Spectral Graph Cut from a Filtering Point of View

We analyze spectral graph theory based image segmentation algorithms and show there is a natural connection with edge preserving filtering. Based on this connection we show that normalized cut algorithm is equivalent to repeated application of bilateral filtering. Then, using this interpretation we present and implement a fast normalized cut algorithm. Experiments show that our implementation can solve the original optimization problem with a 10x-100x speedup. In addition to these practical advantages, our work shows a deep connection between two currently separate approaches to segmentation, which suggests further directions for improvements.