Normalized cuts and image segmentation

Abstract

We propose a novel approach for solving the perceptual grouping problem in vision. Rather than focusing on local features and their consistencies in the image data, our approach aims at extracting the global impression of an image. We treat image segmentation as a graph partitioning problem and propose a novel global criterion, the normalized cut, for segmenting the graph. The normalized cut criterion measures both the total dissimilarity between the different groups as well as the total similarity within the groups. We show that an efficient computational technique based on a generalized eigenvalue problem can be used to optimize this criterion. We have applied this approach to segmenting static images, as well as motion sequences, and found the results to be very encouraging. This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of the University of Pennsylvania's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to pubs-permissions@ieee.org. By choosing to view this document, you agree to all provisions of the copyright laws protecting it. AbstractÐWe propose a novel approach for solving the perceptual grouping problem in vision. Rather than focusing on local features and their consistencies in the image data, our approach aims at extracting the global impression of an image. We treat image segmentation as a graph partitioning problem and propose a novel global criterion, the normalized cut, for segmenting the graph. The normalized cut criterion measures both the total dissimilarity between the different groups as well as the total similarity within the groups. We show that an efficient computational technique based on a generalized eigenvalue problem can be used to optimize this criterion. We have applied this approach to segmenting static images, as well as motion sequences, and found the results to be very encouraging.

An overview of recent developments in genomics and associated statistical methods

“…A huge literature on clustering using spectral properties of appropriate matrices has developed, in particular with so-called graph clustering. The relationships of these methods to natural properties of random walks and diffusions on appropriate spaces have been well explored (Shi & Malik 2000;Meila & Shi 2001;Ng et al 2002;Nadler et al 2005). These methods have only started appearing in the biological literature but are becoming more appreciated given that they provide natural methods of dimension reduction as well as clustering.…”

An endoscopic structured light system using multispectral detection

“…Based on these image conditions, we propose a spot segmentation method based on the "normalized cut" algorithm. This approach, developed by Shi and Malik, treats image segmentation as a graph partitioning problem, by setting a criterion according to inter-group difference and intra-group similarity [16]. They formulated this into a simple spectral clustering problem by using the similarity matrix of a graph and standard linear algebra to cluster data points according to the eigenvectors of matrices, leading to better performance compared to some traditional clustering algorithms like k-means [21].…”

“…This algorithm includes spot segmentation and spot identification. In the former step, an algorithm based on the H-maxima transform [15] and "normalized cut" [16] is used to delineate the spots and find their centroids. Colour and neighbourhood information are considered as criteria to identify the spots, using a "labelling propagation" technique based on local rigid registration.…”

Fusion and community detection in multi-layer graphs

“…To initialize cluster indicator matrix, we use SVD approach for SNMTF [16]. To extract clusters from the obtained cluster indicator matrix, H, we applied Ncut algorithm [17] on the similarity matrix HH T . SNMTF(l): we first apply SNMTF on each network layer, A (i) , separately, and obtain clustering assignment.…”