Slice 2d array into smaller 2d arrays

问题:

Is there a way to slice a 2d array in numpy into smaller 2d arrays?

Example

[[1,2,3,4],   ->    [[1,2] [3,4]   
 [5,6,7,8]]          [5,6] [7,8]]

So I basically want to cut down a 2x4 array into 2 2x2 arrays. Looking for a generic solution to be used on images.

回答1:

You should be able to break your array into \"blocks\" using some combination of reshape and swapaxes:

import numpy as np
def blockshaped(arr, nrows, ncols):
    \"\"\"
    Return an array of shape (n, nrows, ncols) where
    n * nrows * ncols = arr.size

    If arr is a 2D array, the returned array should look like n subblocks with
    each subblock preserving the \"physical\" layout of arr.
    \"\"\"
    h, w = arr.shape
    return (arr.reshape(h//nrows, nrows, -1, ncols)
               .swapaxes(1,2)
               .reshape(-1, nrows, ncols))

turns c

c = np.arange(24).reshape((4,6))
print(c)
# [[ 0  1  2  3  4  5]
#  [ 6  7  8  9 10 11]
#  [12 13 14 15 16 17]
#  [18 19 20 21 22 23]]

into

print(blockshaped(c, 2, 3))
# [[[ 0  1  2]
#   [ 6  7  8]]

#  [[ 3  4  5]
#   [ 9 10 11]]

#  [[12 13 14]
#   [18 19 20]]

#  [[15 16 17]
#   [21 22 23]]]

---

I\'ve posted an inverse function, unblockshaped, here, and an N-dimensional generalization here. The generalization gives a little more insight into the reasoning behind this algorithm.

---

Note that there is also superbatfish\'s blockwise_view. It arranges the blocks in a different format (using more axes) but it has the advantage of (1) always returning a view and (2) being capable of handing arrays of any dimension.

回答2:

There are some other answers that seem well-suited for your specific case already, but your question piqued my interest in the possibility of a memory-efficient solution usable up to the maximum number of dimensions that numpy supports, and I ended up spending most of the afternoon coming up with possible method. (The method itself is relatively simple, it\'s just that I still haven\'t used most of the really fancy features that numpy supports so most of the time was spent researching to see what numpy had available and how much it could do so that I didn\'t have to do it.)

def blockgen(array, bpa):
    \"\"\"Creates a generator that yields multidimensional blocks from the given
array(_like); bpa is an array_like consisting of the number of blocks per axis
(minimum of 1, must be a divisor of the corresponding axis size of array). As
the blocks are selected using normal numpy slicing, they will be views rather
than copies; this is good for very large multidimensional arrays that are being
blocked, and for very large blocks, but it also means that the result must be
copied if it is to be modified (unless modifying the original data as well is
intended).\"\"\"
    bpa = np.asarray(bpa) # in case bpa wasn\'t already an ndarray

    # parameter checking
    if array.ndim != bpa.size:         # bpa doesn\'t match array dimensionality
        raise ValueError(\"Size of bpa must be equal to the array dimensionality.\")
    if (bpa.dtype != np.int            # bpa must be all integers
        or (bpa < 1).any()             # all values in bpa must be >= 1
        or (array.shape % bpa).any()): # % != 0 means not evenly divisible
        raise ValueError(\"bpa ({0}) must consist of nonzero positive integers \"
                         \"that evenly divide the corresponding array axis \"
                         \"size\".format(bpa))


    # generate block edge indices
    rgen = (np.r_[:array.shape[i]+1:array.shape[i]//blk_n]
            for i, blk_n in enumerate(bpa))

    # build slice sequences for each axis (unfortunately broadcasting
    # can\'t be used to make the items easy to operate over
    c = [[np.s_[i:j] for i, j in zip(r[:-1], r[1:])] for r in rgen]

    # Now to get the blocks; this is slightly less efficient than it could be
    # because numpy doesn\'t like jagged arrays and I didn\'t feel like writing
    # a ufunc for it.
    for idxs in np.ndindex(*bpa):
        blockbounds = tuple(c[j][idxs[j]] for j in range(bpa.size))

        yield array[blockbounds]

回答3:

It seems to me that this is a task for numpy.split or some variant.

e.g.

a = np.arange(30).reshape([5,6])  #a.shape = (5,6)
a1 = np.split(a,3,axis=1) 
#\'a1\' is a list of 3 arrays of shape (5,2)
a2 = np.split(a, [2,4])
#\'a2\' is a list of three arrays of shape (2,5), (2,5), (1,5)

If you have a NxN image you can create, e.g., a list of 2 NxN/2 subimages, and then divide them along the other axis.

numpy.hsplit and numpy.vsplit are also available.

回答4:

If you want a solution that also handles the cases when the matrix is not equally divided, you can use this:

from operator import add
half_split = np.array_split(input, 2)

res = map(lambda x: np.array_split(x, 2, axis=1), half_split)
res = reduce(add, res)

回答5:

For now it just works when the big 2d array can be perfectly sliced into equally sized subarrays.

The code bellow slices

a ->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]])

into this

block_array->
    array([[[ 0,  1,  2],
            [ 6,  7,  8]],

           [[ 3,  4,  5],
            [ 9, 10, 11]],

           [[12, 13, 14],
            [18, 19, 20]],

           [[15, 16, 17],
            [21, 22, 23]]])

p ang q determine the block size

Code

a = arange(24)
a = a.reshape((4,6))
m = a.shape[0]  #image row size
n = a.shape[1]  #image column size

p = 2     #block row size
q = 3     #block column size

block_array = []
previous_row = 0
for row_block in range(blocks_per_row):
    previous_row = row_block * p   
    previous_column = 0
    for column_block in range(blocks_per_column):
        previous_column = column_block * q
        block = a[previous_row:previous_row+p,previous_column:previous_column+q]
        block_array.append(block)

block_array = array(block_array)

回答6:

You question practically the same as this one. You can use the one-liner with np.ndindex() and reshape():

def cutter(a, r, c):
    lenr = a.shape[0]/r
    lenc = a.shape[1]/c
    np.array([a[i*r:(i+1)*r,j*c:(j+1)*c] for (i,j) in np.ndindex(lenr,lenc)]).reshape(lenr,lenc,r,c)

To create the result you want:

a = np.arange(1,9).reshape(2,1)
#array([[1, 2, 3, 4],
#       [5, 6, 7, 8]])

cutter( a, 1, 2 )
#array([[[[1, 2]],
#        [[3, 4]]],
#       [[[5, 6]],
#        [[7, 8]]]])

回答7:

Here is a solution based on unutbu\'s answer that handle case where matrix cannot be equally divided. In this case, it will resize the matrix before using some interpolation. You need OpenCV for this. Note that I had to swap ncols and nrows to make it works, didn\'t figured why.

import numpy as np
import cv2
import math 

def blockshaped(arr, r_nbrs, c_nbrs, interp=cv2.INTER_LINEAR):
    \"\"\"
    arr      a 2D array, typically an image
    r_nbrs   numbers of rows
    r_cols   numbers of cols
    \"\"\"

    arr_h, arr_w = arr.shape

    size_w = int( math.floor(arr_w // c_nbrs) * c_nbrs )
    size_h = int( math.floor(arr_h // r_nbrs) * r_nbrs )

    if size_w != arr_w or size_h != arr_h:
        arr = cv2.resize(arr, (size_w, size_h), interpolation=interp)

    nrows = int(size_w // r_nbrs)
    ncols = int(size_h // c_nbrs)

    return (arr.reshape(r_nbrs, ncols, -1, nrows) 
               .swapaxes(1,2)
               .reshape(-1, ncols, nrows))