Some theoretical results on discrete contour trees

• URL: http://arxiv.org/abs/2206.12123v1
• Date: Fri, 24 Jun 2022 07:31:11 GMT
• Title: Some theoretical results on discrete contour trees
• Authors: Yuqing Song
• Abstract summary: We define a discrete contour tree, called the iso-tree, on a scalar graph. We show that the iso-tree model works for data of all dimensions, and develop an axiomatic system formalizing the discrete contour structures.
• Score: 3.1963310035729657
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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