Finding Feature Similarities Between Geometric Trees

Abstract

Geometric trees are graphs with no cycles in which the nodes have spatial co-ordinates and the edges are geometric curves. Many physical systems can be represented effectively using geometric trees, e.g. river beds, animal neurons, respiratory tracks of mammals etc. As these systems undergo structural metamorphosis, temporally or under the effect of some external stimulus, the underlying tree structures also change. Given two snapshots of structurally morphed trees, an algorithm for comparing them based on geometric and topological tree features is presented. Such comparison provides a wealth of information for interpreting the metamorphosis.