Strided convolution of 2D in numpy
How about using signal.convolve2d
from scipy
?
My approach is similar to Jason's one but using indexing.
def strideConv(arr, arr2, s):
return signal.convolve2d(arr, arr2[::-1, ::-1], mode='valid')[::s, ::s]
Note that the kernal has to be reversed. For details, please see discussion here and here. Otherwise use signal.correlate2d
.
Examples:
>>> strideConv(arr, arr2, 1)
array([[ 91, 80, 100, 84, 88],
[ 99, 106, 126, 92, 77],
[ 69, 98, 91, 93, 117],
[ 80, 79, 87, 93, 61],
[ 44, 72, 72, 63, 74]])
>>> strideConv(arr, arr2, 2)
array([[ 91, 100, 88],
[ 69, 91, 117],
[ 44, 72, 74]])
Ignoring the padding argument and trailing windows that won't have enough lengths for convolution against the second array, here's one way with np.lib.stride_tricks.as_strided
-
def strided4D(arr,arr2,s):
strided = np.lib.stride_tricks.as_strided
s0,s1 = arr.strides
m1,n1 = arr.shape
m2,n2 = arr2.shape
out_shp = (1+(m1-m2)//s, m2, 1+(n1-n2)//s, n2)
return strided(arr, shape=out_shp, strides=(s*s0,s*s1,s0,s1))
def stride_conv_strided(arr,arr2,s):
arr4D = strided4D(arr,arr2,s=s)
return np.tensordot(arr4D, arr2, axes=((2,3),(0,1)))
Alternatively, we can use the scikit-image built-in view_as_windows
to get those windows elegantly, like so -
from skimage.util.shape import view_as_windows
def strided4D_v2(arr,arr2,s):
return view_as_windows(arr, arr2.shape, step=s)