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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Klassen, E., Srivastava, A., Mio, W., Joshi, S.H.: Analysis of planar shapes using geodesic paths on shape spaces. IEEE Trans. Pattern Analysis and Machine Intelligence (2004)
Hsu, E.P.: Stochastic analysis on manifold. Graduate Studies in Mathematics, 38
Bishop, R.L., Crittenden, R.J.: Geometry of Manifold. Academic Press, New York (1964)
Kobayashi, S., Nomizu, k.: Foundations of differential geometry, vol. 1. John Wiley & Sons, West Sussex (1996)
Blank, M., Gorelick, L., Shechtman, E., Basri, M.I.R.: Action as Space-Time Shapes. In: IEEE ICCV (2005)
Priestley, M.B., Subba Rao, T.: A Test for Non stationarity of Time-Series. Journal of the Royal Statistical Society. Series B 31(1), 140–149 (1969)
Keogh, E., Chu, S., Hart, D., Pazzani, M.: Segmenting time series: A survey and novel approach, Data Mining in Time Series Databases. World Scientific, Singapore (2004)
Aggarwal, J.K., Cai, Q.: Human Motion Analysis: A Reivew. Computer Vision and Image Understanding 73, 428–440 (1999)
Turaga, P., Chellappa, R., Subrahmanian, V., Udrea, O.: Machine recognition of human activities: A survey. IEEE Transactions on Circuits and Systems for Video Technology 18, 1473–1488 (2008)
Elgammal, A.M., Lee, C.-S.: Inferring 3D body pose from silhouettes using activity manifold learning. In: Proceedings of the Conference on Computer Vision and Pattern Recognition (CVPR 2004), Washington, DC, vol. 2, pp. 681–688 (June 2004)
Veeraraghavan, A., Roy-Chowdhury, A.K., Chellappa, R.: Matching Shape Sequences in Video with Applications in Human Movement Analysis. IEEE Trans. Pattern Analysis and Machine Intelligence 27(12) (December 2005)
Veeraraghavan, A., Chowdhury, A.R., Chellappa, R.: Role of shape and kinematics in human movement analysis. In: IEEE Computer Society Conference on Computer Vision and Pattern Recognition (2004)
Kendall, D.: Shape Manifolds, Procrustean Metrics and Complex Projective Spaces. Bull. London Math. Soc. 16, 81–121 (1984)
Chen, P., Steen, R., Yezzi, A., Krim, H.: Joint brain parametric T1-Map segmentation and RF inhomogeneity calibration. International Journal of Biomedical Imaging (269525), 14 p. (2009)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Yi, S., Krim, H., Norris, L.K. (2012). Human Activity Modeling as Brownian Motion on Shape Manifold. In: Bruckstein, A.M., ter Haar Romeny, B.M., Bronstein, A.M., Bronstein, M.M. (eds) Scale Space and Variational Methods in Computer Vision. SSVM 2011. Lecture Notes in Computer Science, vol 6667. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-24785-9_53
Download citation
DOI: https://doi.org/10.1007/978-3-642-24785-9_53
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-24784-2
Online ISBN: 978-3-642-24785-9
eBook Packages: Computer ScienceComputer Science (R0)