Kernel Active Contour

Abstract

Level sets and graph cuts are two state-of-the-art image segmentation methods in use today. The two methods are apparently different from each other not only because they originate from different theory foundations but also because they employ image information in different ways — level sets typically use image information in a point-wise way, whereas graph cuts use image information in a pairwise way. In this paper, we derive an equivalence relationship between the two methods through kernel technology. In particular, we show that the kernelization of the Chan-Vese (CV) functional — a functional widely used in the level set community — is exactly the energy optimized in the average association — a well-known graph cut criterion. We refer to the level sets method using the kernelized version of the CV functional as kernel active contour. The kernel active contour has computational complexity O(n2) due to the involved kernel technology. We propose a fast implementation for kernel active contour with computational complexity only O(n) using random projection. The kernel active contour is evaluated on synthetic and real images and compared with several existing level set and graph cut methods for image segmentation.