منابع مشابه
On the Reeb spaces of definable maps
We prove that the Reeb space of a proper definable map in an arbitrary o-minimal expansion of the reals is realizable as a proper definable quotient. We also show that the Betti numbers of the Reeb space of a map f can be arbitrarily large compared to those of X, unlike in the special case of Reeb graphs of manifolds. Nevertheless, in the special case when f : X → Y is a semi-algebraic map and ...
متن کاملTopological Morphing Using Reeb Graphs
Metamorphosis between 3D objects is often the transformation between a pair of shapes that have the same topology. This paper presents a new model using Reeb graphs and their contours to create morphing between 3D objects having different topology. The proposed method specifies the correspondence between of the input objects by using the graph isomorphic theory. Then the super Reeb graph, which...
متن کاملCategorified Reeb Graphs
The Reeb graph is a construction which originated in Morse theory to study a real valued function defined on a topological space. More recently, it has been used in various applications to study noisy data which creates a desire to define a measure of similarity between these structures. Here, we exploit the fact that the category of Reeb graphs is equivalent to the category of a particular cla...
متن کاملFeature Tracking Using Reeb Graphs
Tracking features and exploring their temporal dynamics can aid scientists in identifying interesting time intervals in a simulation and serve as basis for performing quantitative analyses of temporal phenomena. In this paper, we develop a novel approach for tracking subsets of isosurfaces, such as burning regions in simulated flames, which are defined as areas of high fuel consumption on a tem...
متن کاملBook embeddings of Reeb graphs
Let X be a simplicial complex with a piecewise linear function f : X → R. The Reeb graph Reeb(f,X) is the quotient of X, where we collapse each connected component of f−1(t) to a single point. Let the nodes of Reeb(f,X) be all homologically critical points where any homology of the corresponding component of the level set f−1(t) changes. Then we can label every arc of Reeb(f,X) with the Betti n...
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ژورنال
عنوان ژورنال: Kyoto Journal of Mathematics
سال: 1976
ISSN: 2156-2261
DOI: 10.1215/kjm/1250522917