Compositional hierarchical representation of shape manifolds for classification of non-manifold shapes

Mete Ozay, Umit Rusen Aktas, Jeremy L. Wyatt, Ale Leonardis

Research output: Chapter in Book/Report/Conference proceedingConference contribution

3 Citations (Scopus)

Abstract

We address the problem of statistical learning of shape models which are invariant to translation, rotation and scale in compositional hierarchies when data spaces of measurements and shape spaces are not topological manifolds. In practice, this problem is observed while modeling shapes having multiple disconnected components, e.g. partially occluded shapes in cluttered scenes. We resolve the aforementioned problem by first reformulating the relationship between data and shape spaces considering the interaction between Receptive Fields (RFs) and Shape Manifolds (SMs) in a compositional hierarchical shape vocabulary. Then, we suggest a method to model the topological structure of the SMs for statistical learning of the geometric transformations of the shapes that are defined by group actions on the SMs. For this purpose, we design a disjoint union topology using an indexing mechanism for the formation of shape models on SMs in the vocabulary, recursively. We represent the topological relationship between shape components using graphs, which are aggregated to construct a hierarchical graph structure for the shape vocabulary. To this end, we introduce a framework to implement the indexing mechanisms for the employment of the vocabulary for structural shape classification. The proposed approach is used to construct invariant shape representations. Results on benchmark shape classification outperform state-of-the-art methods.

Original languageEnglish
Title of host publication2015 International Conference on Computer Vision, ICCV 2015
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages1662-1670
Number of pages9
ISBN (Electronic)9781467383912
DOIs
Publication statusPublished - 2015 Feb 17
Event15th IEEE International Conference on Computer Vision, ICCV 2015 - Santiago, Chile
Duration: 2015 Dec 112015 Dec 18

Publication series

NameProceedings of the IEEE International Conference on Computer Vision
Volume2015 International Conference on Computer Vision, ICCV 2015
ISSN (Print)1550-5499

Other

Other15th IEEE International Conference on Computer Vision, ICCV 2015
CountryChile
CitySantiago
Period15/12/1115/12/18

ASJC Scopus subject areas

  • Software
  • Computer Vision and Pattern Recognition

Fingerprint Dive into the research topics of 'Compositional hierarchical representation of shape manifolds for classification of non-manifold shapes'. Together they form a unique fingerprint.

Cite this