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Behavior of EC2d close to the edges #433
Description
While testing the Euler characteristic computation function, nipy.algorithms.statistics.intvol.EC2d, I found some unexpected behavior that could be reduced to the following :
In [2]: import numpy as np
In [3]: from nipy.algorithms.statistics.intvol import EC2d
In [4]: a = np.ones(shape=(3, 3), dtype='int'); print a, EC2d(a)
[[1 1 1]
[1 1 1]
[1 1 1]] -1
In [5]: a[0, 0] = 0; print a, EC2d(a)
[[0 1 1]
[1 1 1]
[1 1 1]] 1
In [6]: a[0, 0] = 1; a[-1, 0] = 0; print a, EC2d(a)
[[1 1 1]
[1 1 1]
[0 1 1]] -1
Is that a expected consequence of those functions being approximate? Thanks for your help and sorry if I am misunderstanding the intended purpose of the functions.
Activity
matthew-brett commentedon Dec 5, 2017
@jonathan-taylor - any thoughts on this one?
jonathan-taylor commentedon Jan 26, 2018
I think this has to do with how a binary "image" is triangulated. It has been some time since I've looked at the code. If
ais padded with 0s this problem is not there.In [22]: a = np.ones(shape=(3, 3), dtype='int'); print a, EC2d(a)
[[1 1 1]
[1 1 1]
[1 1 1]] -1
In [23]: a1 = a.copy()
In [24]: a2 = a.copy()
In [25]: a1[0, 0] = 0
In [26]: a2[-1, 0] = 0
In [30]: b = np.zeros((5, 5), np.int)
In [31]: b[1:-1][:,1:-1] = a
In [32]: EC2d(b)
Out[32]: 1
In [33]: b1 = np.zeros_like(b)
In [34]: b1[1:-1][:,1:-1] = a1
In [35]: EC2d(b1)
Out[35]: 1
In [36]: b2 = np.zeros_like(b)
In [37]: b2[1:-1][:,1:-1] = a2
In [38]: EC2d(b2)
Out[38]: 1
In [39]: