Posted by
karo03 on
Mar 07, 2010; 10:05am
URL: http://imagej.273.s1.nabble.com/calculation-of-the-distance-between-points-gold-particles-tp3689065p3689071.html
... interesting thread!
Thank you for your remarks, Kenneth and Jim.
May be it is a bit academic or philosophical, but talking about the set of distances from one selected or designated object to all others or from all objects to all others makes a certain difference.
Assuming that from Maria Rubio not the set of all distances was intended (no designated object), my question was which measure can be extracted from the set of all distances from all to all.
By the way, Delaunay triangulation reflects strongly our visual habits. If we look at a set of objects (points) and try to designate neighbors of one point, we mostly select Delaunay neighbors. I think there is a publication starting from the background skeleton (a generalization of Voronoi) from Fernand Meyer and its relation to visual neighboring of objects.
Karsten
Am 07.03.2010 um 02:27 schrieb Kenneth Sloan:
> On Mar 6, 2010, at 17:41 , Karsten Rodenacker wrote:
>
>> Of course not. But if all distances should be calculated, what could be expected from such a measure?
>>
>> Karsten
>>
>
> This is not often what most people want these days - but there are several long-established statistical
> techniques which start with the measurement of ALL the distances between ALL pairs of points. Delaunay triangulation
> is a relatively new technique (gaining favor sometime in the 1980's or so - during the 1980's I can recall
> using both Voronoi/Delaunay based measurements AND all-pairs methods to analyze the packing geometry of photoreceptors in human retina).
>
> Given a histogram of all-pairs distances, it is possible to make inferences about the distances involved in the FIRST ring of neighbors - and also the second, and the third - depending on how regular the arrangement is.
>
>
> --
> Kenneth Sloan
>
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Karsten
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