Spectral Graph Cut from a Filtering Point of View
This work provides a faster algorithm for image segmentation, which is useful for computer vision applications, but it is incremental as it builds on existing normalized cut methods.
The paper connects spectral graph theory-based image segmentation to edge-preserving filtering, showing that normalized cut is equivalent to repeated bilateral filtering, and presents a fast implementation that solves the original optimization problem 10 to 100 times faster.
Spectral graph theory is well known and widely used in computer vision. In this paper, we analyze image segmentation algorithms that are based on spectral graph theory, e.g., normalized cut, and show that there is a natural connection between spectural graph theory based image segmentationand and edge preserving filtering. Based on this connection we show that the normalized cut algorithm is equivalent to repeated iterations of bilateral filtering. Then, using this equivalence we present and implement a fast normalized cut algorithm for image segmentation. Experiments show that our implementation can solve the original optimization problem in the normalized cut algorithm 10 to 100 times faster. Furthermore, we present a new algorithm called conditioned normalized cut for image segmentation that can easily incorporate color image patches and demonstrate how this segmentation problem can be solved with edge preserving filtering.