There are many situations in mathematical programming where cutting planes can be generated by solving a certain “cut generation linear program” whose feasible solutions define a family of valid inequalities for the problem at hand. Disjunctive cuts and Benders cuts are two familiar examples. In this paper we concentrate on classical Benders cuts, as they belong to the basic toolbox for mixed-i...

The lift-and-project closure is the relaxation obtained by computing all lift-and-project cuts from the initial formulation of a mixed integer linear program or equivalently by computing all mixed integer Gomory cuts read from all tableau’s corresponding to feasible and infeasible bases. In this paper, we present an algorithm for approximating the value of the lift-and-project closure. The orig...

In this paper, we present a graph-based image segmentation method (patch-cuts) that incorporates features and spatial relations obtained from image patches. In the first step, patch-cuts extracts a set of patches that can assume arbitrary shape and size. Patches are determined by a combination of intensity quantization and morphological operations and render the proposed method robust against n...

Cut-elimination is the most prominent form of proof transformation in logic. The elimination of cuts in formal proofs corresponds to the removal of intermediate statements (lemmas) in mathematical proofs. The cut-elimination method CERES (cut-elimination by resolution) works by constructing a set of clauses from a proof with cuts. Any resolution refutation of this set then serves as a skeleton ...

In this paper, we propose an interactive method for lung nodule segmentation. Given a seed point, the segmentation process consisting of three steps is done automatically. The first step is intensity normalization. The second one is to build an energy function for graph cuts. The third one is to do the segmentation by graph cuts. In the third step, if there are imperfects in the result, we prov...

This paper presents a multiresolutional brain extraction framework which utilizes graph cuts technique to classify head magnetic resonance (MR) images into brain and non-brain regions. Starting with an over-extracted brain region, we refine the segmentation result by trimming non-brain regions in a coarse-to-fine manner. The extracted brain at the coarser level will be propagated to the finer l...