Homeomorphic manifold analysis (HMA): Generalized separation of style and content on manifolds

Ahmed Elgammal, Chan Su Lee

Research output: Contribution to journalArticlepeer-review

18 Scopus citations


The problem of separation of style and content is an essential element of visual perception, and is a fundamental mystery of perception. This problem appears extensively in different computer vision applications. The problem we address in this paper is the separation of style and content when the content lies on a low-dimensional nonlinear manifold representing a dynamic object. We show that such a setting appears in many human motion analysis problems. We introduce a framework for learning parameterization of style and content in such settings. Given a set of topologically equivalent manifolds, the Homeomorphic Manifold Analysis (HMA) framework models the variation in their geometries in the space of functions that maps between a topologically equivalent common representation and each of them. The framework is based on decomposing the style parameters in the space of nonlinear functions that map between a unified embedded representation of the content manifold and style-dependent visual observations. We show the application of the framework in synthesis, recognition, and tracking of certain human motions that follow this setting, such as gait and facial expressions.

Original languageEnglish (US)
Pages (from-to)291-310
Number of pages20
JournalImage and Vision Computing
Issue number4
StatePublished - 2013

All Science Journal Classification (ASJC) codes

  • Signal Processing
  • Computer Vision and Pattern Recognition


  • Facial expression analysis
  • Gait analysis
  • Human motion analysis
  • Kernel methods
  • Manifold embedding
  • Style and content


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