I have greyscale images as 2D NumPy arrays. I need to rotate around one point inside them of different float angles. The rotation doesn't need to be in place and I allow interpolation.
I'd like to use NumPy but also allow for step in/out. I tried using PIL Image.rotate(theta) but don't understand how to apply that to my arrays and how to get an array back.
Consider scipy.ndimage.interpolation.shift() and rotate() for interpolated translations and rotations of 2D numpy arrays.
The operations are described on Wikipedia's Transformation matrix page. 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 around something other than the origin then shift 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 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.
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
Output:
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
