Re: xcorr2 (signal package)

[Carnë Draug]

On 5 February 2014 19:56, Benjamin Eltzner <address@hidden> wrote:
> when I recently had to use cross correlations in a project, I found
> that the xcorr2 function (especially using the "coeff" option) in the
> signal package of Octave does not yield correct results and
> implemented it quick and dirty myself. My code yields the same result
> as the matlab function.
>
> Referring to this state of the source:
>
> http://sourceforge.net/p/octave/signal/ci/0e2141a26533942734b0d8e1a096eb4d5213fd9d/tree/inst/xcorr2.m
>
> the lines 69-71 and 94-98 would need to be replaced. (I highlight this
> in the source appended to this mail.)

How can it return the same result as Matlab, when Matlab does not even
have a "coeff" option? Your patch actually makes xcorr2 wrong.
Consider the following example, using examples from Matlab
documentation:

I1 = [17  24   1   8  15
      23   5   7  14  16
       4   6  13  20  22
      10  12  19  21   3
      11  18  25   2   9];

 I2 = [8   1   6
      3   5   7
      4   9   2];

xcorr2 (I1, I2)

This will return the following which is exactly the same as Matlab

    34   201   286   121   106   167    60
   165   470   329   244   334   299   109
   271   359   405   570   585   479   256
   186   229   550   615   730   409   206
   116   309   595   760   575   349   221
   137   263   504   434   339   222    51
    66   119   256   181   256    25    72

Ignoring the "coeff" option, your code returns

   -51    -4    76   -44   -14    52   -15
   -35   125   -56   -51    29    34   -46
    51   -36   -95    80     5     4    -9
     1   -71    55    30    55   -71     1
    -9     4     5    80   -95   -36    51
    32     8    29   -51   -56    47    -9
    11   -26   -14   -44    76   -30    27

which is completely different.

Also, while Matlab's xcorr2 does not have the "coeff" option, it says
on its documentation[1]

"""
The normalized cross-correlation of the (2,4) output element is

585/sqrt(sum(dot(I1p,I1p))*sum(dot(I2,I2))) = 0.8070

where I1p = [1 8 15; 7 14 16; 13 20 22].
"""

They're are off by 1 row and 1 column (probably forgot to account for
the extra padding or meant to say "input" instead of "output"), but
the current code returns 0.80696 (at 3,5), while yours returns
0.0345582

> I don't have the time to understand your bug tracking system, but I
> would love to help you fix this function (which is very important in
> scientific computing). I would therefore be glad, if you forwarded my
> code to whom it may concern although I do not follow protocol.

That's probably me. If you want to submit a bug, please do so on the
bug tracker [2]. There is nothing to learn, you don't even have to
create an account. Just a text box and a big submit button at the
bottom of the page. Please, enter at least your email so we can ask
you more details about the bug (like I am now). Bug reports tend to be
lost quickly and forgotten in the mailing list.

Carnë

[1] http://www.mathworks.co.uk/help/signal/ref/xcorr2.html
[2] https://savannah.gnu.org/bugs/?func=additem&group=octave