The Minimum Spanning Tree of Maximum Entropy

TL;DR

This paper introduces MSTME, a new graph construction method based on maximum entropy for more stable point-set graphs in computer vision, improving robustness over traditional triangulation methods.

Contribution

Proposes MSTME, a novel data graph technique balancing weight and entropy, enhancing stability in point-set registration compared to Delaunay triangulation.

Findings

MSTME outperforms Delaunay triangulation in stability across various datasets.

The algorithm effectively balances weight and entropy with a single parameter.

Results demonstrate improved robustness in graph-based point-set registration.

Abstract

In computer vision, we have the problem of creating graphs out of unstructured point-sets, i.e. the data graph. A common approach for this problem consists of building a triangulation which might not always lead to the best solution. Small changes in the location of the points might generate graphs with unstable configurations and the topology of the graph could change significantly. After building the data-graph, one could apply Graph Matching techniques to register the original point-sets. In this paper, we propose a data graph technique based on the Minimum Spanning Tree of Maximum Entropty (MSTME). We aim at a data graph construction which could be more stable than the Delaunay triangulation with respect to small variations in the neighborhood of points. Our technique aims at creating data graphs which could help the point-set registration process. We propose an algorithm with a single free parameter that weighs the importance between the total weight cost and the entropy of the current spanning tree. We compare our algorithm on a number of different databases with the Delaunay triangulation.