(Georgia Institute of Technology, 2010-12)
Kaess, Michael; Ila, Viorela; Roberts, Richard; Dellaert, Frank
We present a novel data structure, the Bayes tree, that provides an algorithmic
foundation enabling a better understanding of existing graphical model
inference algorithms and their connection to sparse matrix factorization methods.
Similar to a clique tree, a Bayes tree encodes a factored probability density, but
unlike the clique tree it is directed and maps more naturally to the square root information
matrix of the simultaneous localization and mapping (SLAM) problem.
In this paper, we highlight three insights provided by our new data structure. First,
the Bayes tree provides a better understanding of batch matrix factorization in terms
of probability densities. Second, we show how the fairly abstract updates to a matrix
factorization translate to a simple editing of the Bayes tree and its conditional
densities. Third, we apply the Bayes tree to obtain a completely novel algorithm for
sparse nonlinear incremental optimization, that combines incremental updates with
fluid relinearization of a reduced set of variables for efficiency, combined with fast
convergence to the exact solution. We also present a novel strategy for incremental
variable reordering to retain sparsity.We evaluate our algorithm on standard datasets
in both landmark and pose SLAM settings.
(Georgia Institute of Technology, 2004-05)
Kaess, Michael; Zboinski, Rafal; Dellaert, Frank
We investigate the automated reconstruction of piecewise
smooth 3D curves, using subdivision curves as a simple but flexible curve
representation. This representation allows tagging corners to model nonsmooth
features along otherwise smooth curves. We present a reversible
jump Markov chain Monte Carlo approach which obtains an approximate
posterior distribution over the number of control points and tags.
In a Rao-Blackwellization scheme, we integrate out the control point locations,
reducing the variance of the resulting sampler. We apply this
general methodology to the reconstruction of piecewise smooth curves
from multiple calibrated views, in which the object is segmented from the
background using a Markov random field approach. Results are shown
for multiple images of two pot shards as would be encountered in archaeological
applications.