19,903 research outputs found
Fast approximation of visibility dominance using topographic features as targets and the associated uncertainty
An approach to reduce visibility index computation time andmeasure the associated uncertainty in terrain visibility analysesis presented. It is demonstrated that the visibility indexcomputation time in mountainous terrain can be reduced substantially,without any significant information loss, if the lineof sight from each observer on the terrain is drawn only to thefundamental topographic features, i.e., peaks, pits, passes,ridges, and channels. However, the selected sampling of targetsresults in an underestimation of the visibility index ofeach observer. Two simple methods based on iterative comparisonsbetween the real visibility indices and the estimatedvisibility indices have been proposed for a preliminary assessmentof this uncertainty. The method has been demonstratedfor gridded digital elevation models
Engineering Art Galleries
The Art Gallery Problem is one of the most well-known problems in
Computational Geometry, with a rich history in the study of algorithms,
complexity, and variants. Recently there has been a surge in experimental work
on the problem. In this survey, we describe this work, show the chronology of
developments, and compare current algorithms, including two unpublished
versions, in an exhaustive experiment. Furthermore, we show what core
algorithmic ingredients have led to recent successes
Compressed sensing for wide-field radio interferometric imaging
For the next generation of radio interferometric telescopes it is of
paramount importance to incorporate wide field-of-view (WFOV) considerations in
interferometric imaging, otherwise the fidelity of reconstructed images will
suffer greatly. We extend compressed sensing techniques for interferometric
imaging to a WFOV and recover images in the spherical coordinate space in which
they naturally live, eliminating any distorting projection. The effectiveness
of the spread spectrum phenomenon, highlighted recently by one of the authors,
is enhanced when going to a WFOV, while sparsity is promoted by recovering
images directly on the sphere. Both of these properties act to improve the
quality of reconstructed interferometric images. We quantify the performance of
compressed sensing reconstruction techniques through simulations, highlighting
the superior reconstruction quality achieved by recovering interferometric
images directly on the sphere rather than the plane.Comment: 15 pages, 8 figures, replaced to match version accepted by MNRA
Second-order Shape Optimization for Geometric Inverse Problems in Vision
We develop a method for optimization in shape spaces, i.e., sets of surfaces
modulo re-parametrization. Unlike previously proposed gradient flows, we
achieve superlinear convergence rates through a subtle approximation of the
shape Hessian, which is generally hard to compute and suffers from a series of
degeneracies. Our analysis highlights the role of mean curvature motion in
comparison with first-order schemes: instead of surface area, our approach
penalizes deformation, either by its Dirichlet energy or total variation.
Latter regularizer sparks the development of an alternating direction method of
multipliers on triangular meshes. Therein, a conjugate-gradients solver enables
us to bypass formation of the Gaussian normal equations appearing in the course
of the overall optimization. We combine all of the aforementioned ideas in a
versatile geometric variation-regularized Levenberg-Marquardt-type method
applicable to a variety of shape functionals, depending on intrinsic properties
of the surface such as normal field and curvature as well as its embedding into
space. Promising experimental results are reported
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