Person:

Dellaert, Frank

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https://hdl.handle.net/1853/71202

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School of Interactive Computing

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Now showing 1 - 10 of 174

Factor Graphs and GTSAM: A Hands-on Introduction

(Georgia Institute of Technology, 2012-09) Dellaert, Frank ; Georgia Institute of Technology. Center for Robotics and Intelligent Machines

In this document I provide a hands-on introduction to both factor graphs and GTSAM. Factor graphs are graphical models (Koller and Friedman, 2009) that are well suited to modeling complex estimation problems, such as Simultaneous Localization and Mapping (SLAM) or Structure from Motion (SFM). You might be familiar with another often used graphical model, Bayes networks, which are directed acyclic graphs. A factor graph, however, is a bipartite graph consisting of factors connected to variables. The variables represent the unknown random variables in the estimation problem, whereas the factors represent probabilistic information on those variables, derived from measurements or prior knowledge. In the following sections I will show many examples from both robotics and vision. The GTSAM toolbox (GTSAM stands for “Georgia Tech Smoothing and Mapping”) toolbox is a BSD-licensed C++ library based on factor graphs, developed at the Georgia Institute of Technology by myself, many of my students, and collaborators. It provides state of the art solutions to the SLAM and SFM problems, but can also be used to model and solve both simpler and more complex estimation problems. It also provides a MATLAB interface which allows for rapid prototype development, visualization, and user interaction. GTSAM exploits sparsity to be computationally efficient. Typically measurements only provide information on the relationship between a handful of variables, and hence the resulting factor graph will be sparsely connected. This is exploited by the algorithms implemented in GTSAM to reduce computational complexity. Even when graphs are too dense to be handled efficiently by direct methods, GTSAM provides iterative methods that are quite efficient regardless. You can download the latest version of GTSAM at http://tinyurl.com/gtsam.
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 ; Georgia Institute of Technology. Center for Robotics and Intelligent Machines ; Georgia Institute of Technology. College of Computing ; Università di Padova.Dipartimento di ingegneria dell'informazione

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.
Using the CONDENSATION Algorithm for Robust, Vision-Based Mobile Robot Localization

(Georgia Institute of Technology, 1999) Burgard, Wolfram ; Dellaert, Frank ; Fox, Dieter ; Thrun, Sebastian ; Carnegie-Mellon University. Computer Science Dept. ; Universität Bonn. Institut für Informatik III

To navigate reliably in indoor environments, a mobile robot must know where it is. This includes both the ability of globally localizing the robot from scratch, as well as tracking the robot’s position once its location is known. Vision has long been advertised as providing a solution to these problems, but we still lack efficient solutions in unmodified environments. Many existing approaches require modification of the environment to function properly, and those that work within unmodified environments seldomly address the problem of global localization. In this paper we present a novel, vision-based localization method based on the CONDENSATION algorithm [17, 18], a Bayesian filtering method that uses a sampling-based density representation. We show how the CONDENSATION algorithm can be used in a novel way to track the position of the camera platform rather than tracking an object in the scene. In addition, it can also be used to globally localize the camera platform, given a visual map of the environment. Based on these two observations, we present a vision-based robot localization method that provides a solution to a difficult and open problem in the mobile robotics community. As evidence for the viability of our approach, we show both global localization and tracking results in the context of a state of the art robotics application.
Concurrent Filtering and Smoothing: A Parallel Architecture for Real-Time Navigation and Full Smoothing

(Georgia Institute of Technology, 2014) Williams, Stephen ; Indelman, Vadim ; Kaess, Michael ; Roberts, Richard ; Leonard, John J. ; Dellaert, Frank ; Georgia Institute of Technology. Institute for Robotics and Intelligent Machines ; Carnegie-Mellon University. School of Computer Science ; Carnegie-Mellon University. Robotics Institute ; Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory

We present a parallelized navigation architecture that is capable of running in real-time and incorporating long-term loop closure constraints while producing the optimal Bayesian solution. This architecture splits the inference problem into a low-latency update that incorporates new measurements using just the most recent states (filter), and a high-latency update that is capable of closing long loops and smooths using all past states (smoother). This architecture employs the probabilistic graphical models of Factor Graphs, which allows the low-latency inference and high-latency inference to be viewed as sub-operations of a single optimization performed within a single graphical model. A specific factorization of the full joint density is employed that allows the different inference operations to be performed asynchronously while still recovering the optimal solution produced by a full batch optimization. Due to the real-time, asynchronous nature of this algorithm, updates to the state estimates from the high-latency smoother will naturally be delayed until the smoother calculations have completed. This architecture has been tested within a simulated aerial environment and on real data collected from an autonomous ground vehicle. In all cases, the concurrent architecture is shown to recover the full batch solution, even while updated state estimates are produced in real-time.
Rao-Blackwellized Importance Sampling of Camera Parameters from Simple User Input with Visibility Preprocessing in Line Space

(Georgia Institute of Technology, 2006-06) Quennesson, Kevin ; Dellaert, Frank ; Georgia Institute of Technology. Center for Robotics and Intelligent Machines ; Georgia Institute of Technology. College of Computing

Users know what they see before where they are: it is more natural to talk about high level visibility information ("I see such object") than about one's location or orientation. In this paper we introduce a method to find in 3D worlds a density of viewpoints of camera locations from high level visibility constraints on objects in this world. Our method is based on Rao-Blackwellized importance sampling. For efficiency purposes, the proposal distribution used for sampling is extracted from a visibility preprocessing technique adapted from computer graphics. We apply the method for finding in a 3D city model of Atlanta the virtual locations of real-world cameras and viewpoints.
Intrinsic Localization and Mapping With 2 Applications: Diffusion Mapping and Marco Polo Localization

(Georgia Institute of Technology, 2003) Alegre, Fernando ; Dellaert, Frank ; Martinson, Eric Beowulf ; Georgia Institute of Technology. College of Computing

We investigate Intrinsic Localization and Mapping (ILM) for teams of mobile robots, a multi-robot variant of SLAM where the robots themselves are used as landmarks. We develop what is essentially a straightforward application of Bayesian estimation to the problem, and present two complimentary views on the associated optimization problem that provide insight into the problem and allows one to devise initialization strategies, indispensable in practice. We also provide a discussion of the degrees of freedom and ambiguities in the solution. Finally, we introduce two applications of ILM that bring out its potential: Diffusion Mapping and Marco Polo localization.
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.
Square Root SAM: Simultaneous Localization and Mapping via Square Root Information Smoothing

(Georgia Institute of Technology, 2005) Dellaert, Frank

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 matrix 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. 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, an interpretation of factorization in terms of the graphical model associated with the SLAM problem, and simulation results that underscore the potential of these methods for use in practice.
Bayesian Surprise and Landmark Detection

(Georgia Institute of Technology, 2009-05) Ranganathan, Ananth ; Dellaert, Frank ; Georgia Institute of Technology. Center for Robotics and Intelligent Machines ; Georgia Institute of Technology. College of Computing ; Honda Research Institute USA, Inc.

Automatic detection of landmarks, usually special places in the environment such as gateways, for topological mapping has proven to be a difficult task. We present the use of Bayesian surprise, introduced in computer vision, for landmark detection. Further, we provide a novel hierarchical, graphical model for the appearance of a place and use this model to perform surprise-based landmark detection. Our scheme is agnostic to the sensor type, and we demonstrate this by implementing a simple laser model for computing surprise. We evaluate our landmark detector using appearance and laser measurements in the context of a topological mapping algorithm, thus demonstrating the practical applicability of the detector.
Inference In The Space Of Topological Maps: An MCMC-based Approach

(Georgia Institute of Technology, 2004-09) Ranganathan, Ananth ; Dellaert, Frank ; Georgia Institute of Technology. Center for Robotics and Intelligent Machines

While probabilistic techniques have been considered extensively in the context of metric maps, no general purpose probabilistic methods exist for topological maps. We present the concept of Probabilistic Topological Maps (PTMs), a sample-based representation that approximates the posterior distribution over topologies given the available sensor measurements. The PTM is obtained through the use of MCMC-based Bayesian inference over the space of all possible topologies. It is shown that the space of all topologies is equivalent to the space of set partitions of all available measurements. While the space of possible topologies is intractably large, our use of Markov chain Monte Carlo sampling to infer the approximate histograms overcomes the combinatorial nature of this space and provides a general solution to the correspondence problem in the context of topological mapping. We present experimental results that validate our technique and generate good maps even when using only odometry as the sensor measurements.