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International Journal of Computer Vision

, Volume 116, Issue 2, pp 161–173 | Cite as

Geometry-Based Symbolic Approximation for Fast Sequence Matching on Manifolds

  • Rushil AnirudhEmail author
  • Pavan Turaga
Article

Abstract

In this paper, we consider the problem of fast and efficient indexing techniques for sequences evolving in non-Euclidean spaces. This problem has several applications in the areas of human activity analysis, where there is a need to perform fast search, and recognition in very high dimensional spaces. The problem is made more challenging when representations such as landmarks, contours, and human skeletons etc. are naturally studied in a non-Euclidean setting where even simple operations are much more computationally intensive than their Euclidean counterparts. We propose a geometry and data adaptive symbolic framework that is shown to enable the deployment of fast and accurate algorithms for activity recognition, dynamic texture recognition, motif discovery. Toward this end, we present generalizations of key concepts of piece-wise aggregation and symbolic approximation for the case of non-Euclidean manifolds. We show that one can replace expensive geodesic computations with much faster symbolic computations with little loss of accuracy in activity recognition and discovery applications. The framework is general enough to work across both Euclidean and non-Euclidean spaces, depending on appropriate feature representations without compromising on the ultra-low bandwidth, high speed and high accuracy. The proposed methods are ideally suited for real-time systems and low complexity scenarios.

Keywords

Manifold sequence indexing Competitive learning Activity recognition Differential geometry Data mining 

Notes

Acknowledgments

Rushil Anirudh and Pavan Turaga were supported by the NSF CCF CIF grant #1320267.

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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.School of Electrical, Computer and Energy EngineeringArizona State UniversityTempeUSA
  2. 2.School of Arts, Media and EngineeringArizona State UniversityTempeUSA

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