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.
Given an undirected graph with two different nonnegative costs associated with every edge e (say, w e for the weight and l e for the length of edge e) and a budget L, consider the problem of finding a spanning tree of total edge length at most L and minimum total weight under this restriction. This constrained minimum spanning tree problem is weakly NP-hard. We present a polynomial-time approximation scheme for this problem. This algorithm always produces a spanning tree of total length at most (1 + e)L and of total weight at most that of any spanning tree of total length at most L, for any fixed e >0. The algorithm uses Lagrangean relaxation, and exploits adjacency relations for matroids.