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Some theoretical results on discrete contour trees

2022-06-24 07:31:11
Yuqing Song
arXiv_CV
   
Abstract

Contour trees have been developed to visualize or encode scalar data in imaging technologies and scientific simulations. Contours are defined on a continuous scalar field. For discrete data, a continuous function is first interpolated, where contours are then defined. In this paper we define a discrete contour tree, called the iso-tree, on a scalar graph, and discuss its properties. We show that the iso-tree model works for data of all dimensions, and develop an axiomatic system formalizing the discrete contour structures. We also report an isomorphism between iso-trees and augmented contour trees, showing that contour tree algorithms can be used to compute discrete contour trees, and vice versa.

Abstract (translated)

URL

https://arxiv.org/abs/2206.12123

PDF

https://arxiv.org/pdf/2206.12123.pdf

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