Combining contour-based and region-based in image segmentation

The Fuzzy C-Means (FCM) algorithm is commonly used for clustering. The weighting exponent c and the clustering number m are the important parameters in FCM algorithm. Conventional fuzzy clustering method must use both of the two prespecified parameters, so in this paper we analyses the original algorithm and studies on the optimal selection methods of the c and m by introducing the fuzzy decision theory and the validity index basing on the geometric structure of the dataset. Experiment results with the IRIS dataset show that this algorithm can obtain the optimal weighting exponent m and the optimal clustering number c. Moreover, the fact that the best value scope of m achieved in practical applications indicates that the method is effective.

As an important classifier, fuzzy c-means clustering technique has been widely used in segmentation of image. It is an adaptive segmentation method for plant disease images. However, it has some uncertain factors, when it is used for specific segmentation problem, that are input parameters value. The input parameters include the feature of the date set, the optimal number of cluster, and the degree of fuzziness. These parameters affect the speed and precision of fuzzy clustering segmentation. In this paper, the optimal choice of parameters in a fuzzy c-means algorithm for segmentation of plant disease image was discussed and investigated. Using the pixels gray and means of neighborhood pixels as input feature data; an adapting the FCM algorithm parameters based on fuzzy partition entropy, fuzzy partition coefficient, and compactness measures was used to choose the optimal cluster number; and experiments was used for choosing the degree of fuzziness. The Results show that the optimal clustering number for disease leaf segmentation problem is 4 and the degree of fuzziness is 2.

Fuzzy C-Means (FCM) algorithm has good clustering efficiency, for which it is widely used in the field of image segmentation. However, problems such as weak robustness of distance measure, the number of initial clustering to be given in advance and not considering local image feature still exist. In essence, FCM is a local search algorithm. Improper selection of initial value will lead to the need for more iterations and convergence to local optimal solution. By combining evolving clustering (ECM) with FCM algorithm, a new method of remote sensing image segmentation is put forward. By using FCM algorithm to solve the choice of ECM's initialization clustering centers and using FCM to optimize the obtained centers, fuzzy clustering is completed. And by converting fuzzy into a certainty classification, clustering segmentation is realized. The algorithm is typical of relatively less iterations of convergence to global optimum, good stability and robustness. Experiment results show that it helps to produce better segmentation effect and improve the efficiency of remote sensing image segmentation.

In this study, clustering based method for activation detection in functional magnetic resonance imaging (fMRI) is employed. Moreover, some features are obtained by fitting two models namely FIR filter and Gamma function, to hemodynamic response function (HRF). After applying clustering methods (that require number of clusters as an input) to feature space, our simulations show that number of clusters can affect activation detection significantly. Therefore a newly proposed clustering algorithm namely evolving neural gas (ENG) that gives optimal number of clusters is exploited. In addition to ENG, the result of four clustering algorithms namely k-means, fuzzy C-means, neural gas, and clara in different number of clusters are evaluated. The results show that the best activation detection is taken place using obtained optimal number of clusters.

In order to overcome the poor anti-noise performance of traditional fuzzy C-Means (FCM) algorithm in image segmentation, a novel improved FCM algorithm was proposed in this paper based on Particle Swarm Optimization (PSO) algorithm and Markov Random Field (MRF) model, which can make full use of the global searching ability of PSO and the spatial information integrating ability of MRF for image segmentation. In this algorithm, the image segmentation is converted to a PSO optimization problem, in which the fitness function is set up to containing the spatial information based on the spectral value and the neighboring pixels modeled by MRFs. And segmentation results can be iteratively obtained during the PSO iterations according to the newly designed membership function of FCM in which the spatial information is integrated. The experiments herein reported in this paper illustrate the better performance of this algorithm than the traditional FCM algorithm and the PSO algorithm for image segmentation.

This paper proposes a multi-level thresholding method based on a weighted FCM(Fuzzy C-Means) algorithm in color image. FCM algorithm can determine a more optimal thresholding value than existing methods and be extended to multi-level thresholding, yet it is sensitive to noise, as it does not include spatial information. To solve this problem, a weight based on the entropy obtained from neighboring pixels is applied to FCM algorithm, and the optimal cluster number is determined using the within-class distance in the code image based on the clustered pixels for each color component. Experiments confirmed that the proposed method was more tolerant to noise and superior to existing methods.

Fuzzy clustering is an essential algorithm in image segmentation, and most of them are based on 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, which is 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 lowrank structure constraint. Experiments performed on artificial and real-world images show that the proposed method is more effective and efficient than the current state-of-the-art methods.

With the development of shale gas reservoirs, various fracture propagation models have been developed to predict hydraulic fracture geometry by considering the stress shadow effects. Also, many researchers have been working on development of various production-simulation approaches to simulate production from the complex fracture geometries. The objective of this study is to combine the fracture propagation modeling and reservoir simulation to optimize production in shale gas reservoirs. First, we have developed a semi-analytical model to simulate shale gas production from the complex non-planar fracture geometry with varying fracture width and fracture permeability along fracture length. The important gas transport mechanisms including gas slippage, gas diffusion, and gas desorption are considered. Second, we integrate the semi-analytical model with a three-dimensional fracture propagation model, which fully couples elastic deformation of the rock and fluid flow to simulate complex hydraulic fracture propagation, to optimize fracture treatment design in Marcellus shale gas reservoirs. Specifically, the fracture propagation model is utilized to predict the more-realistic non-planar fracture geometry with varying fracture width and fracture permeability along fracture length. In this study, the effect of varying number of perforation clusters within a given stage ranging from 2 to 5 on the fracture propagation was investigated. Three values of stage spacing were considered including 100 ft, 200 ft, and 300 ft. After predicting the non-planar fracture geometry, the semi-analytical model is employed to simulate production from such fracture geometries. According to the well productivity, the optimal number of clusters per stage for varying stage spacing is discussed and determined. In addition, we compared the well performance with the optimal number of perforation clusters for the stage spacing of 100 ft, 200 ft, and 300 ft under a given horizontal well length of 2,500 ft. Furthermore, we used the integrated approach to analyze a well performance from Marcellus shale gas reservoirs. Through the field case study, the more-realistic non-planar fracture geometry was quantified. Also, the difference between the non-planar fracture geometry and ideal planar fracture geometry with equal fracture width and fracture half-length was compared. Finally, the optimal fracture treatment design for the field well development was recommended. This work can provide new insights into optimization of number of perforation clusters per stage within a given fracture stage and a better understanding of the non-planar fracture geometry in shale gas reservoirs.

Fuzzy clustering is a popular unsupervised learning method that is used in cluster analysis. Fuzzy clustering allows a data point to belong to two or more clusters. Fuzzy c-means is the most well-known method that is applied to cluster analysis, however, the shortcoming is that the number of clusters need to be predefined. This paper proposes a clustering approach based on Particle Swarm Optimization (PSO). This PSO approach determines the optimal number of clusters automatically with the help of a threshold vector. The algorithm first randomly partitions the data set within a preset number of clusters, and then uses a reconstruction criterion to evaluate the performance of the clustering results. The experiments conducted demonstrate that the proposed algorithm automatically finds the optimal number of clusters. Furthermore, to visualize the results principal component analysis projection, conventional Sammon mapping, and fuzzy Sammon mapping were used

Averaging amplitudes over consecutive time samples (i.e., time window) is widely used to calculate the peak amplitude of event-related potentials (ERPs). Cluster analysis of the spatio-temporal ERP data is a promising tool to determine the time window of an ERP of interest. However, determining an appropriate number of clusters to optimally represent ERPs is still challenging. Here, we develop a new method to estimate the optimal number of clusters utilizing consensus clustering. Various polarity dependent clustering methods, namely, k-means, hierarchical clustering, fuzzy c-means, self-organizing map, spectral clustering, and Gaussian mixture model, are used to configure consensus clustering after assessing them individually. When a range of clusters is applied many times, the optimal number of clusters should correspond to the expectation, which is the average of the obtained mean inner-similarities of estimated time windows across all conditions and groups converge in the satisfactory thresholds. In order to assess our method, the proposed method has been applied to simulated data and prospective memory experiment ERP data aimed to qualify N2 and P3, and N300 and prospective positivity components, respectively. The results of determining the optimal number of clusters meet at six cluster maps for both ERP data. In addition, our results revealed that the proposed method could be reliably applied to ERP data to determine the appropriate time window for the ERP of interest when the measurement interval is not accurately defined.

BackgroundCluster analysis is the most common unsupervised method for finding hidden groups in data. Clustering presents two main challenges: (1) finding the optimal number of clusters, and (2) removing “outliers” among the objects being clustered. Few clustering algorithms currently deal directly with the outlier problem. Furthermore, existing methods for identifying the number of clusters still have some drawbacks. Thus, there is a need for a better algorithm to tackle both challenges.ResultsWe present a new approach, implemented in an R package called Thresher, to cluster objects in general datasets. Thresher combines ideas from principal component analysis, outlier filtering, and von Mises-Fisher mixture models in order to select the optimal number of clusters. We performed a large Monte Carlo simulation study to compare Thresher with other methods for detecting outliers and determining the number of clusters. We found that Thresher had good sensitivity and specificity for detecting and removing outliers. We also found that Thresher is the best method for estimating the optimal number of clusters when the number of objects being clustered is smaller than the number of variables used for clustering. Finally, we applied Thresher and eleven other methods to 25 sets of breast cancer data downloaded from the Gene Expression Omnibus; only Thresher consistently estimated the number of clusters to lie in the range of 4–7 that is consistent with the literature.ConclusionsThresher is effective at automatically detecting and removing outliers. By thus cleaning the data, it produces better estimates of the optimal number of clusters when there are more variables than objects. When we applied Thresher to a variety of breast cancer datasets, it produced estimates that were both self-consistent and consistent with the literature. We expect Thresher to be useful for studying a wide variety of biological datasets.

To find an optimal cluster size and number of clusters for a reasonable estimate of the prevalence of cataract blindness in people aged > or = 50 years in 19 rural districts of a state in India. Cluster sampling methodology was used in 19 rural districts of Karnataka State, India. In each district, 15 clusters were randomly selected and 90 people aged > or = 50 years were examined in each cluster. As a result the visual acuity and lens status of a total of 22,218 people were assessed. For each district, the design effect for cluster size ranging from 20 to 90 was calculated and the optimal cluster size and the required number of clusters to achieve an accuracy of 1% errors and 80% confidence was assessed. The age and gender adjusted prevalence of cataract blindness varied from 1.58% to 7.24%, which justifies district level surveys. The design effect is nearly 1.5 for clusters of sizes 30 and 40. With an average prevalence of 4.93% with 1% error and 80% confidence level, the optimal number of clusters is 37 and 28 for a cluster size of 30 and 40 respectively and the average sample size for a district around 1100. Rapid assessments for cataract blindness in those aged > or = 50 years can be conducted at district level in India with existing resources and at affordable costs. These provide reliable data, essential for effective monitoring and planning. Other parameters, for instance, surgical coverage can also be assessed. The availability of standardized software for data entry and analysis and strict adherence to survey procedures is essential.

Brain tumor segmentation based on a hybrid clustering technique

The aim of this paper is to provide a comprehensive survey of image segmentation method using clustering techniques. In image processing, segmentation plays an important role in the detection and matching of objects. Image segmentation uses number of techniques to find the correct segmented images. Clustering techniques are one such methods used for the segmentation of images. It is the process by the pixels of an image are divided into different partitions on the basis of similarity criteria. This paper presents recent development in image segmentation by using the clustering-based approaches such as K-Means and Fuzzy C-Means.

A fundamental problem in data clustering is how to determine the correct number of clusters. The k-adaptive medoid set ant colony optimization (ACO) clustering (METACOC-K) algorithm is superior in solving clustering problems. However, METACOC-K does not guarantee in finding the best number of clusters. It assumed the number of clusters based on an adaptive parameter strategy that lacks feedback learning. This has restrained the algorithm in producing compact clusters and the optimal number of clusters. In this paper, a self-adaptive ACO clustering (S-ACOC) algorithm is proposed to produce the optimal number of clusters by incorporating a self-adaptive parameter strategy. The S-ACOC algorithm is a centroid-based algorithm that automatically adjusts the number of clusters during the algorithm run. The selection of the number of clusters is based on a construction graph that reflects the influence of a pheromone in algorithm learning. Experiments were conducted on real-world datasets to evaluate the performance of the proposed algorithm. The external evaluation metrics (purity, F-measure, and entropy) were used to compare the results of the proposed algorithm with other swarm clustering algorithms, including a genetic algorithm (GA), particle swarm optimization (PSO), and METACOC-K. Results showed that S-ACOC provides higher purity (50%) and lower entropy (40%) than GA, PSO, and METACOC-K. Experiments were also performed on several predefined clusters, and results demonstrate that the S-ACOC algorithm is superior to GA, PSO, and METACOC-K. Based on the superior performance, S-ACOC can be used to solve clustering problems in various application domains.