Shape Analysis with Trajectory Networks

Abstract

"Image and shape analysis are amongst the most challenging abilities to be replicated artificially. One of the first important steps along these two tasks consists in obtaining comprehensive representations of the involved objects, capable not only of representing most of the original information, but also of emphasizing their less redundant portions. The current work reports an approach to shape characterization and classification which is based on trajectory networks, a special type of knitted geographical networks where the connections take into account not only the proximity between nodes, but also an associated vector field, here assumed to correspond to the electric field induced by the contours of the shapes. In this way, the original shape is mapped into a trajectory network, so that its measurements can reveal important features of the shapes under analysis. Optimal multivariate stochastic methods (namely discriminant analysis) are then applied in order to identify the topological measurements contributing most effectively for the separation between the objects to be analyzed and classified. It is shown that the weveral topological and geometrical measurements contribute differently to the separation between the considered set of shapes. The entropy of the angles defined by the edges, the number of nodes with degree 1, 4 and 5, as well as an alternative type of entropy, are found to contribute more strongly to the discrimination between the considered shapes."