Networks of constraints: Fundamental properties and applications to picture processing

The problem of representation and handling of constraints is here considered, mainly for picture processing purposes. A systematic specification and utilization of the available constraints could significantly reduce the amount of search in picture recognition. On the other hand, formally stated constraints can be embedded in the syntactic productions of picture languages. Only binary constraints are treated here, but they are represented in full generality as binary relations. Constraints among more than two variables are then represented as networks of simultaneous binary relations. In general, more than one equivalent (i.e., representing the same constraint) network can be found: a minimal equivalent network is shown to exist, and its computation is shown to solve most practical problems about constraint handling. No exact solution for this central problem was found. Anyway, constraints are treated algebtaically, and the solution of a system of linear equations in this algebra provides an approximation of the minimal network. This solution is then proved exact in special cases, e.g., for tree-like and series parallel networks and for classes of relations for which a distributive property holds. This latter condition is satisfied in cases of practical interest. This work was supported by the Advanced Research Projects Agency of the Office of the Secretary of Defense (F44620-70-C-0107) and is monitored by the Air Force Office of Scientific Research. This document has been approved for public release and sale; its distribution is unlimited. picture processing*