(Georgia Institute of Technology, 2014-09)
Carlone, Luca; Alcantarilla, Pablo Fernandez; Chiu, Han-Pang; Kira, Zsolt; Dellaert, Frank
Bundle Adjustment (BA) can be seen as an inference process over a
factor graph. From this perspective, the Schur complement trick can be interpreted as an ordering
choice for elimination. The elimination of a single point in the BA graph induces a factor over the set of cameras observing that point. This factor has a very low information content (a point observation enforces a low-rank constraint on the cameras). In this work we show that, when using conjugate gradient solvers, there is a computational advantage in “grouping” factors corresponding to sets of points (fragments) that are co-visible by the same set of cameras. Intuitively, we collapse many factors with low information content into a single factor that imposes a high-rank constraint among the cameras. We provide a grounded way to group factors: the selection of points that are co-observed by the same camera patterns is a data mining problem, and standard tools for frequent pattern mining can be applied to reveal the structure of BA graphs. We demonstrate the computational advantage of grouping in large BA problems and we show that it enables a consistent reduction of BA time with respect to state-of-the-art solvers (Ceres [1]).
(Georgia Institute of Technology, 2014)
Carlone, Luca; Kira, Zsolt; Beall, Chris; Indelman, Vadim; Dellaert, Frank
Factor graphs are a general estimation framework
that has been widely used in computer vision and robotics. In
several classes of problems a natural partition arises among
variables involved in the estimation. A subset of the variables
are actually of interest for the user: we call those
target
variables. The remaining variables are essential for the formulation of the optimization problem underlying maximum a
posteriori (MAP) estimation; however these variables, that we
call
support
variables, are not strictly required as output of the
estimation problem. In this paper, we propose a systematic way
to abstract support variables, defining optimization problems
that are only defined over the set of target variables. This
abstraction naturally leads to the definition of
smart factors, which correspond to constraints among target variables. We
show that this perspective unifies the treatment of heterogeneous problems, ranging from structureless bundle adjustment
to robust estimation in SLAM. Moreover, it enables to exploit
the underlying structure of the optimization problem and the
treatment of degenerate instances, enhancing both computational efficiency and robustness.