Measuring shape relations using r-parallel sets
- URL: http://arxiv.org/abs/2008.03927v1
- Date: Mon, 10 Aug 2020 07:30:51 GMT
- Title: Measuring shape relations using r-parallel sets
- Authors: Hans JT Stephensen, Anne Marie Svane, Carlos Benitez, Steven A.
Goldman, Jon Sporring
- Abstract summary: We present a theory on the geometrical interaction between objects based on the theory of spatial point processes.
Our measures are simple like the volume and area of an object, but describe further details about the shape of individual objects and their pairwise geometrical relation.
- Score: 0.5249805590164901
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: Geometrical measurements of biological objects form the basis of many
quantitative analyses. Hausdorff measures such as the volume and the area of
objects are simple and popular descriptors of individual objects, however, for
most biological processes, the interaction between objects cannot be ignored,
and the shape and function of neighboring objects are mutually influential.
In this paper, we present a theory on the geometrical interaction between
objects based on the theory of spatial point processes. Our theory is based on
the relation between two objects: a reference and an observed object. We
generate the $r$-parallel sets of the reference object, we calculate the
intersection between the $r$-parallel sets and the observed object, and we
define measures on these intersections. Our measures are simple like the volume
and area of an object, but describe further details about the shape of
individual objects and their pairwise geometrical relation. Finally, we propose
a summary statistics for collections of shapes and their interaction.
We evaluate these measures on a publicly available FIB-SEM 3D data set of an
adult rodent.
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