[Numpy-discussion] summarizing blocks of an array using a moving window

[Pauli Virtanen]

Thu, 22 Jul 2010 00:47:20 -0400, Robin Kraft wrote:
[clip]
> Let's say the image looks like this: np.random.randint(0,2,
> 16).reshape(4,4)
> 
> array([[0, 0, 0, 1],
>        [0, 0, 1, 1],
>        [1, 1, 0, 0],
>        [0, 0, 0, 0]])
> 
> I want to use a square, non-overlapping moving window for resampling, so
> that I get a count of all the 1's in each 2x2 window.
> 
> 0, 0,   0, 1
> 0, 0,   1, 1                 0  3
>                     =>       2  0
> 1, 1,   0, 0
> 0, 0,   0, 0
> 
> In another situation with similar data I'll need the average, or the
> maximum value, etc..

Non-overlapping windows can be done by reshaping:

x = np.array([[0, 0, 0, 1, 1, 1],
              [0, 0, 1, 1, 0, 0],
              [1, 1, 0, 0, 1, 1],
              [0, 0, 0, 0, 1, 1],
              [1, 0, 1, 0, 1, 1],
              [0, 0, 1, 0, 0, 0]])

y = x.reshape(3,2,3,2)
y2 = y.sum(axis=3).sum(axis=1)

# -> array([[0, 3, 2],
#           [2, 0, 4],
#           [1, 2, 2]])

y2 = x.reshape(3,2,3,2).transpose(0,2,1,3).reshape(3,3,4).sum(axis=-1)

# -> array([[0, 3, 2],
#           [2, 0, 4],
#           [1, 2, 2]])


The above requires no copying of data, and should be relatively fast. If 
you need overlapping windows, those can be emulated with strides:

	http://mentat.za.net/numpy/scipy2009/stefanv_numpy_advanced.pdf
	http://conference.scipy.org/scipy2010/slides/tutorials
	/stefan_vd_walt_numpy_advanced.pdf

-- 
Pauli Virtanen