One of the main challenges of high level analysis of human behavior is the high dimension of the feature space. To overcome the curse of dimensionality, we propose in this paper, a space curve representation of the high dimensional behavior features. The features of interest here, are restricted to sequences of shapes of the human body such as those extracted from a video sequence. This evolution is a one dimensional sub-manifold in shape space. The central idea of the proposed representation takes root in the Whitney embedding theorem which guarantees an embedding of a one dimensional manifold in as a space curve. The resulting of such dimension reduction, is a simplification of comparing two behaviors to that of comparing two curves in R³. This comparison is additionally theoretically and numerically easier to implement for statistical analysis. By exploiting sampling theory, we are moreover able to achieve a computationally efficient embedding that is invertible. Specifically, we first construct a global coordinates expression for the one dimension manifold and sampled along a generating curve.As experiment result, we provide substantiating modeling examples and illustrations of behavior classification.

Date Published: 4 September 2009
PDF: 8 pages
Proc. SPIE 7446, Wavelets XIII, 74460E (4 September 2009); doi: 10.1117/12.825541

Published in SPIE Proceedings Vol. 7446:
Wavelets XIII
Vivek K. Goyal; Manos Papadakis; Dimitri Van De Ville, Editor(s)