28,119 research outputs found
Impact of anisotropy and fracture density on the approximation of the effective permeability of a fractured rock mass using 2D models
Imperial Users onl
Flipping Cubical Meshes
We define and examine flip operations for quadrilateral and hexahedral
meshes, similar to the flipping transformations previously used in triangular
and tetrahedral mesh generation.Comment: 20 pages, 24 figures. Expanded journal version of paper from 10th
International Meshing Roundtable. This version removes some unwanted
paragraph breaks from the previous version; the text is unchange
Geometric Multi-Model Fitting with a Convex Relaxation Algorithm
We propose a novel method to fit and segment multi-structural data via convex
relaxation. Unlike greedy methods --which maximise the number of inliers-- this
approach efficiently searches for a soft assignment of points to models by
minimising the energy of the overall classification. Our approach is similar to
state-of-the-art energy minimisation techniques which use a global energy.
However, we deal with the scaling factor (as the number of models increases) of
the original combinatorial problem by relaxing the solution. This relaxation
brings two advantages: first, by operating in the continuous domain we can
parallelize the calculations. Second, it allows for the use of different
metrics which results in a more general formulation.
We demonstrate the versatility of our technique on two different problems of
estimating structure from images: plane extraction from RGB-D data and
homography estimation from pairs of images. In both cases, we report accurate
results on publicly available datasets, in most of the cases outperforming the
state-of-the-art
Topological Data Analysis with Bregman Divergences
Given a finite set in a metric space, the topological analysis generalizes
hierarchical clustering using a 1-parameter family of homology groups to
quantify connectivity in all dimensions. The connectivity is compactly
described by the persistence diagram. One limitation of the current framework
is the reliance on metric distances, whereas in many practical applications
objects are compared by non-metric dissimilarity measures. Examples are the
Kullback-Leibler divergence, which is commonly used for comparing text and
images, and the Itakura-Saito divergence, popular for speech and sound. These
are two members of the broad family of dissimilarities called Bregman
divergences.
We show that the framework of topological data analysis can be extended to
general Bregman divergences, widening the scope of possible applications. In
particular, we prove that appropriately generalized Cech and Delaunay (alpha)
complexes capture the correct homotopy type, namely that of the corresponding
union of Bregman balls. Consequently, their filtrations give the correct
persistence diagram, namely the one generated by the uniformly growing Bregman
balls. Moreover, we show that unlike the metric setting, the filtration of
Vietoris-Rips complexes may fail to approximate the persistence diagram. We
propose algorithms to compute the thus generalized Cech, Vietoris-Rips and
Delaunay complexes and experimentally test their efficiency. Lastly, we explain
their surprisingly good performance by making a connection with discrete Morse
theory
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