Map-based exploration of intrinsic shape differences and variability

Abstract

We develop a novel formulation for the notion of shape differences, aimed at providing detailed information about the location and nature of the differences or distortions between the two shapes being compared. Our difference operator, derived from a shape map, is much more informative than just a scalar global shape similarity score, rendering it useful in a variety of applications where more refined shape comparisons are necessary. The approach is intrinsic and is based on a linear algebraic framework, allowing the use of many common linear algebra tools (e.g, SVD, PCA) for studying a matrix representation of the operator. Remarkably, the formulation allows us not only to localize shape differences on the shapes involved, but also to compare shape differences across pairs of shapes, and to analyze the variability in entire shape collections based on the differences between the shapes. Moreover, while we use a map or correspondence to define each shape difference, consistent correspondences between the shapes are not necessary for comparing shape differences, although they can be exploited if available. We give a number of applications of shape differences, including parameterizing the intrinsic variability in a shape collection, exploring shape collections using local variability at different scales, performing shape analogies, and aligning shape collections.

Document Details

Document Type
Pub Defense Publication
Publication Date
Jul 21, 2013
Source ID
10.1145/2461912.2461959

Entities

People

  • Frédéric Chazal
  • Leonidas J. Guibas
  • Maks Ovsjanikov
  • Mirela Ben-chen
  • Omri Azencot
  • Raif M. Rustamov

Organizations

  • Agence Nationale de la Recherche
  • Air Force Office of Scientific Research
  • Division of Computing and Communication Foundations
  • Google
  • Institut National de Recherche en Informatique et en Automatique
  • Israel Science Foundation
  • National Center for Scientific Research
  • National Science Foundation Division of Mathematical Sciences
  • Seventh Framework Programme
  • Stanford University
  • Technion – Israel Institute of Technology
  • Volkswagen Foundation
  • École polytechnique

Tags

Readers

  • Computer Vision.
  • Theoretical Analysis.