(Georgia Institute of Technology, 2006)
Oh, Sang Min; Rehg, James M.; Balch, Tucker; Dellaert, Frank
Switching Linear Dynamic System (SLDS) models are a popular technique for modeling complex nonlinear dynamic systems. An SLDS has significantly more descriptive power than an HMM by using continuous hidden states. However, the use of SLDS models in practical applications is challenging for several reasons. First, exact inference in SLDS models is computationally intractable. Second, the geometric duration model induced in standard SLDSs limits their representational power. Third, standard SLDSs do not provide a systematic way to robustly interpret systematic variations governed by higher order parameters.
The contributions in this paper address all three challenges above. First, we present a data-driven MCMC sampling method for SLDSs as a robust and efficient approximate inference method. Second, we present segmental switching linear dynamic systems (S-SLDS), where the geometric distributions are replaced with arbitrary duration models. Third, we extend the standard model with a parametric model that can capture systematic temporal and spatial variations. The resulting parametric SLDS model (P-SLDS) uses EM to robustly interpret parametrized motions by incorporating additional global parameters that underly systematic variations of the overall motion.
The overall development of the proposed inference methods and extensions for SLDSs provide a robust framework to interpret complex motions. The framework is applied to the honey bee dance interpretation task in the context of the ongoing BioTracking project at Georgia Institute of Technology. The experimental results suggest that the enhanced models provide an effective framework for a wide range of motion analysis applications.
(Georgia Institute of Technology, 2003)
Khan, Zia; Balch, Tucker; Dellaert, Frank
We describe a Markov chain Monte Carlo based particle filter that effectively deals with interacting targets, i.e., targets that are influenced by the proximity and/or behavior of other targets. Such interactions cause problems for traditional approaches to the data association problem. In response, we developed a joint tracker that includes a more sophisticated motion model to maintain the identity of targets throughout an interaction, drastically reducing tracker failures. The paper presents two main contributions: (1) we show how a Markov random field (MRF) motion prior, built on the fly at each time step, can substantially improve tracking when targets interact, and (2) we show how this can be done efficiently using Markov chain Monte Carlo (MCMC) sampling. We prove that incorporating an MRF to model interactions is equivalent to adding an additional interaction factor to the importance weights in a joint particle filter. Since a joint particle filter suffers from exponential complexity in the number of tracked targets, we replace the traditional importance sampling step in the particle filter with an MCMC sampling step. The resulting filter deals efficiently and effectively with complicated interactions when targets approach each other. We present both qualitative and quantitative results to substantiate the claims made in the paper, including a large scale experiment on a video-sequence of over 10,000 frames in length.