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Tabish
129 lines
3.9 KiB
Python
129 lines
3.9 KiB
Python
import numpy as np
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def integral_image(img):
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"""Integral image / summed area table.
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The integral image contains the sum of all elements above and to the
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left of it, i.e.:
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.. math::
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S[m, n] = \sum_{i \leq m} \sum_{j \leq n} X[i, j]
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Parameters
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----------
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img : ndarray
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Input image.
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Returns
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-------
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S : ndarray
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Integral image/summed area table of same shape as input image.
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References
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----------
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.. [1] F.C. Crow, "Summed-area tables for texture mapping,"
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ACM SIGGRAPH Computer Graphics, vol. 18, 1984, pp. 207-212.
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"""
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S = img
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for i in range(img.ndim):
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S = S.cumsum(axis=i)
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return S
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def integrate(ii, start, end, *args):
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"""Use an integral image to integrate over a given window.
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Parameters
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----------
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ii : ndarray
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Integral image.
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start : tuple of length equal to dimension of ii
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Coordinates of top left corner of window(s).
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For multiple windows each coordinate should be a list
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using same format as numpy multi-indexing conventions.
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end : tuple of length equal to dimension of ii
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Coordinates of bottom right corner of window(s).
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For multiple windows each coordinate should be a list
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using same format as numpy multi-indexing conventions.
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args: optional
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For backward compatibility with versions prior to 0.10
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The earlier function signature was integrate(ii, r0, c0, r1, c1),
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where r0, c0 are int(lists) specifying start coordinates
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of window(s) to be integrated and r1, c1 the end coordinates.
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Returns
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-------
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S : scalar or ndarray
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Integral (sum) over the given window(s).
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Examples
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--------
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>>> arr = np.ones((5,6), dtype=np.float)
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>>> ii = integral_image(arr)
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>>> print(integrate(ii,(1,0), (1,2))) # sum from (1,0) -> (1,2)
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[ 3.]
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>>> print(integrate(ii,(3,3), (4,5))) # sum form (3,3) -> (4,5)
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[ 6.]
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>>> print(integrate(ii,([1,3], [0,3]), ([1,4], [2,5]))) # sum from (1,0) -> (1,2) and (3,3) -> (4,5)
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[ 3. 6.]
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>>> print(integrate(ii, [1,3], [0,3], [1,4], [2,5])) # deprecated usage
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[ 3. 6.]
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"""
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rows = 1
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# handle input from new input format
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if(len(args) == 0):
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if(not(isinstance(start[0], int))):
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rows = len(start[0])
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start = np.array(start).T
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end = np.array(end).T
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# handle deprecated input format
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else:
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if(not(isinstance(start, int))):
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rows = len(start)
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args = (start , end) + args
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start = np.array(args[:len(args)/2]).T
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end = np.array(args[len(args)/2:]).T
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total_shape = ii.shape
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total_shape = np.tile(total_shape, [rows, 1])
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# take care of negative coordinates
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start_negatives = start < 0
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end_negatives = end < 0
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start = (start + total_shape) * start_negatives + \
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start * np.invert(start_negatives)
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end = (end + total_shape) * end_negatives + \
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end * np.invert(end_negatives)
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if(np.any((end - start) < 0)):
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raise IndexError('end coordinates must be greater or equal to start')
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S = np.zeros(rows)
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bit_perm = 2**(ii.ndim) # total number of elements in expression of S
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width = len(bin(bit_perm - 1)[2:])
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for i in range(bit_perm): # for all permutations
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# boolean permutation array eg [True, False] for '10'
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binary = bin(i)[2:].zfill(width)
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bool_mask = [bit == '1' for bit in binary]
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sign = (-1)**sum(bool_mask) # determine sign of permutation
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bad = [np.any(((start[r] - 1) * bool_mask) < 0)
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for r in range(rows)] # find out bad start rows
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corner_points = (end * (np.invert(bool_mask))) + \
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((start - 1) * bool_mask) # find corner for each row
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S += [sign * ii[tuple(corner_points[r])] if(bad[r] == False) else 0
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for r in range(rows)] # add only good rows
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return S
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