Polynomial Time Algorithms for Ratio Regions and a Variant of Normalized Cut

—In partitioning, clustering, and grouping problems, a typical goal is to group together similar objects, or pixels in the case of image processing. At the same time, another goal is to have each group distinctly dissimilar from the rest and possibly to have the group size fairly large. These goals are often combined as a ratio optimization problem. One example of such a problem is a variant of the normalized cut problem, another is the ratio regions problem. We devise here the first polynomial time algorithms solving optimally the ratio region problem and the variant of normalized cut, as well as a few other ratio problems. The algorithms are efficient and combinatorial, in contrast with nonlinear continuous approaches used in the image segmentation literature, which often employ spectral techniques. Such techniques deliver solutions in real numbers which are not feasible to the discrete partitioning problem. Furthermore, these continuous approaches are computationally expensive com...

• Type: Journal
• Year: 2010
• Where: PAMI
• Authors: Dorit S. Hochbaum
• Keywords: Continuous Approaches, Normalized Cut, PAMI 2010, Ratio Problem