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.

Solution 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.

Solution 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.

Solution 3

I would like take help of above and solve this by an example:

import pandas as pd
import numpy as np
bd = np.matrix([[44., -1., 40., 42., 40., 39., 37., 36., -1.],
                [42., -1., 43., 42., 39., 39., 41., 40., 36.],
                [37., 37., 37., 35., 38., 37., 37., 33., 34.],
                [35., 38., -1., 35., 37., 36., 36., 35., -1.],
                [36., 35., 36., 35., 34., 33., 32., 29., 28.],
                [38., 37., 35., -1., 30., -1., 29., 30., 32.]])

def rotate45(array):
    rot = []
    for i in range(len(array)):
        rot.append([0] * (len(array)+len(array[0])-1))
        for j in range(len(array[i])):
            rot[i][int(i + j)] = array[i][j]
    return rot

df_bd = pd.DataFrame(data=np.matrix(rotate45(bd.transpose().tolist())))
df_bd = df_bd.transpose()
print df_bd

of which output will be like:

44   0   0   0   0   0   0   0   0
42  -1   0   0   0   0   0   0   0
37  -1  40   0   0   0   0   0   0
35  37  43  42   0   0   0   0   0
36  38  37  42  40   0   0   0   0
38  35  -1  35  39  39   0   0   0
0   37  36  35  38  39  37   0   0
0    0  35  35  37  37  41  36   0
0    0   0  -1  34  36  37  40  -1
0    0   0   0  30  33  36  33  36
0    0   0   0   0  -1  32  35  34
0    0   0   0   0   0  29  29  -1
0    0   0   0   0   0   0  30  28
0    0   0   0   0   0   0   0  32

Comments

[BlackBear]

I changed your 'greyscale' tag to the 'image processing' one. I think it describes better your intentions. Feel free to change it back

[Josh Bleecher Snyder]

You can do this directly in numpy, but for converting back and forth, see effbot.org/zone/pil-numpy.htm.

[astabada]

Thank you for the advice, I just noticed this box!

[tiago]

@cgohlke your second link has a typo (domain name should be scikit-image.org), as it stands it currently links to a spammer.

[cgohlke]

scikits-image was renamed to scikit-image after my comment.

[astabada]

This would have been the hard way... in case you didn't check cgohlke's solution, I implemented it in 120±13 seconds.

[Nathan]

Thanks @Vasco. Are there any functions that preserve the shape while they rotate only the "on" bits?

[Grayscale]

In SciPy v1.1, I think this is now scipy.ndimage.rotate() rather than scipy.ndimage.interpolation.rotate().