"Shape Activity": a continuous-state HMM for moving/deforming shapes with application to abnormal activity detection

The aim is to model "activity" performed by a group of moving and interacting objects (which can be people, cars, or different rigid components of the human body) and use the models for abnormal activity detection. Previous approaches to modeling group activity include co-occurrence statistics (individual and joint histograms) and dynamic Bayesian networks, neither of which is applicable when the number of interacting objects is large. We treat the objects as point objects (referred to as "landmarks") and propose to model their changing configuration as a moving and deforming "shape" (using Kendall\´s shape theory for discrete landmarks). A continuous-state hidden Markov model is defined for landmark shape dynamics in an activity. The configuration of landmarks at a given time forms the observation vector, and the corresponding shape and the scaled Euclidean motion parameters form the hidden-state vector. An abnormal activity is then defined as a change in the shape activity model, which could be slow or drastic and whose parameters are unknown. Results are shown on a real abnormal activity-detection problem involving multiple moving objects.