Human Activity Modeling as Brownian Motion on Shape Manifold

  • Sheng Yi
  • Hamid Krim
  • Larry K. Norris
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6667)

Abstract

In this paper we propose a stochastic modeling of human activity on a shape manifold. From a video sequence, human activity is extracted as a sequence of shape. Such a sequence is considered as one realization of a random process on shape manifold. Then Different activities are modeled by manifold valued random processes with different distributions. To solve the problem of stochastic modeling on a manifold, we first regress a manifold values process to a Euclidean process. The resulted process then could be modeled by linear models such as a stationary incremental process and a piecewise stationary incremental process. The mapping from manifold to Euclidean space is known as a stochastic development. The idea is to parallelly transport the tangent along curve on manifold to a single tangent space. The advantage of such technique is the one to one correspondence between the process in Euclidean space and the one on manifold. The proposed algorithm is tested on database [5] and compared with the related work in [5]. The result demonstrate the high accuracy of our modeling in characterizing different activities.

Keywords

Brownian Motion Random Process Video Sequence Tangent Space Curve Development 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Sheng Yi
    • 1
  • Hamid Krim
    • 1
  • Larry K. Norris
    • 1
  1. 1.North Carolina Sate UniversityUSA

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