Homeomorphic manifold analysis (HMA): Untangling complex manifolds

Research output: Contribution to journalArticle

Abstract

Many problems in the fields of computer vision deal with image data that is embedded in very high-dimensional spaces. However, a typical assumption behind many algorithms is that the data lie on a low-dimensional manifold. Modeling the visual manifolds is quite challenging. Typically, image manifolds are neither smooth nor differentiable. This chapter presents the theory and applications of the concept of homeomorphic manifold analysis (HMA). Given a set of topologically equivalent manifolds, HMA models the variation in their geometries in the space of functions that map between a topologically equivalent common representation and each of them. This setting is suitable to different problems in visual learning. In particular, this chapter focuses on the applications of the framework to modeling the manifold of human motion in the image space.

Original languageEnglish (US)
Pages (from-to)1-81
Number of pages81
JournalAdvances in Imaging and Electron Physics
Volume187
DOIs
StatePublished - Jan 1 2015

All Science Journal Classification (ASJC) codes

  • Condensed Matter Physics
  • Nuclear and High Energy Physics
  • Electrical and Electronic Engineering

Keywords

  • Computer vision
  • facial expression analysis
  • gait analysis
  • human motion analysis
  • image manifolds
  • manifold learning
  • visual learning

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