How can I get the new coordinates of a point after rotation of an image (2D)?

I have got the coordinates of a point (P) in my main image (2D). The main image (im) is now rotated using imrotate and the angle alpha. Now, I want to know what the coordinates of P are in the rotated image.

P = [5;8];    % coordinates of point
alpha = 45;   % angle for rotation
RotatedIm = imrotate(im,alpha);   % rotation of the main image (im)
RotMatrix = [cosd(alpha) -sind(alpha); sind(alpha) cosd(alpha)]; 
ImCenter = (size(im)/2)';         % Center of the main image
RotatedP = RotMatrix*(P-ImCenter)+ImCenter;  % Rotation of point P over center of the image with angle alpha

The rotatedP coordinates are not the right ones. The problem is that there are zeros added on the borders of RotatedIm. I think that that is the reason why the coordinates of RotatedP are not correct. Can someone help me to find the coordinates of point P in the rotated image?

[Rik]

If you use the 'crop' switch, the method would be correct, but now you'll have to account for the shift of the image center. A sketch on paper should help a lot in finding a formula.

[was]

Thanks!

[Marco A.]

Dear @was, @Matt J and @Rik,

I know this is a thread from more than 5 years ago but, after transformation, I encountered a +/-1 px shift between the image and the coordinates of the points (when they are at the corners of the image input). In this script, I use the corners of the input to re-locate an extracted (and transformed) patch in its original position (before the transformation). I have managed to improve the shift to a minimum.

See attached.

I hope this script helps someone trying to reconstruct and image from its pieces. :)

Cheers,

Marco

[Matt J]

That might be because the OP defined the center of the rotation as

ImCenter = (size(im)/2)';  

when really, in 1-based pixel coordinates, the geometric center of the image grid would be at

ImCenter = ((size(im)+1)/2)';  

Answer 1

[Matt J]

P = [5;8];    % coordinates of point
alpha = 45;   % angle for rotation
RotatedIm = imrotate(im,alpha);   % rotation of the main image (im)
RotMatrix = [cosd(alpha) -sind(alpha); sind(alpha) cosd(alpha)]; 

ImCenterA = (size(im)/2)';         % Center of the main image
ImCenterB = (size(RotatedIm )/2)';  % Center of the transformed image

RotatedP = RotMatrix*(P-ImCenterA)+ImCenterB;

[Rik]

Nice one. It seems I was on the right track.