Image Segmentation Based on Fuzzy Low-Rank Structural Clustering

Abstract

Fuzzy clustering is an essential algorithm in image segmentation, and most of them are fuzzy c-mean (FCM) algorithms. However, it is sensitive to noise, center point selection, cluster number, and distance metric. To address this problem, we propose a new fuzzy clustering method based on low-rank representation (LRR) for image segmentation, which integrates low-rank structure with fuzzy theory. First, we improve the morphological reconstruction super-pixel method based on edge detection by introducing anisotropy to enhance the image edge. Thus, on the one hand, the improved morphological reconstruction super-pixel method can improve its noise-resistance performance; on the other hand, the complexity of the subsequent low-rank computation can be reduced by enhancing the superpixels constructed by the edges. Second, inspired by the fact that rank can represent correlation, we propose the concept of fuzzy low-rank structure, where fuzzy means not dealing with data directly but with the relationship between data. Specifically, we perform rank minimization on the constructed membership matrix to obtain the optimal matrix. To obtain better clustering results, we added the Frobenius norm of the fuzzy matrix as a fuzzy regularization term in the LRR model to achieve global convergence and obtain a membership matrix with a strong element correlation. Finally, we obtain the final clustering results by clustering the processed membership matrix using a subspace clustering with a low-rank structure constraint. Experiments performed on artificial and real-world images show that the proposed method is effective and efficient, which is more competitive than state-of-the-art methods.