Speeding up linear interpolation of many pixel locations in NumPy

Question

I've tried to replicate the main bottleneck in one of my programs.

I want to get the linearly (or rather bilinearly) interpolated values of several non-integer pixel values simultaneously. It is not the case that each pixel coordinate is perturbed in the same way. Below is a complete/minimal script along with comments that demonstrates the problem. How can I speed up the calculation of result?

import numpy as np
import time

im = np.random.rand(640,480,3) # my "image"
xx, yy = np.meshgrid(np.arange(im.shape[1]), np.arange(im.shape[0]))
print "Check these are the right indices:",np.sum(im - im[yy,xx,:])

# perturb the indices slightly
# I want to calculate the interpolated
# values of "im" at these locations
xx = xx + np.random.normal(size=im.shape[:2])
yy = yy + np.random.normal(size=im.shape[:2])

# integer value/pixel locations
x_0 = np.int_(np.modf(xx)[1])
y_0 = np.int_(np.modf(yy)[1])
x_1, y_1 = x_0 + 1, y_0 + 1

# the real-valued offsets/coefficients pixels
a = np.modf(xx)[0][:,:,np.newaxis]
b = np.modf(yy)[0][:,:,np.newaxis]

# make sure we don't go out of bounds at edge pixels
np.clip(x_0,0,im.shape[1]-1,out=x_0)
np.clip(x_1,0,im.shape[1]-1,out=x_1)
np.clip(y_0,0,im.shape[0]-1,out=y_0)
np.clip(y_1,0,im.shape[0]-1,out=y_1)

# now perform linear interpolation: THIS IS THE BOTTLENECK!
tic = time.time()
result = ((1-a) * (1-b) * im[y_0, x_0, :] +
             a  * (1-b) * im[y_1, x_0, :] +
          (1-a) *    b  * im[y_0, x_1, :] +
             a  *    b  * im[y_1, x_1, :] )
toc = time.time()

print "interpolation time:",toc-tic

Answer 1

Thanks to @JoeKington for the suggestion. Here's the best I can come up with using scipy.ndimage.map_coordinates

# rest as before
from scipy import ndimage
tic = time.time()
new_result = np.zeros(im.shape)
coords = np.array([yy,xx,np.zeros(im.shape[:2])])
for d in range(im.shape[2]):
    new_result[:,:,d] = ndimage.map_coordinates(im,coords,order=1)
    coords[2] += 1
toc = time.time()
print "interpolation time:",toc-tic

Update: Added the tweaks suggested in the comments and tried one or two other things. This is the fastest version:

tic = time.time()
new_result = np.zeros(im.shape)
coords = np.array([yy,xx])
for d in range(im.shape[2]):
    ndimage.map_coordinates(im[:,:,d],
                            coords,order=1,
                            prefilter=False,
                            output=new_result[:,:,d] )
toc = time.time()

print "interpolation time:",toc-tic

Example running time:

 original version: 0.463063955307
   better version: 0.204537153244
     best version: 0.121845006943