correlate2d's output does not agree with correlate's output in scipy.signal module (Trac #1443)

[scipy-gitbot]

Original ticket http://projects.scipy.org/scipy/ticket/1443 on 2011-05-23 by trac user SevenSea, assigned to unknown.

When the 2-dimensional array size is even, correlate2d's output does not agree with correlate's output in scipy.signal module. There is a shift of index in the output of correlate2d function. (Information for comparition: convolv2d works good.)

Testing code:

import numpy as np
import scipy.signal as sn

d = np.ones((4,4))
print "data: "
print d

print "correlate(d,d,'same'): "
print sn.correlate(d,d,'same')

print "correlate2d(d,d,'same'): "
print sn.correlate2d(d,d,'same')

The output:

data: 
[[ 1.  1.  1.  1.]
 [ 1.  1.  1.  1.]
 [ 1.  1.  1.  1.]
 [ 1.  1.  1.  1.]]
correlate(d,d,'same'): 
[[  4.   6.   8.   6.]
 [  6.   9.  12.   9.]
 [  8.  12.  16.  12.]
 [  6.   9.  12.   9.]]
correlate2d(d,d,'same'): 
[[  9.  12.   9.   6.]
 [ 12.  16.  12.   8.]
 [  9.  12.   9.   6.]
 [  6.   8.   6.   4.]]

[orodbhen]

What is the purpose of correlate2d anyways? I don't see the purpose of having a redundant function, when correlate can do the same thing. Especially when it appears to be broken, and has been for quite some time. What am I missing here?

[endolith]

@orodbhen correlate2d has different boundary options for image processing

[orodbhen]

@endolith That makes sense then. correlate doesn't appear to allow explicitly setting the boundary, though. Is it assumed to be zero-padded? Then anything else would have to be done manually in the input, correct?

I'm not clear on why this difference would cause the output to be offset, though. Is that really a bug, or expected behavior? I see this using same and the default boundary setting, like the OP.

[endolith]

correlate doesn't appear to allow explicitly setting the boundary, though. Is it assumed to be zero-padded? Then anything else would have to be done manually in the input, correct?

Yes

I'm not clear on why this difference would cause the output to be offset, though.

It wouldn't, that's unrelated.

The full output of convolve/correlate is always odd-length, so for odd-length input, same mode is unambiguous, you center the truncated output:

a = [[1, 0, 1], [0, 1, 1], [1, 1, 2]]

b = [[0, 1, 1], [2, 1, 1], [2, 0, 1]]

correlate(a, b)
Out[6]: 
array([[1, 0, 3, 0, 2],
       [1, 2, 4, 3, 4],
       [2, 3, 7, 6, 6],
       [1, 3, 7, 5, 4],
       [1, 2, 3, 2, 0]])

correlate2d(a, b)
Out[7]: 
array([[1, 0, 3, 0, 2],
       [1, 2, 4, 3, 4],
       [2, 3, 7, 6, 6],
       [1, 3, 7, 5, 4],
       [1, 2, 3, 2, 0]])

correlate(a, b, 'same')
Out[8]: 
array([[2, 4, 3],
       [3, 7, 6],
       [3, 7, 5]])

correlate2d(a, b, 'same')
Out[9]: 
array([[2, 4, 3],
       [3, 7, 6],
       [3, 7, 5]])

But for even-length input you can't center the output, so you have to shift it one way or the other. correlate author chose one option and correlate2d author chose the other.

a = [[1, 0], [1, 2]]

b = [[0, 1], [2, 0]]

correlate(a, b)
Out[12]: 
array([[0, 2, 0],
       [1, 2, 4],
       [1, 2, 0]])

correlate2d(a, b)
Out[13]: 
array([[0, 2, 0],
       [1, 2, 4],
       [1, 2, 0]])

correlate(a, b, 'same')
Out[14]: 
array([[0, 2],
       [1, 2]])

correlate2d(a, b, 'same')
Out[15]: 
array([[2, 4],
       [2, 0]])

I'm not sure if one choice makes more sense in certain contexts or if this is just an accident.

It might be this way for consistency with other software, too. Should compare with Octave and Matlab.

[larsoner]

Based on what @endolith concluded, I'm marking this as a documentation issue. I think we need to add to the Notes section of these about which outputs are used in the "same" modes for even-length inputs. Probably not worth a deprecation cycle to unify the behaviors.