358 research outputs found
Spectral Motion Synchronization in SE(3)
This paper addresses the problem of motion synchronization (or averaging) and
describes a simple, closed-form solution based on a spectral decomposition,
which does not consider rotation and translation separately but works straight
in SE(3), the manifold of rigid motions. Besides its theoretical interest,
being the first closed form solution in SE(3), experimental results show that
it compares favourably with the state of the art both in terms of precision and
speed
Semidefinite Relaxations for Robust Multiview Triangulation
We propose an approach based on convex relaxations for certifiably optimal
robust multiview triangulation. To this end, we extend existing relaxation
approaches to non-robust multiview triangulation by incorporating a least
squares cost function. We propose two formulations, one based on epipolar
constraints and one based on fractional reprojection constraints. The first is
lower dimensional and remains tight under moderate noise and outlier levels,
while the second is higher dimensional and therefore slower but remains tight
even under extreme noise and outlier levels. We demonstrate through extensive
experiments that the proposed approaches allow us to compute provably optimal
reconstructions even under significant noise and a large percentage of
outliers
Robust Rotation Synchronization via Low-rank and Sparse Matrix Decomposition
This paper deals with the rotation synchronization problem, which arises in
global registration of 3D point-sets and in structure from motion. The problem
is formulated in an unprecedented way as a "low-rank and sparse" matrix
decomposition that handles both outliers and missing data. A minimization
strategy, dubbed R-GoDec, is also proposed and evaluated experimentally against
state-of-the-art algorithms on simulated and real data. The results show that
R-GoDec is the fastest among the robust algorithms.Comment: The material contained in this paper is part of a manuscript
submitted to CVI
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