# Some theoretical results on discrete contour trees

arXiv: https://arxiv.org/abs/2206.12123 · HTML: https://mlsanity.com/paper/2206.12123/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 1 of its 21 references that are in the map.
- First posted on arXiv 24 Jun 2022.

## Builds on (most cited first, 1 of 1)

- [Deep Neural Network for 3D Surface Segmentation based on Contour Tree Hierarchy](https://mlsanity.com/paper/2008.11269/) (2020)

## Abstract (arXiv)

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.