A brief discussion on Python convolution function

This article mainly introduces Python’s understanding of convolution. There are detailed code examples in the article, which have good reference value. I hope it will be helpful to everyone.

convolution function

pythonProvides a variety of convolution schemes. In comparison, the convolution function defined in is slightly more complex ndimagein function than the convolution in numpyand . This can be glimpsed just from the number of input parameters.signal

numpy.convolve(a, v, mode='full')
scipy.ndimage.convolve1d(input, weights, axis=-1, output=None, mode='reflect', cval=0.0, origin=0)

scipy.signal.convolve(in1, in2, mode='full', method='auto')
scipy.ndimage.convolve(input, weights, output=None, mode='reflect', cval=0.0, origin=0)

The first two are 1-dimensional convolution functions, and ndimage can perform convolution operations on multi-dimensional arrays along a single coordinate axis, and the latter two are multi-dimensional convolutions.

The convolution functions in numpy and signal have three modes, which are used to adjust the edge characteristics after convolution. If the dimensions of the two input convolution objects are N NN and M MM respectively, then the output of these three modes The result is

• full: The output dimension is N + M − 1 N+M-1N+M−1. The signals at the last point do not overlap at all, so the edge effect is obvious.
• same: Output dimension max ⁡ ( M , N ) \max(M,N)max(M,N), edge effects are still visible
• valid: Output dimension ∣ M − N ∣ |MN|∣M−N∣, only returns completely overlapping areas, which is equivalent to eliminating all points with edge effects.

 ndimageIn convolveview of the edge effect, the image is expanded, and what it modedetermines is the filling format after expansion. Assume that the array to be filtered is a b c d, then in different modes, the edges are filled as follows

	left padding	data	right padding
reflect	d c b a	a b c d	d c b a
constant	k k k k	a b c d	k k k k
nearest	a a a a	a b c d	d d d d
mirror	d c b	a b c d	c b a
wrap	a b c d	a b c d	a b c d

Among them, it is set kthrough parameters cval.

These five methods of modifying boundaries scipy.ndimageare very common in functions, especially filter functions involving convolution, which are standard.

comparison test

Next, do a performance test for these different convolution functions. Use a 5 × 5 convolution template to perform convolution calculations on a 1000 × 1000 matrix. Let’s take a look at the speed of convolution in different implementations.

import numpy as np
import scipy.signal as ss
import scipy.ndimage as sn
from timeit import timeit


A = np.random.rand(1000,1000)
B = np.random.rand(5,5)

timeit(lambda : ss.convolve(A, B), number=10)
# 0.418
timeit(lambda : sn.convolve(A, B), number=10)
# 0.126

In comparison, ndimagethe convolution in is obviously more efficient.

接下来测试一下一维卷积的表现

A = np.random.rand(10000)
B = np.random.rand(15)

timeit(lambda : np.convolve(A, B), number=1000)
# 0.15256029999727616
timeit(lambda : ss.convolve(A, B), number=1000)
# 0.1231262000001152
timeit(lambda : sn.convolve(A, B), number=1000)
# 0.09218210000108229
timeit(lambda : sn.convolve1d(A, B), number=1000)
# 0.03915820000111125

相比之下，convolve1d不愧是写明了1d的卷积函数，速度最快，而numpy中提供的函数速度最慢。

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