We present a graph cuts-based image segmentation technique that incorporates an elliptical shape prior. Inclusion of this shape constraint restricts the solution space of the segmentation result, increasing robustness to misleading information that results from noise, weak boundaries, and clutter. We argue that combining a shape prior with a graph cuts method suggests an iterative approach that...

Plural (or multiple-conclusion) cuts are inferences made by applying a structural rule introduced by Gentzen for his sequent formulation of classical logic. As singular (singleconclusion) cuts yield trees, which underlie ordinary natural deduction derivations, so plural cuts yield graphs of a more complicated kind, related to trees, which this paper defines. Besides the inductive definition of ...

It is already known that for very small edge cuts in graphs, the crossing number of the graph is at least the sum of the crossing number of (slightly augmented) components resulting from the cut. Under stronger connectivity condition in each cut component that was formalized as a graph operation called zip product, a similar result was obtained for edge cuts of any size, and a natural question ...

The graph bisection problem asks to partition the n vertices of a graph into two sets of equal size so that the number of edges across the cut is minimum. We study finite, connected subgraphs of the infinite twodimensional grid that do not have holes. Since bisection is an intricate problem, our interest is in the tradeoff between runtime and solution quality that we get by limiting ourselves t...