Question

I’m trying to improve the speed of a function that calculates the normalized cross-correlation between a search image and a template image by using the anfft module, which provides Python bindings for the FFTW C library and seems to be ~2-3x quicker than scipy.fftpack for my purposes.

When I take the FFT of my template, I need the result to be padded to the same size as my search image so that I can convolve them. Using scipy.fftpack.fftn I would just use the shape parameter to do padding/truncation, but anfft.fftn is more minimalistic and doesn’t do any zero-padding itself.

When I try and do the zero padding myself, I get a very different result to what I get using shape. This example uses just scipy.fftpack, but I have the same problem with anfft:

import numpy as np
from scipy.fftpack import fftn
from scipy.misc import lena

img = lena()
temp = img[240:281,240:281]

def procrustes(a,target,padval=0):

    # Forces an array to a target size by either padding it with a constant or
    # truncating it

    b = np.ones(target,a.dtype)*padval
    aind = [slice(None,None)]*a.ndim
    bind = [slice(None,None)]*a.ndim
    for dd in xrange(a.ndim):
        if a.shape[dd] > target[dd]:
            diff = (a.shape[dd]-b.shape[dd])/2.
            aind[dd] = slice(np.floor(diff),a.shape[dd]-np.ceil(diff))
        elif a.shape[dd] < target[dd]:
            diff = (b.shape[dd]-a.shape[dd])/2.
            bind[dd] = slice(np.floor(diff),b.shape[dd]-np.ceil(diff))
    b[bind] = a[aind]
    return b

# using scipy.fftpack.fftn's shape parameter
F1 = fftn(temp,shape=img.shape)

# doing my own zero-padding
temp_padded = procrustes(temp,img.shape)
F2 = fftn(temp_padded)

# these results are quite different
np.allclose(F1,F2)

I suspect I’m probably making a very basic mistake, since I’m not overly familiar with the discrete Fourier transform.

Answer 1

Just do the inverse transform and you’ll see that scipy does slightly different padding (only to top and right edges):

plt.imshow(ifftn(fftn(procrustes(temp,img.shape))).real)

plt.imshow(ifftn(fftn(temp,shape=img.shape)).real)