How can I efficiently process a numpy array in blocks similar to Matlab's blkproc (blockproc) function


Question

I'm looking for a good approach for efficiently dividing an image into small regions, processing each region separately, and then re-assembling the results from each process into a single processed image. Matlab had a tool for this called blkproc (replaced by blockproc in newer versions of Matlab).

In an ideal world, the function or class would support overlap between the divisions in the input matrix too. In the Matlab help, blkproc is defined as:

B = blkproc(A,[m n],[mborder nborder],fun,...)

  • A is your input matrix,
  • [m n] is the block size
  • [mborder, nborder] is the size of your border region (optional)
  • fun is a function to apply to each block

I have kluged together an approach, but it strikes me as clumsy and I bet there's a much better way. At the risk of my own embarrassment, here's my code:


import numpy as np

def segmented_process(M, blk_size=(16,16), overlap=(0,0), fun=None):
    rows = []
    for i in range(0, M.shape[0], blk_size[0]):
        cols = []
        for j in range(0, M.shape[1], blk_size[1]):
            cols.append(fun(M[i:i+blk_size[0], j:j+blk_size[1]]))
        rows.append(np.concatenate(cols, axis=1))
    return np.concatenate(rows, axis=0)

R = np.random.rand(128,128)
passthrough = lambda(x):x
Rprime = segmented_process(R, blk_size=(16,16), 
                           overlap=(0,0), 
                           fun=passthrough)

np.all(R==Rprime)
1
25
11/5/2013 3:02:35 PM

Accepted Answer

Here are some examples of a different (loop free) way to work with blocks:

import numpy as np
from numpy.lib.stride_tricks import as_strided as ast

A= np.arange(36).reshape(6, 6)
print A
#[[ 0  1  2  3  4  5]
# [ 6  7  8  9 10 11]
# ...
# [30 31 32 33 34 35]]

# 2x2 block view
B= ast(A, shape= (3, 3, 2, 2), strides= (48, 8, 24, 4))
print B[1, 1]
#[[14 15]
# [20 21]]

# for preserving original shape
B[:, :]= np.dot(B[:, :], np.array([[0, 1], [1, 0]]))
print A
#[[ 1  0  3  2  5  4]
# [ 7  6  9  8 11 10]
# ...
# [31 30 33 32 35 34]]
print B[1, 1]
#[[15 14]
# [21 20]]

# for reducing shape, processing in 3D is enough
C= B.reshape(3, 3, -1)
print C.sum(-1)
#[[ 14  22  30]
# [ 62  70  78]
# [110 118 126]]

So just trying to simply copy the matlab functionality to numpy is not all ways the best way to proceed. Sometimes a 'off the hat' thinking is needed.

Caveat:
In general, implementations based on stride tricks may (but does not necessary need to) suffer some performance penalties. So be prepared to all ways measure your performance. In any case it's wise to first check if the needed functionality (or similar enough, in order to easily adapt for) has all ready been implemented in numpy or scipy.

Update:
Please note that there is no real magic involved here with the strides, so I'll provide a simple function to get a block_view of any suitable 2D numpy-array. So here we go:

from numpy.lib.stride_tricks import as_strided as ast

def block_view(A, block= (3, 3)):
    """Provide a 2D block view to 2D array. No error checking made.
    Therefore meaningful (as implemented) only for blocks strictly
    compatible with the shape of A."""
    # simple shape and strides computations may seem at first strange
    # unless one is able to recognize the 'tuple additions' involved ;-)
    shape= (A.shape[0]/ block[0], A.shape[1]/ block[1])+ block
    strides= (block[0]* A.strides[0], block[1]* A.strides[1])+ A.strides
    return ast(A, shape= shape, strides= strides)

if __name__ == '__main__':
    from numpy import arange
    A= arange(144).reshape(12, 12)
    print block_view(A)[0, 0]
    #[[ 0  1  2]
    # [12 13 14]
    # [24 25 26]]
    print block_view(A, (2, 6))[0, 0]
    #[[ 0  1  2  3  4  5]
    # [12 13 14 15 16 17]]
    print block_view(A, (3, 12))[0, 0]
    #[[ 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 25 26 27 28 29 30 31 32 33 34 35]]
21
2/26/2011 6:37:25 PM

Process by slices/views. Concatenation is very expensive.

for x in xrange(0, 160, 16):
    for y in xrange(0, 160, 16):
        view = A[x:x+16, y:y+16]
        view[:,:] = fun(view)

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