8,062 research outputs found
The Edit Distance for Reeb Graphs of Surfaces
No full textReeb graphs are structural descriptors that capture shape properties of a
topological space from the perspective of a chosen function. In this work, we define a
combinatorial distance for Reeb graphs of orientable surfaces in terms of the cost necessary
to transform one graph into another by edit operations. The main contributions
of this paper are the stability property and the optimality of this edit distance. More precisely,
the stability result states that changes in the Reeb graphs, measured by the edit
distance, are as small as changes in the functions, measured by the maximum norm.
The optimality result states that the edit distance discriminates Reeb graphs better than
any other distance for Reeb graphs of surfaces satisfying the stability property
Reeb Graphs of Piecewise Linear Functions
No full textThe Reeb graph is a popular tool in the field of computational
topology for shape analysis. The Reeb graph is usually thought of
as a transform from shapes, viewed as spaces endowed with functions, to
graphs. It finds its roots in the classical Morse theory, where the Reeb
graph transform is granted to produce a graph, but it finds its applications
mostly in Computer Graphics. Therefore it is usually applied on
objects that are not smooth but polyhedral. While the definition of the
Reeb graph perfectly makes sense also in the polyhedral case, it is not
straightforward to see that the output of the transform in this case is a
graph. This paper is devoted to provide a formal guarantee of this fact
An edit distance for Reeb graphs
No full textWe consider the problem of assessing the similarity of 3D shapes
using Reeb graphs from the standpoint of robustness under
perturbations. For this purpose, 3D objects are viewed as spaces
endowed with real-valued functions, while the similarity between
the resulting Reeb graphs is addressed through a graph edit
distance. The cases of smooth functions on manifolds and piecewise
linear functions on polyhedra stand out as the most interesting
ones. The main contribution of this paper is the introduction of a
general edit distance suitable for comparing Reeb graphs in these
settings. This edit distance promises to be useful for
applications in 3D object retrieval because of its stability
properties in the presence of noise
Barbara James
No full textDate:1943Barbara was born in Holdredge, Nebraska in the United States of America in 1943. In 1960 she arrived in Darwin working in a variety of occupations such as a journalist, historian, author, activist, advocate and editor. Barbara wrote 13 books including "No Man's Land" which explored the contributions of women in the Northern Territory. She also received a number of awards including 2001 NT Heritage Award, the 2000 NT Literary Essay Awards and the Chief Minister's Women's Achievement Award in 1999.JournalistHistorianAuthorActivistEditorAmerica
Stability of Reeb Graphs of Closed Curves
No full textReeb graphs are very popular shape descriptors in computational frameworks as they capture both geometrical properties of the shape, and its topological features. Some different methodologies have been proposed in the literature to estimate the similarity of shapes through the comparison of the associated Reeb graphs. In this context, one of the most important open questions is whether Reeb graphs are robust against function perturbations. In fact, it is clear that any data acquisition is subject to perturbations, noise and approximation errors and, if Reeb graphs were not stable, then distinct computational investigations of the same object could produce completely different results. In this paper we present an initial contribution to establishing stability properties for Reeb graphs. More precisely, focusing our attention on 1-dimensional manifolds, we define an editing distance between Reeb graphs, in terms of the cost necessary to transform one graph into another. Our main result is that changes in Morse functions imply smaller changes in the editing distance between Reeb graphs
An Edit Distance for Reeb Graphs
No full textWe consider the problem of assessing the similarity of 3D shapes using Reeb graphs from the standpoint of robustness under perturbations. For this purpose, 3D objects are viewed as spaces endowed with real-valued functions, while the similarity between the resulting Reeb graphs is addressed through a graph edit distance. The cases of smooth functions on manifolds and piecewise linear functions on polyhedra stand out as the most interesting ones. The main contribution of this paper is the introduction of a general edit distance suitable for comparing Reeb graphs in these settings. This edit distance promises to be useful for applications in 3D object retrieval because of its stability properties in the presence of noise.Eurographics Workshop on 3D Object RetrievalFull Paper
Barbara Ras - Sowell Conference 2017
No full textBarbara Ras, San Antonio, Poet, author of "Bite Every Sorrow" and "The Last Skin
Reeb graphs of curves are stable under function perturbations
No full textReeb graphs provide a method to combinatorially describe the shape of a manifold endowed with a Morse function. One question deserving attention is whether Reeb graphs are robust against function perturbations. Focusing on 1-dimensional manifolds, we define an editing distance between Reeb graphs of curves, in terms of the cost necessary to transform one graph into another through editing moves. Our main result is that changes in Morse functions induce smaller changes in the editing distance between Reeb graphs of curves, implying stability of Reeb graphs under function perturbations. We also prove that our editing distance is equal to the natural pseudo-distance, and, moreover, that it is lower bounded by the bottleneck distance of persistent homology
Stable shape comparison of surfaces via Reeb graphs
No full textReeb graphs are combinatorial signatures that capture shape properties from the perspective of a chosen function. One of the most important questions is whether Reeb graphs are robust against function perturbations that may occur because of noise and approximation errors in the data acquisition process. In this work we tackle the problem of stability by providing an editing distance between Reeb graphs of orientable surfaces in terms of the cost necessary to transform one graph into another by edit operations. Our main result is that the editing distance between two Reeb graphs is upper bounded by the extent of the difference of the associated functions, measured by the maximum norm. This yields the stability property under function perturbations
Exclusive interview with author Barbara Kingsolver
No full textExclusive interview with author Barbara Kingsolver for her 2018 novel *Unsheltered
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