Partial Single- and Multishape Dense Correspondence Using Functional Maps

Or Litany, Emanuele Rodolà, Alex Bronstein, Michael Bronstein, Daniel Cremers

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review

Abstract

Shape correspondence is a fundamental problem in computer graphics and vision, with applications in various problems including animation, texture mapping, robotic vision, medical imaging, archaeology and many more. In settings where the shapes are allowed to undergo nonrigid deformations and only partial views are available, the problem becomes very challenging. In this chapter we describe recent techniques designed to tackle such problems. Specifically, we explain how the renown functional maps framework can be extended to tackle the partial setting. We then present a further extension to the multipart case in which one tries to establish correspondence between a collection of shapes. Finally, we focus on improving the technique efficiency, by disposing of its spatial ingredient and thus keeping the computation in the spectral domain. Extensive experimental results are provided along with the theoretical explanations, to demonstrate the effectiveness of the described methods in these challenging scenarios.

Original languageEnglish
Title of host publicationProcessing, Analyzing and Learning of Images, Shapes, and Forms
Subtitle of host publicationPart 1
EditorsRon Kimmel, Xue-Cheng Tai
PublisherElsevier B.V.
Pages55-90
Number of pages36
ISBN (Print)9780444642059
DOIs
StatePublished - 2018
Externally publishedYes

Publication series

NameHandbook of Numerical Analysis
Volume19
ISSN (Print)1570-8659

Keywords

  • 65D18
  • 68U05
  • Computational geometry
  • Functional maps
  • Shape analysis

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