Conceptualization of Object Compositions Using Persistent Homology
This work addresses shape analysis for computer vision or graphics researchers, but it appears incremental as it applies existing topological methods to a specific task.
The authors tackled the problem of learning shape concepts from object segmentations by proposing a topological shape analysis method that uses persistent homology to reveal hidden groups of shape commonalities, with experiments showing that these groups represent semantically meaningful concepts and generalize to external datasets.
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.