Normalized Cut with Adaptive Similarity and Spatial Regularization

In this paper, we propose a normalized cut segmentation algorithm with spatial regularization priority and adaptive similarity matrix. We integrate the well-known expectation-maximum(EM) method in statistics and the regularization technique in partial differential equation (PDE) method into normalized cut (Ncut). The introduced EM technique makes our method can adaptively update the similarity matrix, which can help us to get a better classification criterion than the classical Ncut method. While the regularization priority can guarantee the proposed algorithm has a robust performance under noise. To unify the three totally different methods including EM, spatial regularization, and spectral graph clustering, we built a variational framework to combine them and get a general normalized cut segmentation algorithm. The well-defined theory of the proposed model is also given in the paper. Compared with some existing spectral clustering methods such as the traditional Ncut algorithm and the variational based Chan-Vese model, the numerical experiments show that our methods can achieve promising segmentation performance.