Posted by
Kenneth Sloan-2 on
May 29, 2007; 3:56pm
URL: http://imagej.273.s1.nabble.com/Re-distance-between-adjacent-particles-tp3699248p3699250.html
On May 29, 2007, at 7:59 AM, Noel BONNET wrote:
> Hi all,
>
> I do not completely agree with these statements, especially the one
> considering that "the user need to decide how many of the closest
> neighbors
> he want to include in the average".
> Instead, I think "the image is as it is" and "the closest neighbors
> are as
> they are" ...
> In the framework of Computational Geometry (the framework in which the
> contributions of Gabriel Landini and Karsten Rodenacker are), the
> number of
> neighbors is perfectly defined (at least in an Euclidean
> framework): it is
> the number of Voronoï zones that are adjacent to the Voronoï zone
> associated
> to the current object.
But...but...while this approach is the currently predominant one, not
EVERY problem fits the mold. If adjacent particles interact with
each other in ways *other* than common borders, then neighbors which
are not nearest-neighbors in the Delaunay/Voronoi sense may still be
relevant.
The current combinatorial-oriented version of "computational
geometry" is near and dear to my heart, but I still think it is
relevant to lookd at older methods. I agree with a previous poster's
recommendation of Ripley's book on spatial statistics.
and...just for the record...the Delaunay/Voronoi definitions of
nearest-neighbor is not the *only* view (although it is certainly the
most popular).
--
Kenneth Sloan
[hidden email]
Computer and Information Sciences +1-205-934-2213
University of Alabama at Birmingham FAX +1-205-934-5473
Birmingham, AL 35294-1170
http://www.cis.uab.edu/sloan/