Differential geometric representations and algorithms for some pattern recognition and computer vision problems

Ruonan Li, Pavan Turaga, Anuj Srivastava, Rama Chellappa

Research output: Contribution to journalArticle

3 Scopus citations

Abstract

Scene geometry, imaging laws, as well as computational mechanisms generate mathematical constraints on both raw data and computed features. In many cases, these constraints place the patterns on geometrically well-defined spaces, described as manifolds. In such cases, we argue that exploiting the geometry of these manifolds is important to our understanding of the objects and semantics in the imagery. Statistics and algorithms accounting for manifolds also yield improved performance in many vision applications. We justify these arguments by presenting our recent research efforts based on manifold theory for addressing a variety of pattern recognition and computer vision problems, including hashing on manifolds for efficient search, statistical modeling on Grassmann/Stiefel manifolds for activity recognition, discriminative learning for group motion recognition, stochastic optimization for spatio-temporal alignment, and shape matching. We also discuss the manifolds of re-parameterizations and elastic shapes, as well as applications of manifolds to face recognition and unsupervised adaptation of classification model from one domain to another.

Original languageEnglish (US)
Pages (from-to)3-16
Number of pages14
JournalPattern Recognition Letters
Volume43
Issue number1
DOIs
StatePublished - Jul 1 2014

Keywords

  • Activity recognition
  • Hashing
  • Manifold
  • Shape analysis
  • Video alignment

ASJC Scopus subject areas

  • Software
  • Signal Processing
  • Computer Vision and Pattern Recognition
  • Artificial Intelligence

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