Human Activity Modeling on Shape Manifold

Abstract

In this paper we propose a stochastic modeling of human activity on shape manifold. From a video sequence, human activity are extracted as a sequence of shape. Such sequence is considered as one realization of a random process on shape manifold. Then Different activity is modeled by manifold valued random process with different distribution. To solve the stochastic modeling on manifold, we first map the process on the shape manifold to a Euclidean process. Then the process is modeled by linear models such as stationary incremental process and a piecewise stationary incremental process. The mapping from manifold valued process to Euclidean process is known as stochastic development. The idea is to parallelly transport the tangent of curve on manifold to a single tangent space. The advantage of such technique is the one to one correspondence between the process in flat space and the one on manifold. The proposed algorithm is tested on two activity data base [RS01] [BGSB05]. The result demonstrate the high accuracy of our modeling in characterizing different activities.