Posted by
Jeremy Adler on
URL: http://imagej.273.s1.nabble.com/Delaunay-Voronoi-intersected-with-boundary-tp5016272p5016276.html
The Voronoi gives distances to some of the nearest neighbors - there can be neighboring particles closer than some of particles that are identified by the Voronoi that are excluded because there is a closer particle in that direction. The Voronoi is really about dividing up an area based on proximity to the nearest object not assessing nearest neighbors.
If you really want the average distance to a given number of neighbors you could to trawl through a list of coordinates - which can get slow if the numbers are very large.
Edges are definitely a problem and of course you need to work with a 3D dataset as 2D distances may not reflect the 3D.
Edge effects can be eliminated by also examining the volume around each object - a distance transform that is then masked by the volume of the cell will work. If you then multiply the binary image showing all objects with the DT around one particle, the histogram of this image gives the distance of every object from your source object. So you can get the profile of the volume around a single object and a profile of the number of objects around your chosen object - compare the two. Repeat for many objects.
It is also good idea to compare the distribution you have with a randomized distribution.
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From: ImageJ Interest Group [
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Sent: 28 April 2016 23:06
To:
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Subject: Delaunay/Voronoi intersected with boundary
Hello,
I have the following problem: I have a number of particles within a certain
boundary shape (the cell). I am interested in measuring the average distance
of a particle to its neighbours. A neighbor would be defined by the Voronoi
diagramm as particles with a common edge in the Voronio map.
I am aware that the Delaunay triangulation can gives me precisely that, but
there is one problem: It doesn't take into account the boundary of the
domain. I.e. two particles will be considered neighbors, even if their
Voronoi domains intersect OUTSIDE of the full domain (the cell).
Does anyone have an idea to avoid this?
Thank you and many regards,
Angelika
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