Normalized Cuts Revisited: A Reformulation for Segmentation with Linear Grouping Constraints

Indisputably Normalized Cuts is one of the most popular segmentation algorithms in computer vision. It has been applied to a wide range of segmentation tasks with great success. A number of extensions to this approach have also been proposed, ones that can deal with multiple classes or that can incorporate a priori information in the form of grouping constraints. However, what is common for all these suggested methods is that they are noticeably limited and can only address segmentation problems on a very specific form. In this paper, we present a reformulation of Normalized Cut segmentation that in a unified way can handle all types of linear equality constraints for an arbitrary number of classes. This is done by restating the problem and showing how linear constraints can be enforced exactly through duality. This allows us to add group priors, for example, that certain pixels should belong to a given class. In addition, it provides a principled way to perform multi-class segmentation for tasks like interactive segmentation. The method has been tested on real data with convincing results.