Feature matching by searching maximum clique on high order association graph

In this work we consider the most important problem in computer vision of performing matching among elementary features of objects when observed from different points of view. We formulate the problem in terms of subgraph isomorphism between relational graphs characterized by nodes representing interested object features and linking edges weighted by projective invariant values. The matching involves determination of all nodes in the association graph mutually compatible according to the similarity of the imposed invariant relations encoded on the edges. The solution requires us to determine subsets of nodes totally interconnected by edges with highest weights. Moreover, in most contexts, relations among more than two features can be involved, giving rise to association graphs of higher order. Recently it has been recognized that a particular class of dynamical equations are able to solve the maximum clique problem in an optimal manner. In our work, we have extended and applied such results to solve the most general problem of searching for the maximum edge-weighted clique on high-order association graphs. Moreover we have applied the method to a classical problem in computer vision of planar 3D surface reconstruction which is of fundamental importance for an autonomous moving vehicle in order to accomplish some elementary tasks, such as detection of ground floor obstacles or independent moving objects.