Mapping Dynamic Bayesian Networks to $\alpha$ -Shapes: Application to Human Faces Identification Across Ages

We propose to map a dynamic Bayesian network (DBN) to an ordered family of α -shapes to improve DBNs classification power. This mission is achieved by: 1) embedding a DBN into a topological manifold and 2) applying the α-shape geometric constructor to build hierarchical structures assigned to the DBN. This continuous representation of traditional DBNs as α-shapes allows more information to be obtained about the objects to be classified. These latter are viewed as hierarchies of geometrical objects with different levels of detail. Topological signatures are therefore unraveled and classification accuracy is enhanced. We have applied the proposed formalism to the task of facial identification across ages. Preliminary results demonstrate that the proposed formalism is a powerful tool since it has outperformed some DBN models, the k-NN classifier, and some recent approaches.