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Dellaert, Frank

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    CAREER: Markov Chain Monte Carlo methods for large scale correspondence problems in computer vision and robotics
    (Georgia Institute of Technology, 2011-05-17) Dellaert, Frank ; Khan, Zia ; Potthast, Christian
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    Robust Generative Subspace Modeling: The Subspace t Distribution
    (Georgia Institute of Technology, 2004) Khan, Zia ; Dellaert, Frank
    Linear latent variable models such as statistical factor analysis (SFA) and probabilistic principal component analysis (PPCA) assume that the data are distributed according to a multivariate Gaussian. A drawback of this assumption is that parameter learning in these models is sensitive to outliers in the training data. Approaches that rely on M-estimation have been introduced to render principal component analysis (PCA) more robust to outliers. M-estimation approaches assume the data are distributed according to a density with heavier tails than a Gaussian. Yet, these methods are limited in that they fail to define a probability model for the data. Data cannot be generated from these models, and the normalized probability of new data cannot evaluated. To address these limitations, we describe a generative probability model that accounts for outliers. The model is a linear latent variable model in which the marginal density over the data is a multivariate t, a distribution with heavier tails than a Gaussian. We present a computationally efficient expectation maximization (EM) algorithm for estimating the model parameters, and compare our approach with that of PPCA on both synthetic and real data sets.
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    An MCMC-based Particle Filter for Tracking Multiple Interacting Targets
    (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.