  The structural analysis of shape boundaries leads to the characterization of
objects as well as to the understanding of shape properties. The literature on
graphs and networks have contributed to the structural characterization of
shapes with different theoretical approaches. We performed a study on the
relationship between the shape architecture and the network topology
constructed over the shape boundary. For that, we used a method for network
modeling proposed in 2009. Firstly, together with curvature analysis, we
evaluated the proposed approach for regular polygons. This way, it was possible
to investigate how the network measurements vary according to some specific
shape properties. Secondly, we evaluated the performance of the proposed shape
descriptor in classification tasks for three datasets, accounting for both
real-world and synthetic shapes. We demonstrated that not only degree related
measurements are capable of distinguishing classes of objects. Yet, when using
measurements that account for distinct properties of the network structure, the
construction of the shape descriptor becomes more computationally efficient.
Given the fact the network is dynamically constructed, the number of iterations
can be reduced. The proposed approach accounts for a more robust set of
structural measurements, that improved the discriminant power of the shape
descriptors.
