Optimization problems associated withmanifold-valued curves with applications in computer vision

Rushil Anirudh, Pavan Turaga, Anuj Srivastava

Research output: Chapter in Book/Report/Conference proceedingChapter

Abstract

A commonly occurring need in many computer vision applications is the need to represent, compare, and manipulate manifold-valued curves, while allowing for enough flexibility to operate in resource constrained environments. We address these concerns in this chapter, by proposing a dictionary learning scheme that takes geometry and time into account, while performing better than the original data in applications such as activity recognition. We are able to do this with the use of the transport square-root velocity function, which provides an elastic representation for trajectories on Riemannian manifolds. Since these operations can be computationally very expensive, we also present a geometry-based symbolic approximation framework, as a result of which low-bandwidth transmission and accurate real-time analysis for recognition or searching through sequential data become fairly straightforward. We discuss the different optimization problems encountered in this context-learning a sparse representation for actions using extrinsic and intrinsic features, solving the registration problem between two Riemannian trajectories, and learning an optimal clustering scheme for symbolic approximation.

Original languageEnglish (US)
Title of host publicationHandbook of Convex Optimization Methods in Imaging Science
PublisherSpringer International Publishing
Pages207-228
Number of pages22
ISBN (Electronic)9783319616094
ISBN (Print)9783319616087
DOIs
StatePublished - Jan 1 2017

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Computer vision
Trajectories
Geometry
Glossaries
Bandwidth

ASJC Scopus subject areas

  • Computer Science(all)
  • Engineering(all)

Cite this

Anirudh, R., Turaga, P., & Srivastava, A. (2017). Optimization problems associated withmanifold-valued curves with applications in computer vision. In Handbook of Convex Optimization Methods in Imaging Science (pp. 207-228). Springer International Publishing. https://doi.org/10.1007/978-3-319-61609-4_9

Optimization problems associated withmanifold-valued curves with applications in computer vision. / Anirudh, Rushil; Turaga, Pavan; Srivastava, Anuj.

Handbook of Convex Optimization Methods in Imaging Science. Springer International Publishing, 2017. p. 207-228.

Research output: Chapter in Book/Report/Conference proceedingChapter

Anirudh, R, Turaga, P & Srivastava, A 2017, Optimization problems associated withmanifold-valued curves with applications in computer vision. in Handbook of Convex Optimization Methods in Imaging Science. Springer International Publishing, pp. 207-228. https://doi.org/10.1007/978-3-319-61609-4_9
Anirudh R, Turaga P, Srivastava A. Optimization problems associated withmanifold-valued curves with applications in computer vision. In Handbook of Convex Optimization Methods in Imaging Science. Springer International Publishing. 2017. p. 207-228 https://doi.org/10.1007/978-3-319-61609-4_9
Anirudh, Rushil ; Turaga, Pavan ; Srivastava, Anuj. / Optimization problems associated withmanifold-valued curves with applications in computer vision. Handbook of Convex Optimization Methods in Imaging Science. Springer International Publishing, 2017. pp. 207-228
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