Some theoretical results on discrete contour trees
This work provides a theoretical foundation for discrete contour trees, which is incremental for researchers in data visualization and scientific computing.
The paper tackled the problem of defining contour trees for discrete scalar data by introducing the iso-tree model, which works for all dimensions and is shown to be isomorphic to augmented contour trees, enabling mutual algorithm use.
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.