Rotated image coordinates after scipy.ndimage.interpolation.rotate?

Question

I have a numpy array for an image that I read in from a FITS file. I rotated it by N degrees using scipy.ndimage.interpolation.rotate. Then I want to figure out

Answer 1

As usual with rotations, one needs to translate to the origin, then rotate, then translate back. Here, we can take the center of the image as origin.

import numpy as np
import matplotlib.pyplot as plt
from scipy import misc
from scipy.ndimage import rotate

data_orig = misc.face()
x0,y0 = 580,300 # left eye; (xrot,yrot) should point there

def rot(image, xy, angle):
    im_rot = rotate(image,angle) 
    org_center = (np.array(image.shape[:2][::-1])-1)/2.
    rot_center = (np.array(im_rot.shape[:2][::-1])-1)/2.
    org = xy-org_center
    a = np.deg2rad(angle)
    new = np.array([org[0]*np.cos(a) + org[1]*np.sin(a),
            -org[0]*np.sin(a) + org[1]*np.cos(a) ])
    return im_rot, new+rot_center


fig,axes = plt.subplots(2,2)

axes[0,0].imshow(data_orig)
axes[0,0].scatter(x0,y0,c="r" )
axes[0,0].set_title("original")

for i, angle in enumerate([66,-32,90]):
    data_rot, (x1,y1) = rot(data_orig, np.array([x0,y0]), angle)
    axes.flatten()[i+1].imshow(data_rot)
    axes.flatten()[i+1].scatter(x1,y1,c="r" )
    axes.flatten()[i+1].set_title("Rotation: {}deg".format(angle))

plt.show()