17,121 research outputs found
Data-Driven Shape Analysis and Processing
Data-driven methods play an increasingly important role in discovering
geometric, structural, and semantic relationships between 3D shapes in
collections, and applying this analysis to support intelligent modeling,
editing, and visualization of geometric data. In contrast to traditional
approaches, a key feature of data-driven approaches is that they aggregate
information from a collection of shapes to improve the analysis and processing
of individual shapes. In addition, they are able to learn models that reason
about properties and relationships of shapes without relying on hard-coded
rules or explicitly programmed instructions. We provide an overview of the main
concepts and components of these techniques, and discuss their application to
shape classification, segmentation, matching, reconstruction, modeling and
exploration, as well as scene analysis and synthesis, through reviewing the
literature and relating the existing works with both qualitative and numerical
comparisons. We conclude our report with ideas that can inspire future research
in data-driven shape analysis and processing.Comment: 10 pages, 19 figure
Permutation and Grouping Methods for Sharpening Gaussian Process Approximations
Vecchia's approximate likelihood for Gaussian process parameters depends on
how the observations are ordered, which can be viewed as a deficiency because
the exact likelihood is permutation-invariant. This article takes the
alternative standpoint that the ordering of the observations can be tuned to
sharpen the approximations. Advantageously chosen orderings can drastically
improve the approximations, and in fact, completely random orderings often
produce far more accurate approximations than default coordinate-based
orderings do. In addition to the permutation results, automatic methods for
grouping calculations of components of the approximation are introduced, having
the result of simultaneously improving the quality of the approximation and
reducing its computational burden. In common settings, reordering combined with
grouping reduces Kullback-Leibler divergence from the target model by a factor
of 80 and computation time by a factor of 2 compared to ungrouped
approximations with default ordering. The claims are supported by theory and
numerical results with comparisons to other approximations, including tapered
covariances and stochastic partial differential equation approximations.
Computational details are provided, including efficiently finding the orderings
and ordered nearest neighbors, and profiling out linear mean parameters and
using the approximations for prediction and conditional simulation. An
application to space-time satellite data is presented
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