Efficiently Solving the Fractional Trust Region Problem

Normalized Cuts has successfully been applied to a wide range of tasks in computer vision, it is indisputably one of the most popular segmentation algorithms in use today. 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. It was recently shown how a general linearly constrained Normalized Cut problem can be solved. This was done by proving that strong duality holds for the Lagrangian relaxation of such problems. This provides a principled way to perform multi-class partitioning while enforcing any linear constraints exactly. The Lagrangian relaxation requires the maximization of the algebraically smallest eigenvalue over a one-dimensional matrix sub-space. This is an unconstrained, piece-wise differentiable and concave problem. In this paper we show how to solve this optimization efficiently even for very large-scale problems. The method has been tes...

• Type: Conference
• Year: 2007
• Where: ACCV
• Authors: Anders P. Eriksson, Carl Olsson, Fredrik Kahl
• Keywords: ACCV 2007, Computer Vision, Constrained Normalized Cut, Lagrangian Relaxation, Normalized Cut