Some theoretical results on discrete contour trees

Yuqing Song

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arXiv · 2206.12123

Some theoretical results on discrete contour trees

Yuqing Song

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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.

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Yuqing Song. 2022-06-24. Some theoretical results on discrete contour trees. https://arxiv.org/abs/2206.12123

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