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Maths sign

Posted on 2014-10-09
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Last Modified: 2014-10-13
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
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Question by:zizi21
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Expert Comment

by:Mohammed Khawaja
ID: 40370303
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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by:zizi21
ID: 40370308
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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Expert Comment

by:ozo
ID: 40370334
I don't see attached sum.jpg, but are you referring to the normalized derivatives?
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Author Comment

by:zizi21
ID: 40370356
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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by:ozo
ID: 40370372
It looks liks Lindberg's ° normalized derivative operator http://www.itu.dk/people/stud3154/Assignment2_1/Lindeberg98a.pdf.
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by:zizi21
ID: 40370382
I am referring to Edge Detection and ridge detection with automatic scale selection paper by the same author (Tony Lindeberg).
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ozo earned 400 total points
ID: 40370395
In his  paper referenced in http:#a40370372 he defines it at (6)
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Expert Comment

by:Mohammed Khawaja
ID: 40370495
As mentioned by ozo, it is Lindberg's normalized derivative operator and is part of formula used in scaling algorithms.
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Assisted Solution

by:ShannonEE
ShannonEE earned 1600 total points
ID: 40371927
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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Author Comment

by:zizi21
ID: 40378782
Thanks all for your help. Apologies for coming late as something happened which prevented me frm accessing the computer
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