Title: Conceptualization of Object Compositions Using Persistent Homology,
Abstract: A topological shape analysis is proposed and utilized to learn concepts that
reflect shape commonalities. Our approach is two-fold: i) a spatial topology
analysis of point cloud segment constellations within objects. Therein
constellations are decomposed and described in an hierarchical manner - from
single segments to segment groups until a single group reflects an entire
object. ii) a topology analysis of the description space in which segment
decompositions are exposed in. Inspired by Persistent Homology, hidden groups
of shape commonalities are revealed from object segment decompositions.
Experiments show that extracted persistent groups of commonalities can
represent semantically meaningful shape concepts. We also show the
generalization capability of the proposed approach considering samples of
external datasets.