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Erschienen in:
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2018 | OriginalPaper | Buchkapitel

9. Optimization Problems Associated with Manifold-Valued Curves with Applications in Computer Vision

verfasst von : Rushil Anirudh, Pavan Turaga, Anuj Srivastava

Erschienen in: Handbook of Convex Optimization Methods in Imaging Science

Verlag: Springer International Publishing

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Abstract

A commonly occurring requirement 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.

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Vorheriges Kapitel Sparsity Constrained Estimation in Image Processing and Computer Vision
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1
We are following the notation to denote the vector space (\(\xi \in \mathbb{R}^{6}\)) and the equivalent Lie algebra representation (\(\widehat{\xi }\in \mathfrak{s}\mathfrak{e}(3)\)) as described in p. 411 of [31].
 
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Metadaten
Titel
Optimization Problems Associated with Manifold-Valued Curves with Applications in Computer Vision
verfasst von
Rushil Anirudh
Pavan Turaga
Anuj Srivastava
Copyright-Jahr
2018
Buch
Handbook of Convex Optimization Methods in Imaging Science

Print ISBN: 978-3-319-61608-7

Electronic ISBN: 978-3-319-61609-4

Copyright-Jahr: 2018

DOI
https://doi.org/10.1007/978-3-319-61609-4_9