Constraint Satisfaction Problem with Bilevel Constraint: Application to Interpretation of Over-Segmented Images

Abstract In classical finite-domain constraint satisfaction problems, the assumption made is that only one value is associated with only one variable. For example, in pattern recognition one variable is associated with only one segmented region. However, in practice, regions are often oversegmented which results in failure of any one to one mapping. This paper proposes a definition of finite-domain constraint satisfaction problems with bilevel constraints in order to take into account a many to one relation between the values and the variables. The additional level of constraint concerns the data assigned to the same complex variable. Then, we give a definition of the arc-consistency problem for bilevel constraint satisfaction checking. A new algorithm for arc consistency to deal with these problems is presented as well. This extension of the arc-consistency algorithm retains its good properties and has a time complexity in O( en 3 d 2 ) in the worst case. This algorithm was tested on medical images. These tests demonstrate its reliability in correctly identifying the segmented regions even when the image is over-segmented.