trying to find 2D similarity patterns by xcorr2

From: lucy (losemind_at_yahoo.com)
Date: 12/21/04 

Date: Tue, 21 Dec 2004 12:15:20 -0800

Hi all,

I am trying to find 2D similarity patterns in order to match two image
objects...

For simplicity, I want to ask this question in terms of 1D case:

Easy cases are zeros and non-zeros:

But I still don't know the relationship between the position of the peak of
XCORR result and the relative shifting of y that I should do in order to do
a matching...

I mean, I know I should shift "y" a little bit in order for the best
matching... but how much?

>> x=[0 0 0 1 1 1 0 0 0 0];
>> y=[0 0 0 0 0 0 1 1 1 1 0 0 0];
>> xcorr(x, y)

ans =

  Columns 1 through 7

    0.0000 0 -0.0000 -0.0000 0.0000 -0.0000 1.0000

  Columns 8 through 14

    2.0000 3.0000 3.0000 2.0000 1.0000 0.0000 -0.0000

  Columns 15 through 21

         0 -0.0000 0.0000 0 0.0000 0.0000 -0.0000

  Columns 22 through 25

    0.0000 -0.0000 0 -0.0000

>> x1=[1 1 1 0 0 0 0];
>> y

y =

  Columns 1 through 12

     0 0 0 0 0 0 1 1 1 1 0 0

  Column 13

     0

>> xcorr(x1, y)

ans =

  Columns 1 through 7

    0.0000 0.0000 0.0000 1.0000 2.0000 3.0000 3.0000

  Columns 8 through 14

    2.0000 1.0000 -0.0000 0.0000 0.0000 0.0000 0.0000

  Columns 15 through 21

   -0.0000 -0.0000 0.0000 -0.0000 -0.0000 -0.0000 -0.0000

  Columns 22 through 25

   -0.0000 0 0 -0.0000

>>

Now suppose the similar patterns are embedded in a noisy setting... the
following two vectors have similar patterns of 1 2 3 4 4 ...

How do I detect such a similar pattern? How to decide how many shifts should
my y2 have?

>> x=[1 0 1 1 2 3 4 4 1 0 1 0 1];
>> y2=[1 1 1 1 1 1 2 3 4 4 1 0 1 0 1];
>> xcorr(x, y2)

ans =

  Columns 1 through 7

    1.0000 0.0000 2.0000 1.0000 4.0000 8.0000 11.0000

  Columns 8 through 14

   15.0000 17.0000 23.0000 32.0000 42.0000 51.0000 43.0000

  Columns 15 through 21

   34.0000 26.0000 22.0000 22.0000 20.0000 16.0000 12.0000

  Columns 22 through 28

    7.0000 3.0000 2.0000 2.0000 1.0000 1.0000 0

  Column 29

    0.0000

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