Normalized Cut Criterion Research Articles

Brain Tumor Localization Using N-Cut

A brain tumor is an abnormal collection of tissue in the brain. When tumors form, they are classified as either malignant or benign. It is critical to notice and identify the existence of tumors in brain images since they can be life threatening. This paper illustrates a novel segmentation method in which threshold technique is combined with normalized cut (Ncut) for the segregation of the tumors from brain magnetic resonance (MR) images. Image segmentation is a technique for grouping images. It is a method of splitting an image into sections with comparable attributes such as intensity, texture, colour, and so on. In thresholding, an object is distinguished from the background, and for the proposed segmentation methodology, the threshold value is determined by normalized graph cut. A weighted graph is divided into disjointed sets (groups) in which the similarity within a group is high and the similarity across groups is low. A graph-cut is a grouping approach in which the total weight of edges eliminated between these two pieces is used to calculate the degree of dissimilarity between these two groups. The normalized cut criterion is used to calculate the total likeness within the groups as well as the dissimilarity between the different groups.

Segmentation of multi-temporal polarimetric SAR data based on mean-shift and spectral graph partitioning.

Polarimetric SAR (PolSAR) image segmentation is a key step in its interpretation. For the targets with time series changes, the single-temporal PolSAR image segmentation algorithm is difficult to provide correct segmentation results for its target recognition, time series analysis and other applications. For this, a new algorithm for multi-temporal PolSAR image segmentation is proposed in this paper. Firstly, the over-segmentation of single-temporal PolSAR images is carried out by the mean-shift algorithm, and the over-segmentation results of single-temporal PolSAR are combined to get the over-segmentation results of multi-temporal PolSAR images. Secondly, the edge detectors are constructed to extract the edge information of single-temporal PolSAR images and fuse them to get the edge fusion results of multi-temporal PolSAR images. Then, the similarity measurement matrix is constructed based on the over-segmentation results and edge fusion results of multi-temporal PolSAR images. Finally, the normalized cut criterion is used to complete the segmentation of multi-temporal PolSAR images. The performance of the proposed algorithm is verified based on three temporal PolSAR images of Radarsat-2, and compared with the segmentation algorithm of single-temporal PolSAR image. Experimental results revealed the following findings: (1) The proposed algorithm effectively realizes the segmentation of multi-temporal PolSAR images, and achieves ideal segmentation results. Moreover, the segmentation details are excellent, and the region consistency is good. The objects which can’t be distinguished by the single-temporal PolSAR image segmentation algorithm can be segmented. (2) The segmentation accuracy of the proposed multi-temporal algorithm is up to 86.5%, which is significantly higher than that of the single-temporal PolSAR image segmentation algorithm. In general, the segmentation result of proposed algorithm is closer to the optimal segmentation. The optimal segmentation of farmland parcel objects to meet the needs of agricultural production is realized. This lays a good foundation for the further interpretation of multi-temporal PolSAR image.

Good (K-means) clusterings are unique (up to small perturbations)

If we have found a “good” clustering C of a data set, can we prove that C is not far from the (unknown) best clustering Copt of these data? Perhaps surprisingly, the answer to this question is sometimes yes. This paper gives spectral bounds on the distance d(C,Copt) for the case when “goodness” is measured by a quadratic cost, such as the squared distortion of K-means clustering or the Normalized Cut criterion of spectral clustering. The bounds exist only if the data admit a “good”, low-cost clustering. The results in this paper are non-asymptotic and model-free, in the sense that no assumptions are made on the data generating process. The bounds do not depend on undefined constants, and can be computed tractably from the data.

Spectral clustering based on similarity and dissimilarity criterion

The clustering assumption is to maximize the within-cluster similarity and simultaneously to minimize the between-cluster similarity for a given unlabeled dataset. This paper deals with a new spectral clustering algorithm based on a similarity and dissimilarity criterion by incorporating a dissimilarity criterion into the normalized cut criterion. The within-cluster similarity and the between-cluster dissimilarity can be enhanced to result in good clustering performance. Experimental results on toy and real-world datasets show that the new spectral clustering algorithm has a promising performance.

An Evolutionary Approach for Image Segmentation

The paper explores the use of evolutionary techniques in dealing with the image segmentation problem. An image is modeled as a weighted undirected graph, where nodes correspond to pixels, and edges connect similar pixels. A genetic algorithm that uses a fitness function based on an extension of the normalized cut criterion is proposed. The algorithm employs the locus-based representation of individuals, which allows for the partitioning of images without setting the number of segments beforehand. A new concept of nearest neighbor that takes into account not only the spatial location of a pixel, but also the affinity with the other pixels contained in the neighborhood, is also defined. Experimental results show that our approach is able to segment images in a number of regions that conform well to human visual perception. The visual perceptiveness is substantiated by objective evaluation methods based on uniformity of pixels inside a region, and comparison with ground-truth segmentations available for part of the used test images.

Parameters Selection of LLE Algorithm for Classification Tasks

The crux in the locally linear embedding algorithm or LLE is the selection of embedding dimensionality and neighborhood size. A method of parameters selection based on the normalized cut criterion or Ncut for classification tasks is proposed. Differing from current techniques based on the neighborhood topology preservation criterion, the proposed method capitalizes on class separability of embedding result. By taking it into consideration, the intrinsic capability of LLE can be more faithfully reflected, and hence more rational features for classification in real-life applications can be offered. The theoretical argument is supported by experimental results from synthetic and real data sets.

Blind image clustering based on the Normalized Cuts criterion for camera identification

Camera identification is a well known problem in image forensics, addressing the issue to identify the camera a digital image has been shot by. In this paper, we pose our attention to the task of clustering images, belonging to a heterogenous set, in groups coming from the same camera and of doing this in a blind manner; this means that side information neither about the sources nor, above all, about the number of expected clusters is requested. A novel methodology based on Normalized Cuts (NC) criterion is presented and evaluated in comparison with other state-of-the-art techniques, such as Multi-Class Spectral Clustering (MCSC) and Hierarchical Agglomerative Clustering (HAC). The proposed method well fits the problem of blind image clustering because it does not a priori require the knowledge of the amount of classes in which the dataset has to be divided but it needs only a stop threshold; such a threshold has been properly defined by means of a ROC curves approach by relying on the goodness of cluster aggregation. Several experimental tests have been carried out in different operative conditions and the proposed methodology globally presents superior performances in terms of clustering accuracy and robustness as well as a reduced computational burden.

A Graph-Partitioning Framework for Aligning Hierarchical Topic Structures to Presentations

This paper studies the problem of imposing an existing hierarchical semantic structure onto a corresponding spoken document in which the structures are embedded, with the goal of indexing such documents for easier access. We propose a graph-partitioning framework to solve a semantic tree-to-string alignment problem through optimizing a normalized-cut criterion. We present models with different modeling capabilities and time complexities in this framework and provide experimental evidence of their performance. We relate graph partitioning to conventional dynamic time warping (DTW) as it applies to this problem, and show that the proposed framework can naturally include topic segmentation to accommodate cohesion constraints.

Evaluating performance of image segmentation criteria and techniques

The image segmentation problem is to delineate, or segment, a salient feature in an image. As such, this is a bipartition problem with the goal of separating the foreground from the background. An NP-hard optimization problem, the Normalized Cut problem, is often used as a model for image segmentation. The common approach for solving the normalized cut problem is the spectral method which generates heuristic solutions based upon finding the Fiedler eigenvector. Recently, Hochbaum (IEEE Trans Pattern Anal Mach Intell 32(5):889–898, 2010) presented a new relaxation of the normalized cut problem, called normalized cut $$^\prime $$ problem, which is solvable in polynomial time by a combinatorial algorithm. We compare this new algorithm with the spectral method and present experimental evidence that the combinatorial algorithm provides solutions which better approximate the optimal normalized cut solution. In addition, the subjective visual quality of the segmentations provided by the combinatorial algorithm greatly improves upon those provided by the spectral method. Our study establishes an interesting observation about the normalized cut criterion that the segmentation which provides the subjectively best visual bipartition rarely corresponds to the segmentation which minimizes the objective function value of the normalized cut problem. We conclude that modeling the image segmentation problem as normalized cut criterion might not be appropriate. Instead, normalized cut $$^\prime $$ not only provides better visual segmentations but is also solvable in polynomial time. Therefore, normalized cut $$^\prime $$ should be the preferred segmentation criterion for both complexity and good segmentation quality reasons.

GANC: Greedy agglomerative normalized cut for graph clustering

This paper describes a graph clustering algorithm that aims to minimize the normalized cut criterion and has a model order selection procedure. The performance of the proposed algorithm is comparable to spectral approaches in terms of minimizing normalized cut. However unlike spectral approaches, the proposed algorithm scales to graphs with millions of nodes and edges. The algorithm consists of three components that are processed sequentially: a greedy agglomerative hierarchical clustering procedure, model order selection, and a local refinement.

Multi-level pixel-based texture classification through efficient prototype selection via normalized cut

This paper presents a new efficient technique for supervised pixel-based classification of textured images. A prototype selection algorithm that relies on the normalized cut criterion is utilized for automatically determining a subset of prototypes in order to characterize each texture class at the local level based on the outcome of a multichannel Gabor filter bank. Then, a simple minimum distance classifier fed with the previously determined prototypes is used to classify every image pixel into one of the given texture classes. Multi-sized evaluation windows following a top-down approach are used during classification in order to improve accuracy near frontiers of regions of different texture. Results with standard Brodatz, VisTex and MeasTex compositions and with complex real images are presented and discussed. The proposed technique is also compared with alternative texture classifiers.

Inappropriateness of the criterion of k-way normalized cuts for deciding the number of clusters

Spectral clustering is a completely different algorithm from other existing clustering algorithms in that it relies on a linear algebraic approach including spectral decomposition. Normalized Cuts is a representative algorithm of spectral clustering. It incorporates a criterion for deciding the number k of clusters to partition. This paper shows that the criterion is not appropriate for deciding k. We showed this by proving that the optimal bipartition (that is, when k = 2) becomes the optimal clustering. Namely, based on the criterion, the evaluation becomes better when k is small. We also show that the criterion is inappropriate for comparing approximate solutions with various k. Especially we prove that a bipartition which surpasses the best given approximate solution H ˆ k ˆ can be constructed from H ˆ k ˆ within the time complexity at most O ( k ˆ 3 ) , where k ˆ is the number of clusters contained in H ˆ k ˆ . Based on these two reasons, the Normalized Cuts Criterion is not appropriate for deciding k. An alternative criterion is necessary.

A framework for sound source separation using spectral clustering

Clustering based on the normalized cut criterion, and more generally, spectral clustering methods, are techniques originally proposed to model perceptual grouping tasks, such as image segmentation in computer vision. In this work, it is shown how such techniques can be applied to the problem of dominant melodic source separation in polyphonic music audio signals. One of the main advantages of this approach is the ability to incorporate mutiple perceptually‐inspired grouping criteria into a single framework without requiring multiple processing stages, as many existing computational auditory science analysis approaches do. Experimental results for several tasks, including dominant melody pitch detection, are presented. The system is based on a sinusoidal modeling analysis front‐end. A novel similarity cue based on harmonicity (harmonically‐wrapped peak similariy) is also introduced. The proposed system is data‐driven (i.e., requires no prior knowledge about the extracted source), causal, robust, practical, and efficient (close to real‐time on a fast computer). Although a specific implementation is presented, one of the main advantages of the proposed approach is its ability to utilize different analysis front‐ends and grouping criteria in a straightforward manner.