@article {12745,
	title = {Activity modeling and recognition using shape theory},
	journal = {Behavior Representation in Modeling and Simulation},
	year = {2003},
	month = {2003///},
	abstract = {Understanding activities arising out of the interactions of aconfiguration of moving objects is an important problem in
video understanding, with applications in surveillance and
monitoring, animation, medicine, etc. In this paper, we in-
troduce a novel method for activity modeling based on the
observation that that every activity has with it an associated
structure characterized by a non-rigid shape and a dynamic
model that characterizes the variations in the structure as
the activity unfolds. We propose two mathematical models
to characterize the non-rigid shape and its dynamics. In
our first approach, we propose to model an activity by the
polygonal shape formed by joining the locations of these
point masses at any time
, and its deformation over time.
This uses the statistical shape theory of Kendall. The second
approach models the trajectories of each separate class of
moving objects in 3D shape space, and thus can identify dif-
ferent kinds of activities. It is based on the factorization the-
orem for matrices, which has been used before in computer
vision for structure estimation. Deviations from the learned
normal shape for each activity is used to identify abnormal
ones. We demonstrate the applicability of our algorithms
using real-life video sequences in an airport surveillance
environment. We are able to identify the major activities
that take place in that setting and detect abnormal ones.
},
	author = {Chellapa, Rama and Vaswani, N. and Chowdhury, A.K.R.}
}
