Conceptualization of Object Compositions Using Persistent Homology
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.
Code (0)
등록된 구현이 없습니다.
Tasks
ObjectSimilar Papers 제목 키워드 기반
A Framework for Fast and Stable Representations of Multiparameter Persistent Homology Decompositions
Topological data analysis (TDA) is an area of data science that focuses on using invariants from algebraic topology to provide multiscale shape descriptors for geometric data sets such as point clouds. One of the most im…
Topological Data AnalysisReLU Neural Networks, Polyhedral Decompositions, and Persistent Homolog
A ReLU neural network leads to a finite polyhedral decomposition of input space and a corresponding finite dual graph. We show that while this dual graph is a coarse quantization of input space, it is sufficiently robust…
QuantizationTopological Data Analysis for Word Sense Disambiguation
We develop and test a novel unsupervised algorithm for word sense induction and disambiguation which uses topological data analysis. Typical approaches to the problem involve clustering, based on simple low level feature…
ClusteringTopological Data AnalysisWord EmbeddingsWord Sense Disambiguation+1Persistent Topology of Syntax
We study the persistent homology of the data set of syntactic parameters of the world languages. We show that, while homology generators behave erratically over the whole data set, non-trivial persistent homology appears…
PositionG-invariant Persistent Homology
Classical persistent homology is a powerful mathematical tool for shape comparison. Unfortunately, it is not tailored to study the action of transformation groups that are different from the group Homeo(X) of all self-ho…