Spectral Graph Cut from a Filtering Point of View

TL;DR

This paper reveals a connection between spectral graph-based image segmentation and edge-preserving filtering, leading to a faster normalized cut algorithm and a new segmentation method incorporating color patches.

Contribution

It demonstrates the equivalence between normalized cut and bilateral filtering, enabling a significantly faster segmentation algorithm and introduces conditioned normalized cut for improved segmentation.

Findings

Normalized cut is equivalent to repeated bilateral filtering.

The proposed algorithm is 10 to 100 times faster than traditional methods.

Conditioned normalized cut effectively incorporates color image patches.

Abstract

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.