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Dellaert, Frank

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    Binding Balls: Fast Detection of Binding Sites Using a Property of Spherical Fourier Transform
    (Georgia Institute of Technology, 2009) Comin, Matteo ; Guerra, Concettina ; Dellaert, Frank
    The functional prediction of proteins is one of the most challenging problems in modern biology. An established computational technique involves the identification of threedimensional local similarities in proteins. In this article, we present a novel method to quickly identify promising binding sites. Our aim is to efficiently detect putative binding sites without explicitly aligning them. Using the theory of Spherical Harmonics, a candidate binding site is modeled as a Binding Ball. The Binding Ball signature, offered by the Spherical Fourier coefficients, can be efficiently used for a fast detection of putative regions. Our contribution includes the Binding Ball modeling and the definition of a scoring function that does not require aligning candidate regions. Our scoring function can be computed efficiently using a property of Spherical Fourier transform (SFT) that avoids the evaluation of all alignments. Experiments on different ligands show good discrimination power when searching for known binding sites. Moreover, we prove that this method can save up to 40% in time compared with traditional approaches.
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    Learning and Inferring Motion Patterns Using Parametric Segmental Switching Linear Dynamic Systems
    (Georgia Institute of Technology, 2008) 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 provides the possibility to describe complex temporal patterns more concisely and accurately 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 on-going 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.
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    MCMC Data Association and Sparse Factorization Updating for Real Time Multitarget Tracking with Merged and Multiple Measurements
    (Georgia Institute of Technology, 2006-12) Khan, Zia ; Balch, Tucker ; Dellaert, Frank
    In several multitarget tracking applications, a target may return more than one measurement per target and interacting targets may return multiple merged measurements between targets. Existing algorithms for tracking and data association, initially applied to radar tracking, do not adequately address these types of measurements. Here, we introduce a probabilistic model for interacting targets that addresses both types of measurements simultaneously. We provide an algorithm for approximate inference in this model using a Markov chain Monte Carlo (MCMC)-based auxiliary variable particle filter. We Rao-Blackwellize the Markov chain to eliminate sampling over the continuous state space of the targets. A major contribution of this work is the use of sparse least squares updating and downdating techniques, which significantly reduce the computational cost per iteration of the Markov chain. Also, when combined with a simple heuristic, they enable the algorithm to correctly focus computation on interacting targets. We include experimental results on a challenging simulation sequence. We test the accuracy of the algorithm using two sensor modalities, video, and laser range data. We also show the algorithm exhibits real time performance on a conventional PC.
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    Square Root SAM Simultaneous Localization and Mapping via Square Root Information Smoothing
    (Georgia Institute of Technology, 2006) Dellaert, Frank ; Kaess, Michael
    Solving the SLAM problem is one way to enable a robot to explore, map, and navigate in a previously unknown environment. We investigate smoothing approaches as a viable alternative to extended Kalman filter-based solutions to the problem. In particular, we look at approaches that factorize either the associated information matrix or the measurement Jacobian into square root form. Such techniques have several significant advantages over the EKF: they are faster yet exact, they can be used in either batch or incremental mode, are better equipped to deal with non-linear process and measurement models, and yield the entire robot trajectory, at lower cost for a large class of SLAM problems. In addition, in an indirect but dramatic way, column ordering heuristics automatically exploit the locality inherent in the geographic nature of the SLAM problem. In this paper we present the theory underlying these methods, along with an interpretation of factorization in terms of the graphical model associated with the SLAM problem. We present both simulation results and actual SLAM experiments in large-scale environments that underscore the potential of these methods as an alternative to EKF-based approaches.
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    EM, MCMC, and Chain Flipping for Structure from Motion with Unknown Correspondence
    (Georgia Institute of Technology, 2003) Dellaert, Frank ; Seitz, Steven M. ; Thorpe, Charles E. ; Thrun, Sebastian
    Learning spatial models from sensor data raises the challenging data association problem of relating model parameters to individual measurements. This paper proposes an EM-based algorithm, which solves the model learning and the data association problem in parallel. The algorithm is developed in the context of the the structure from motion problem, which is the problem of estimating a 3D scene model from a collection of image data. To accommodate the spatial constraints in this domain, we compute virtual measurements as sufficient statistics to be used in the M-step. We develop an efficient Markov chain Monte Carlo sampling method called chain flipping, to calculate these statistics in the E-step. Experimental results show that we can solve hard data association problems when learning models of 3D scenes, and that we can do so efficiently. We conjecture that this approach can be applied to a broad range of model learning problems from sensor data, such as the robot mapping problem.