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Dellaert,
Frank
Dellaert,
Frank
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ItemParameterized Duration Modeling for Switching Linear Dynamic Systems(Georgia Institute of Technology, 2006-06) Oh, Sang Min ; Rehg, James M. ; Dellaert, FrankWe introduce an extension of switching linear dynamic systems (SLDS) with parameterized duration modeling capabilities. The proposed model allows arbitrary duration models and overcomes the limitation of a geometric distribution induced in standard SLDSs. By incorporating a duration model which reflects the data more closely, the resulting model provides reliable inference results which are robust against observation noise. Moreover, existing inference algorithms for SLDSs can be adopted with only modest additional effort in most cases where an SLDS model can be applied. In addition, we observe the fact that the duration models would vary across data sequences in certain domains, which complicates learning and inference tasks. Such variability in duration is overcome by introducing parameterized duration models. The experimental results on honeybee dance decoding tasks demonstrate the robust inference capabilities of the proposed model.
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ItemLearning and Inference in Parametric Switching Linear Dynamic Systems(Georgia Institute of Technology, 2005-10) Oh, Sang Min ; Rehg, James M. ; Balch, Tucker ; Dellaert, FrankWe introduce parametric switching linear dynamic systems (P-SLDS) for learning and interpretation of parametrized motion, i.e., motion that exhibits systematic temporal and spatial variations. Our motivating example is the honeybee dance: bees communicate the orientation and distance to food sources through the dance angles and waggle lengths of their stylized dances. Switching linear dynamic systems (SLDS) are a compelling way to model such complex motions. However, SLDS does not provide a means to quantify systematic variations in the motion. Previously, Wilson & Bobick presented parametric HMMs [21], an extension to HMMs with which they successfully interpreted human gestures. Inspired by their work, we similarly extend the standard SLDS model to obtain parametric SLDS. We introduce additional global parameters that represent systematic variations in the motion, and present general expectation-maximization (EM) methods for learning and inference. In the learning phase, P-SLDS learns canonical SLDS model from data. In the inference phase, P-SLDS simultaneously quantifies the global parameters and labels the data. We apply these methods to the automatic interpretation of honey-bee dances, and present both qualitative and quantitative experimental results on actual bee-tracks collected from noisy video data.
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ItemData-Driven MCMC for Learning and Inference in Switching Linear Dynamic Systems(Georgia Institute of Technology, 2005-07) Oh, Sang Min ; Rehg, James M. ; Balch, Tucker ; Dellaert, FrankSwitching 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, but inference in SLDS models is computationally intractable. This paper describes a novel inference algorithm for SLDS models based on the Data- Driven MCMC paradigm. We describe a new proposal distribution which substantially increases the convergence speed. Comparisons to standard deterministic approximation methods demonstrate the improved accuracy of our new approach. We apply our approach to the problem of learning an SLDS model of the bee dance. Honeybees communicate the location and distance to food sources through a dance that takes place within the hive. We learn SLDS model parameters from tracking data which is automatically extracted from video. We then demonstrate the ability to successfully segment novel bee dances into their constituent parts, effectively decoding the dance of the bees.
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ItemMixture Trees for Modeling and Fast Conditional Sampling with Applications in Vision and Graphics(Georgia Institute of Technology, 2005-06) Dellaert, Frank ; Kwatra, Vivek ; Oh, Sang MinWe introduce mixture trees, a tree-based data-structure for modeling joint probability densities using a greedy hierarchical density estimation scheme. We show that the mixture tree models data efficiently at multiple resolutions, and present fast conditional sampling as one of many possible applications. In particular, the development of this datastructure was spurred by a multi-target tracking application, where memory-based motion modeling calls for fast conditional sampling from large empirical densities. However, it is also suited to applications such as texture synthesis, where conditional densities play a central role. Results will be presented for both these applications.
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ItemMap-based Priors for Localization(Georgia Institute of Technology, 2004-09) Oh, Sang Min ; Tariq, Sarah ; Walker, Bruce N. ; Dellaert, FrankLocalization from sensor measurements is a fundamental task for navigation. Particle filters are among the most promising candidates to provide a robust and realtime solution to the localization problem. They instantiate the localization problem as a Bayesian filtering problem and approximate the posterior density over location by a weighted sample set. In this paper, we introduce map-based priors for localization, using the semantic information available in maps to bias the motion model toward areas of higher probability. We show that such priors, under a particular assumption , can easily be incorporated in the particle filter by means of a pseudo likelihood. The resulting filter is more reliable and more accurate. We show experimental results on a GPS-based outdoor people tracker that illustrate the approach and highlight its potential.