [1;1], not at [0.5;0.5]. Accordingly, my final result for the coordinate of the rotated point should be right as well,

  >> p_new = R*(p-c)+c

p_new =

  302.9243
   64.2024