Maths sign

Hi,

I am trying to understand scale space article at http://en.wikipedia.org/wiki/Scale_space

I don't understand a maths sign that is used by the article. Attached is the print screen of that maths sign. It is the E sign at L and derivative. Thus it mean sum ?

Thanks a lot.
Zizi
zizi21Asked:
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Mohammed KhawajaManager - Infrastructure:  Information TechnologyCommented:
I believe you are talking about the upside down triangle which is the laplace operator.  Refer to wikipedia for more:

http://en.wikipedia.org/wiki/Laplace_operator
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zizi21Author Commented:
Sorry, that is not it.

It is the curly E that becomes the subscript for L and derivative. Please refer to the attached sum.jpg.
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ozoCommented:
I don't see attached sum.jpg, but are you referring to the normalized derivatives?
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zizi21Author Commented:
Sorry, thought i had uploaded it. just uploaded it.. could you please take a look at it. yes,i am referring to L and derivatives..
sum.jpg
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ozoCommented:
It looks liks Lindberg's ° normalized derivative operator http://www.itu.dk/people/stud3154/Assignment2_1/Lindeberg98a.pdf.
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zizi21Author Commented:
I am referring to Edge Detection and ridge detection with automatic scale selection paper by the same author (Tony Lindeberg).
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ozoCommented:
In his  paper referenced in http:#a40370372 he defines it at (6)
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Mohammed KhawajaManager - Infrastructure:  Information TechnologyCommented:
As mentioned by ozo, it is Lindberg's normalized derivative operator and is part of formula used in scaling algorithms.
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IanStatisticianCommented:
zizi,

The curly e is the greek letter  Xi.  Refer to wikipedia explanation for more on the greek letters.

Ξ   Capital xi is written as three horizontal bars with the middle one slightly shorter than the top and bottom.
ξ  Lower case xi  is written as your funny E.

In the article using xi the author is using these greek letters because he ran out of roman ones. In fact he also uses greek eta ( Η η ) which in lower case looks like an lowercase n that has been extended downwards on the right side.

In his mathematics both x and y are variables, and he changes variables to help with the algebra.  x  -> ξ,  y -> η

As used in this paper they are not operators, they are just variable placeholders (as in x ranges from a min value to a max value for horizontal position and y ranges from a bottom to a top value to give vertical position).  xi and eta (ξ,  η) are each (in this case linearly) related to x and y respectively.

In this article, and L appear to be operators and the subscripts x, y, ξ,  η are just there to specify different operators.

Hope this helps,

Ian
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zizi21Author Commented:
Thanks all for your help. Apologies for coming late as something happened which prevented me frm accessing the computer
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