Demonstrates how fourier transforms can be used to speed up a sliding window sum operation.

slidingWindowSum.py

import numpy as np
import scipy.signal as signal
import scipy.ndimage as nd
import time


def slidingWindow(field, window):
    """
    Gold standard sliding window operator. This slides along the field
    and sums gridcells in a window.

    @param field: nd-array of binary hits/misses.
    @param window: window size, tuple.
    """

    def accumulator(values):
        return values.sum()

    return nd.generic_filter(
        field,
        accumulator,
        size=window,
        mode='constant',
        cval=0,
        )


def fourierWindow(field, window):
    """
    A fast sliding window operation that applies the convolution theorem.

    @param field: nd-array of binary hits/misses.
    @param window: window size, tuple.
    """

    return signal.fftconvolve(field, np.ones(window), mode='same')


# Example of the difference in speed between approaches.
cube = np.ones((10, 200, 200))

start = time.time()
fsum = slidingWindow(cube, (2, 40, 40))
stop = time.time()
print 'Sliding window method: {} seconds'.format(stop - start)

start = time.time()
fsum = fourierWindow(cube, (2, 40, 40))
stop = time.time()
print 'Fourier method: {} seconds'.format(stop - start)