Smooth Chan–Vese segmentation via graph cuts

Abstract

The graph cut framework presents an efficient method for approximating the minimum of the popular Chan–Vese functional for image segmentation. However, a fundamental drawback of graph cuts is a need for a dense neighbourhood system in order to avoid geometric artefacts and jagged boundaries. The increasing connectivity leads to excessive memory consumption and burdens the efficiency of the method. In this paper, we address the issue by introducing a two-stage connectivity scaling approach. First, coarse segmentation is calculated using a sparse neighbourhood over the whole image. In the second stage, the segmentation is refined by employing a dense neighbourhood in a narrow band around the boundary from the first stage. We demonstrate that this method fits well with the Chan–Vese functional and yields smooth boundaries without increasing the computational demands significantly. Moreover, under specific conditions, the construction has no negative effect on the optimality of the solution.