Flux Graphs for 2D Shape Analysis

Abstract

We consider a method for computing skeletal representations based on the average outward flux through a shrinking region, of the gradient of the Euclidean distance function to the object’s boundary. We show how the original method, developed by Dimitrov et al. (Proceedings of the IEEE conference on computer vision and pattern recognition, vol. 1, pp. 835–841, 2003) can be used to exploit a relationship between the average outward flux and the object angle at endpoints, branch points and regular points of the skeleton to reconstruct the boundary. Using this method, new measures for skeletal branch simplification are proposed based on two criteria: the uniqueness of an inscribed disk to a branch, and the average outward flux value. The simplified skeleton when abstracted as a directed graph is shown to be less complex than popular skeletal graphs in the literature, such as the shock graph, by several graph complexity measures, with little loss in representation power. We conclude the chapter by applying the simplified graph to a view-based object recognition experiment previously arranged for shock graphs. The results suggest that our new simplified graph yields recognition scores very close to shock graphs but with a smaller number of nodes, edges, and skeletal points.