10,715 research outputs found
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
Rotation Averaging and Strong Duality
In this paper we explore the role of duality principles within the problem of
rotation averaging, a fundamental task in a wide range of computer vision
applications. In its conventional form, rotation averaging is stated as a
minimization over multiple rotation constraints. As these constraints are
non-convex, this problem is generally considered challenging to solve globally.
We show how to circumvent this difficulty through the use of Lagrangian
duality. While such an approach is well-known it is normally not guaranteed to
provide a tight relaxation. Based on spectral graph theory, we analytically
prove that in many cases there is no duality gap unless the noise levels are
severe. This allows us to obtain certifiably global solutions to a class of
important non-convex problems in polynomial time.
We also propose an efficient, scalable algorithm that out-performs general
purpose numerical solvers and is able to handle the large problem instances
commonly occurring in structure from motion settings. The potential of this
proposed method is demonstrated on a number of different problems, consisting
of both synthetic and real-world data
Feedback Control Goes Wireless: Guaranteed Stability over Low-power Multi-hop Networks
Closing feedback loops fast and over long distances is key to emerging
applications; for example, robot motion control and swarm coordination require
update intervals of tens of milliseconds. Low-power wireless technology is
preferred for its low cost, small form factor, and flexibility, especially if
the devices support multi-hop communication. So far, however, feedback control
over wireless multi-hop networks has only been shown for update intervals on
the order of seconds. This paper presents a wireless embedded system that tames
imperfections impairing control performance (e.g., jitter and message loss),
and a control design that exploits the essential properties of this system to
provably guarantee closed-loop stability for physical processes with linear
time-invariant dynamics. Using experiments on a cyber-physical testbed with 20
wireless nodes and multiple cart-pole systems, we are the first to demonstrate
and evaluate feedback control and coordination over wireless multi-hop networks
for update intervals of 20 to 50 milliseconds.Comment: Accepted final version to appear in: 10th ACM/IEEE International
Conference on Cyber-Physical Systems (with CPS-IoT Week 2019) (ICCPS '19),
April 16--18, 2019, Montreal, QC, Canad
A Riemannian low-rank method for optimization over semidefinite matrices with block-diagonal constraints
We propose a new algorithm to solve optimization problems of the form for a smooth function under the constraints that is positive
semidefinite and the diagonal blocks of are small identity matrices. Such
problems often arise as the result of relaxing a rank constraint (lifting). In
particular, many estimation tasks involving phases, rotations, orthonormal
bases or permutations fit in this framework, and so do certain relaxations of
combinatorial problems such as Max-Cut. The proposed algorithm exploits the
facts that (1) such formulations admit low-rank solutions, and (2) their
rank-restricted versions are smooth optimization problems on a Riemannian
manifold. Combining insights from both the Riemannian and the convex geometries
of the problem, we characterize when second-order critical points of the smooth
problem reveal KKT points of the semidefinite problem. We compare against state
of the art, mature software and find that, on certain interesting problem
instances, what we call the staircase method is orders of magnitude faster, is
more accurate and scales better. Code is available.Comment: 37 pages, 3 figure
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