Calculating coordinates of a pixel in a rotated image

I have a binary image and I know the coordinates of a pixel (r, c). I rotate the image by some degrees (I use a rotation matrix) and I need to calculate the new coordinates of the same pixel, in the rotated image. I tried to use common formulas such as

x_new = x_original * cos(angle) - y_original * sin(angle)

y_new = x_original * sin(angle) + y_original * cos(angle)

but this didn't work. Maybe it's because of the MATLAB coordinates system.

After calculating the new coordinates, I need to move the rotated image so that the pixel overlaps another pixel in another image (de facto I am creating a new image right now).

How can I solve the problem?

Thanks in advance.

[Rik]

imrotate rotates images around the center, while these coordinates tend to assume your origin is in the corner. Did you account for this?

[Banzai]

In the end I managed to calculate the point in another way.

Now I need to overlap the two images on a specific point. I tried using imtranslate to move one image by the vector

[x_1-x_2, y_1-y_2] and imfuse to fuse them together. It kinda works but imfuse changes the color of the images (and I don't want that) and crops the image I have moved (and I don't want that either). How can I solve this issue?

Answer 1

[Matt J]

Rather than fussing with your own rotation matrices, you should probably be using imregister or imregtform.

In any case, using your rotation matrix R should have worked, but you need to keep in mind that if spatial coordinates are rotated by θ, then objects in the image will rotate by . Therefore, you might find you get the correct pixel coordinates if you use R.' instead of R.