Lecture 16: Computation of Reeb Graphs Topics in Computational Topology: An Algorithmic View
نویسنده
چکیده
Given a manifold X and a function f : X → IR, the level set of X containing the point q is the set {x ∈ X : f(x) = f(q)}. Each connected component of the level set is called a contour. Recall from last lecture that the Reeb graph Rf (X) of X on f is defined to be the continuous contraction of each contour to a point. Recall furthermore that if the manifold is simply-connected (i.e., all loops are contractible to a point), then the Reeb graph has a tree structure, and the resulting Reeb graph is called a contour tree. In this lecture, we first discuss an efficient algorithm for computing contour trees. After that, a survey of various algorithms for computing Reeb graphs will be given.
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