Convolve2d just by using Numpy
You could generate the subarrays using as_strided
:
import numpy as npa = np.array([[ 0, 1, 2, 3, 4], [ 5, 6, 7, 8, 9], [10, 11, 12, 13, 14], [15, 16, 17, 18, 19], [20, 21, 22, 23, 24]])sub_shape = (3,3)view_shape = tuple(np.subtract(a.shape, sub_shape) + 1) + sub_shapestrides = a.strides + a.stridessub_matrices = np.lib.stride_tricks.as_strided(a,view_shape,strides)
To get rid of your second "ugly" sum, alter your einsum
so that the output array only has j
and k
. This implies your second summation.
conv_filter = np.array([[0,-1,0],[-1,5,-1],[0,-1,0]])m = np.einsum('ij,ijkl->kl',conv_filter,sub_matrices)# [[ 6 7 8]# [11 12 13]# [16 17 18]]
Cleaned up using as_strided
and @Crispin 's einsum
trick from above. Enforces the filter size into the expanded shape. Should even allow non-square inputs if the indices are compatible.
def conv2d(a, f): s = f.shape + tuple(np.subtract(a.shape, f.shape) + 1) strd = numpy.lib.stride_tricks.as_strided subM = strd(a, shape = s, strides = a.strides * 2) return np.einsum('ij,ijkl->kl', f, subM)
You can also use fft (one of the faster methods to perform convolutions)
from numpy.fft import fft2, ifft2import numpy as npdef fft_convolve2d(x,y): """ 2D convolution, using FFT""" fr = fft2(x) fr2 = fft2(np.flipud(np.fliplr(y))) m,n = fr.shape cc = np.real(ifft2(fr*fr2)) cc = np.roll(cc, -m/2+1,axis=0) cc = np.roll(cc, -n/2+1,axis=1) return cc
- https://gist.github.com/thearn/5424195
- you must pad the filter to be the same size as image ( place it in the middle of a zeros_like mat.)
cheers,Dan