(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.
(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.
(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.