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Re: How to average to find 'circular' symmetry in a SQUARE matrix?

From: Robert A. Macy
Subject: Re: How to average to find 'circular' symmetry in a SQUARE matrix?
Date: Mon, 15 Jan 2007 18:01:29 -0800


I have an x-y matrix of an axisymmetric structure.  

It is true that I can create a new matrix, whose individual
values are determined by drawing a circle through EACH
point and filling in that specific data point with the
integrated average around each circle arc.  Note there
would be duplicate values as each single arc should
coincide with 4 locations.  

It seems possible to find the average around the arc by
using very small angle steps. and probably get away with
linear interpolation between any 4 data points closest to
each position along the arc.  That means a lot of pieces as
I go around the arc and tiny angle steps along the arc to
make certain it's small enough.  A lot of work.

I guess my question is after doing all that effort does it
come out about the same as if I had just averaged quadrants
together and mirror images of quadrants together?  

Or, is there a gain in complexing up the solution?

To understand what I'm doing.  picture the sombrero as
shown in x-y plane.  Add noise to the image.  Now, find the
sombrero again without the noise in it.  

             - Robert -

On Mon, 15 Jan 2007 20:45:37 -0500
 Doug Stewart <address@hidden> wrote:
> Obviously if you wanted the average of the array then
> there would be no question: so what do you want the
> average of?
> If you want the average of a doughnut  section then if
> you do rectangular to polar conversion and select all the
> point that have a radius  between m and n   you could
> average them.
> I'm not sure what you want.
> Doug

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