Human activity as a manifold valued random process

IEEE Transactions on Image Processing : a Publication of the IEEE Signal Processing Society
Sheng YiLarry K Norris

Abstract

Most of previous shape based human activity models were built with either a linear assumption or an extrinsic interpretation of the nonlinear geometry of the shape space, both of which proved to be problematic on account of the nonlinear intrinsic geometry of the associated shape spaces. In this paper we propose an intrinsic stochastic modeling of human activity on a shape manifold. More importantly, within an elegant and theoretically sound framework, our work effectively bridges the nonlinear modeling of human activity on a nonlinear space, with the classic stochastic modeling in a Euclidean space, and thereby provides a foundation for a more effective and accurate analysis of the nonlinear feature space of activity models. From a video sequence, human activity is extracted as a sequence of shapes. Such a sequence is considered as one realization of a random process on a shape manifold. Different activities are then modeled as manifold valued random processes with different distributions. To address the problem of stochastic modeling on a manifold, we first construct a nonlinear invertible map of a manifold valued process to a Euclidean process. The resulting process is then modeled as a global or piecewise Brownian motion. T...Continue Reading

References

Sep 21, 2004·IEEE Transactions on Pattern Analysis and Machine Intelligence·Eric KlassenShantanu H Joshi
Dec 17, 2005·IEEE Transactions on Pattern Analysis and Machine Intelligence·Ashok VeeraraghavanRama Chellappa
Aug 28, 2009·International Journal of Biomedical Imaging·Ping-Feng ChenHamid Krim
Oct 6, 2010·IEEE Transactions on Pattern Analysis and Machine Intelligence·Anuj SrivastavaIan H Jermyn

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Citations

Sep 24, 2014·IEEE Transactions on Image Processing : a Publication of the IEEE Signal Processing Society·Sheng Yi, Hamid Krim

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