Rotate numpy 2D array

Question

I have a set of greyscale images as a 2D numpy arrays.

I need to rotate the images about one point (inside them) of different, float angles. The rotation doesn't need to be in place, and I will allow (of course, if I explained well so far) for interpolation.

I'd like to remain in numpy, as I need to perform numerical operations on the result, but I can also (if that's impossible) allow for step in/out; for example I tried using PIL, namely Image.rotate(theta) but don't understand how to apply that to my arrays, and how to get an array back.

Thank you for your input.

Answer 1

See the comment of cgohlke Nov 10 '11 at 18:34:

Consider scipy.ndimage.interpolation.shift() and rotate() for interpolated translations and rotations of 2D numpy arrays.

Answer 2

The basic operations are described in the Wikipedia transformation matrix page - I'm not going to try to do ascii matrix art here, but the output P' = R*P where P' is the output point, R is the 2x2 transformation matrix containing sine and cosine of the rotation angle, and P is the input point. If you want to rotate about something other than the origin, then shift the the origin prior to rotation: P' = T + R*(P-T) where T is the translation coordinate. The basic matrix operations don't do interpolation, so if you aren't using a numpy-based image processing library, you'll want to do a reverse transform: for each (integer-valued) output coordinate, find the (floating point) coordinate of the point that would be rotated into it, and interpolate the value of that input point from the surrounding pixels.