Top-down partitioning has focused on minimum cut or ratio cut objectives, while bottom-up clustering has focused on density-based objectives. In seeking a more uni ed perspective, we propose a new sum of densities measure for multi-way circuit decomposition, where the density of a subhypergraph is the ratio of the number of edges to the number of nodes in the subhypergraph. Finding a k-way part...

Abstract. The problem of interactive foreground/background segmentation in still images is of great practical importance in image editing. The state of the art in interactive segmentation is probably represented by the graph cut algorithm of Boykov and Jolly (ICCV 2001). Its underlying model uses both colour and contrast information, together with a strong prior for region coherence. Estimation...

Identification of sepsis is a major issue due to limitations in diagnosis and severity of outcome. Different combinations of tests are used to screen babies at risk for infection, none specific enough to avoid treatment of noninfected newborns. 193 newborns with 35 weeks of gestational age admitted in the maternity were screened for infection using a protocol scoring system involving haematolog...

Max-cut problem is one of many NP-hard graph theory problems which attracted many researchers over the years. Though there is almost no hope in finding a polynomialtime algorithm for max-cut problem, various heuristics, or combination of optimization and heuristic methods have been developed to solve this problem. Among them is the efficient algorithm of Goemans and Williamson. Their algorithm ...

The Sliding Scale Conjecture in PCP states that there are PCP verifiers with a constant number of queries and soundness error that is exponentially small in the randomness of the verifier and the length of the prover’s answers. The Sliding Scale Conjecture is one of the oldest open problems in PCP, and it implies hardness of approximation up to polynomial factors for problems like Max-CSP (with...

The segmentation of video sequences into shots is the first step towards video content analysis. Two kinds of shot boundaries can be distinguished: abrupt scene changes (“cuts”) and gradual transitions. In this paper, we present a technique to reduce the error rates of cut detection algorithms based on pixel-wise or histogram-based frame difference metrics when operating directly on compressed ...

Recursive spectral bisection (RSB) is a heuristic technique for finding a minimum cut graph bisection. To use this method the second eigenvector of the Laplacian of the graph is computed and from it a bisection is obtained. The most common method is to use the median of the components of the second eigenvector to induce a bisection. We prove here that this median cut method is optimal in the se...

We describe a hybrid modeling-discretization numerical method for approximating the solution of an elliptic problem with a discontinuous diffusion coefficient that is suited for cut-cell problems in which the discontinuity interface is not resolved by the mesh. The method is inspired by the well-known Ghost Fluid Method. We carry out an a posteriori error analysis for the numerical solution for...

Minimum spanning tree and normalized cut based segmentation method are evaluated with respect to segmentations made by humans. The segmentation error is determined by two discrepancy measures, as a sum of miss-counted segmented pixels. Gray value images are used for the evaluation. This benchmarking is well suited in finding the class of images best suited for a particular method.

Sum of Squares Error and Normalized Cut are two widely used clustering functional. It is known their minimum values are monotone with respect to the input number of clusters and this monotonicity does not allow for a simple automatic selection of a correct number of clusters. Here we study monotonicity not just on the minimizers but on the entire clustering lattice. We show the value of Sum of ...