A Novel Approach to the Approximation of Conformal Mappings and Emerging Applications to Shape Recognition of Planar-Domain

Sa'Ar Hersonsky, Hamid R. Arabnia, Thiab R. Taha

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

1 Scopus citations

Abstract

There have been significant advances in computer graphics and computer vision for description and recognition of rigid shapes and objects. However, the problem of description and recognition of non-rigid shapes and objects is still an open problem. In an earlier study [10], we proposed a geodesic field space-based approach to describe and analyze non-rigid shapes from a point correspondence perspective. In this current study, we describe a canonical set of shapes, very much like a dictionary with mathematical structures that are inherently relevant to the shape classification task. We propose a novel method of representing 2D shapes where every planar shape will be assigned a unique fingerprint, which is a conformal map of the shape to a canonical shape in the plan. We believe that the study presented in this paper can be extended to describe and recognize both, rigid and non-rigid shapes and objects. The main focus of this paper is to provide an insight into the mathematical and geometrical fundamentals. We will restrict our attention to the case of doubly-connected planar domains.

Original languageEnglish
Title of host publicationProceedings - 2017 International Conference on Computational Science and Computational Intelligence, CSCI 2017
EditorsFernando G. Tinetti, Quoc-Nam Tran, Leonidas Deligiannidis, Mary Qu Yang, Mary Qu Yang, Hamid R. Arabnia
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages532-534
Number of pages3
ISBN (Electronic)9781538626528
DOIs
StatePublished - 4 Dec 2018
Externally publishedYes
Event2017 International Conference on Computational Science and Computational Intelligence, CSCI 2017 - Las Vegas, United States
Duration: 14 Dec 201716 Dec 2017

Publication series

NameProceedings - 2017 International Conference on Computational Science and Computational Intelligence, CSCI 2017

Conference

Conference2017 International Conference on Computational Science and Computational Intelligence, CSCI 2017
Country/TerritoryUnited States
CityLas Vegas
Period14/12/1716/12/17

Keywords

  • computer vision
  • conformal mapping
  • shape recognition

ASJC Scopus subject areas

  • Computer Science (miscellaneous)
  • Artificial Intelligence
  • Computer Networks and Communications
  • Computer Science Applications
  • Safety, Risk, Reliability and Quality

Fingerprint

Dive into the research topics of 'A Novel Approach to the Approximation of Conformal Mappings and Emerging Applications to Shape Recognition of Planar-Domain'. Together they form a unique fingerprint.

Cite this