  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.
