5,425 research outputs found
Sinkhorn Barycenters with Free Support via Frank-Wolfe Algorithm
We present a novel algorithm to estimate the barycenter of arbitrary
probability distributions with respect to the Sinkhorn divergence. Based on a
Frank-Wolfe optimization strategy, our approach proceeds by populating the
support of the barycenter incrementally, without requiring any pre-allocation.
We consider discrete as well as continuous distributions, proving convergence
rates of the proposed algorithm in both settings. Key elements of our analysis
are a new result showing that the Sinkhorn divergence on compact domains has
Lipschitz continuous gradient with respect to the Total Variation and a
characterization of the sample complexity of Sinkhorn potentials. Experiments
validate the effectiveness of our method in practice.Comment: 46 pages, 8 figure
Scale Invariant Interest Points with Shearlets
Shearlets are a relatively new directional multi-scale framework for signal
analysis, which have been shown effective to enhance signal discontinuities
such as edges and corners at multiple scales. In this work we address the
problem of detecting and describing blob-like features in the shearlets
framework. We derive a measure which is very effective for blob detection and
closely related to the Laplacian of Gaussian. We demonstrate the measure
satisfies the perfect scale invariance property in the continuous case. In the
discrete setting, we derive algorithms for blob detection and keypoint
description. Finally, we provide qualitative justifications of our findings as
well as a quantitative evaluation on benchmark data. We also report an
experimental evidence that our method is very suitable to deal with compressed
and noisy images, thanks to the sparsity property of shearlets
SCONCE: A cosmic web finder for spherical and conic geometries
The latticework structure known as the cosmic web provides a valuable insight
into the assembly history of large-scale structures. Despite the variety of
methods to identify the cosmic web structures, they mostly rely on the
assumption that galaxies are embedded in a Euclidean geometric space. Here we
present a novel cosmic web identifier called SCONCE (Spherical and CONic Cosmic
wEb finder) that inherently considers the 2D (RA,DEC) spherical or the 3D
(RA,DEC,) conic geometry. The proposed algorithms in SCONCE generalize the
well-known subspace constrained mean shift (SCMS) method and primarily address
the predominant filament detection problem. They are intrinsic to the
spherical/conic geometry and invariant to data rotations. We further test the
efficacy of our method with an artificial cross-shaped filament example and
apply it to the SDSS galaxy catalogue, revealing that the 2D spherical version
of our algorithms is robust even in regions of high declination. Finally, using
N-body simulations from Illustris, we show that the 3D conic version of our
algorithms is more robust in detecting filaments than the standard SCMS method
under the redshift distortions caused by the peculiar velocities of halos. Our
cosmic web finder is packaged in python as SCONCE-SCMS and has been made
publicly available.Comment: 20 pages, 9 figures, 2 table
Automated sequence and motion planning for robotic spatial extrusion of 3D trusses
While robotic spatial extrusion has demonstrated a new and efficient means to
fabricate 3D truss structures in architectural scale, a major challenge remains
in automatically planning extrusion sequence and robotic motion for trusses
with unconstrained topologies. This paper presents the first attempt in the
field to rigorously formulate the extrusion sequence and motion planning (SAMP)
problem, using a CSP encoding. Furthermore, this research proposes a new
hierarchical planning framework to solve the extrusion SAMP problems that
usually have a long planning horizon and 3D configuration complexity. By
decoupling sequence and motion planning, the planning framework is able to
efficiently solve the extrusion sequence, end-effector poses, joint
configurations, and transition trajectories for spatial trusses with
nonstandard topologies. This paper also presents the first detailed computation
data to reveal the runtime bottleneck on solving SAMP problems, which provides
insight and comparing baseline for future algorithmic development. Together
with the algorithmic results, this paper also presents an open-source and
modularized software implementation called Choreo that is machine-agnostic. To
demonstrate the power of this algorithmic framework, three case studies,
including real fabrication and simulation results, are presented.Comment: 24 pages, 16 figure
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