A study on neutrosophic [Formula: see text]-semantic segmentation for iris image recognition with Gaussian and Poisson noises

In this article, we introduce an innovative methodology for image segmentation utilizing neutrosophic sets. Neutrosophic set components exhibit superior reliability in image processing due to their adeptness at managing uncertainty. The swift proliferation of neutrosophic sets research is attributed to its efficacy in addressing uncertainties in practical scenarios. Effective segmentation requires the resolution of uncertainties. This article's principal aim is to achieve multi-class segmentation through uncertainty analysis. The [Formula: see text] segmentation method pertains to type 1, encompassing truth and falsity membership functions. In this method, multiclass segmentation is possible based on the image intensity values of the neutrosophic membership functions. As a result of this research, the article proposes the finding of image segmentation through the neutrosophic set. An experimental set of biometric iris data will be the main focus of the experiment. The analysis employs real-time iris image data. The image data were sourced from the CASIA V1 iris image database. Noise was introduced into the images for analytical purposes, specifically Gaussian and Poisson noise. The evaluation metrics include the Jaccard, MIOU, precision, recall, F1 score, and accuracy. As a result of the application of this methodology, an impressive segmentation score of 85% was obtained.

On the Consistency and Large-Scale Extension of Multiple Kernel Clustering

Existing multiple kernel clustering (MKC) algorithms have two ubiquitous problems. From the theoretical perspective, most MKC algorithms lack sufficient theoretical analysis, especially the consistency of learned parameters, such as the kernel weights. From the practical perspective, the high complexity makes MKC unable to handle large-scale datasets. This paper tries to address the above two issues. We first make a consistency analysis of an influential MKC method named Simple Multiple Kernel k-Means (SimpleMKKM). Specifically, suppose that ∧γn are the kernel weights learned by SimpleMKKM from the training samples. We also define the expected version of SimpleMKKM and denote its solution as γ*. We establish an upper bound of ||∧γn-γ*||∞ in the order of ~O(1/√n), where n is the sample number. Based on this result, we also derive its excess clustering risk calculated by a standard clustering loss function. For the large-scale extension, we replace the eigen decomposition of SimpleMKKM with singular value decomposition (SVD). Consequently, the complexity can be decreased to O(n) such that SimpleMKKM can be implemented on large-scale datasets. We then deduce several theoretical results to verify the approximation ability of the proposed SVD-based method. The results of comprehensive experiments demonstrate the superiority of the proposed method.

Segmentation of Brain Tissues from MRI Images Using Multitask Fuzzy Clustering Algorithm

In recent years, brain magnetic resonance imaging (MRI) image segmentation has drawn considerable attention. MRI image segmentation result provides a basis for medical diagnosis. The segmentation result influences the clinical treatment directly. Nevertheless, MRI images have shortcomings such as noise and the inhomogeneity of grayscale. The performance of traditional segmentation algorithms still needs further improvement. In this paper, we propose a novel brain MRI image segmentation algorithm based on fuzzy C-means (FCM) clustering algorithm to improve the segmentation accuracy. First, we introduce multitask learning strategy into FCM to extract public information among different segmentation tasks. It combines the advantages of the two algorithms. The algorithm enables to utilize both public information among different tasks and individual information within tasks. Then, we design an adaptive task weight learning mechanism, and a weighted multitask fuzzy C-means (WMT-FCM) clustering algorithm is proposed. Under the adaptive task weight learning mechanism, each task obtains the optimal weight and achieves better clustering performance. Simulated MRI images from McConnell BrainWeb have been used to evaluate the proposed algorithm. Experimental results demonstrate that the proposed method provides more accurate and stable segmentation results than its competitors on the MRI images with various noise and intensity inhomogeneity.

Maximum Joint Probability With Multiple Representations for Clustering

Classical generative models in unsupervised learning intend to maximize p(X) . In practice, samples may have multiple representations caused by various transformations, measurements, and so on. Therefore, it is crucial to integrate information from different representations, and lots of models have been developed. However, most of them fail to incorporate the prior information about data distribution p(X) to distinguish representations. In this article, we propose a novel clustering framework that attempts to maximize the joint probability of data and parameters. Under this framework, the prior distribution can be employed to measure the rationality of diverse representations. K -means is a special case of the proposed framework. Meanwhile, a specific clustering model considering both multiple kernels and multiple views is derived to verify the validity of the designed framework and model.

Statistical Modeling of RPCA-FCM in Spatiotemporal Rainfall Patterns Recognition

This study was conducted to identify the spatiotemporal torrential rainfall patterns of the East Coast of Peninsular Malaysia, as it is the region most affected by the torrential rainfall of the Northeast Monsoon season. Dimension reduction, such as the classical Principal Components Analysis (PCA) coupled with the clustering approach, is often applied to reduce the dimension of the data while simultaneously performing cluster partitions. However, the classical PCA is highly insensitive to outliers, as it assigns equal weights to each set of observations. Hence, applying the classical PCA could affect the cluster partitions of the rainfall patterns. Furthermore, traditional clustering algorithms only allow each element to exclusively belong to one cluster, thus observations within overlapping clusters of the torrential rainfall datasets might not be captured effectively. In this study, a statistical model of torrential rainfall pattern recognition was proposed to alleviate these issues. Here, a Robust PCA (RPCA) based on Tukey’s biweight correlation was introduced and the optimum breakdown point to extract the number of components was identified. A breakdown point of 0.4 at 85% cumulative variance percentage efficiently extracted the number of components to avoid low-frequency variations or insignificant clusters on a spatial scale. Based on the extracted components, the rainfall patterns were further characterized based on cluster solutions attained using Fuzzy C-means clustering (FCM) to allow data elements to belong to more than one cluster, as the rainfall data structure permits this. Lastly, data generated using a Monte Carlo simulation were used to evaluate the performance of the proposed statistical modeling. It was found that the proposed RPCA-FCM performed better using RPCA-FCM compared to the classical PCA coupled with FCM in identifying the torrential rainfall patterns of Peninsular Malaysia’s East Coast.

Ambiguous D-means fusion clustering algorithm based on ambiguous set theory: Special application in clustering of CT scan images of COVID-19

Coronavirus Disease 2019 (COVID-19) has been considered one of the most critical diseases of the 21st century. Only early detection can aid in the prevention of personal transmission of the disease. Recent scientific research reports indicate that computed tomography (CT) images of COVID-19 patients exhibit acute infections and lung abnormalities. However, analyzing these CT scan images is very difficult because of the presence of noise and low-resolution. Therefore, this study suggests the development of a new early detection method to detect abnormalities in chest CT scan images of COVID-19 patients. By this motivation, a novel image clustering algorithm, called ambiguous D-means fusion clustering algorithm (ADMFCA), is introduced in this study. This algorithm is based on the newly proposed ambiguous set theory and associated concepts. The ambiguous set is used in the proposed technique to characterize the ambiguity associated with grayscale values of pixels as true, false, true-ambiguous and false-ambiguous. The proposed algorithm performs the clustering operation on the CT scan images based on the entropies of different grayscale values. Finally, a final outcome image is obtained from the clustered images by image fusion operation. The experiment is carried out on 40 different CT scan images of COVID-19 patients. The clustered images obtained by the proposed algorithm are compared to five well-known clustering methods. The comparative study based on statistical metrics shows that the proposed ADMFCA is more efficient than the five existing clustering methods.

Segmentation of Brain MR Image Using Modified Student’s t-Mixture Model

In conventional brain image analysis, it is a critical step to segment brain magnetic resonance (MR) image into three major tissues: Gray Matter (GM), White Matter (WM) and Cerebrospinal Fluid (CSF). The main difficulties for segmenting brain MR image are partial volume effect, intensity inhomogeneity and noise, which result in challenging segmentation task. In this paper, we propose a novel modified method based on the basis of the conventional Student’s t-Mixture Model (SMM), for segmentation of brain MR image and correction of bias field. The advantages of our model are introduced as follows. First, we take account of the influence on the probabilities of the pixels in the adjacent region and take full advantage of the local spatial information and class information. Second, our modified SMM is derived from the traditional finite mixture model (FMM) by adding the bias field correction model; the logarithmic likelihood function of traditional FMM is revised. Third, the noise and bias field can be easily extended to combine with the SMM model and EM algorithm. Last but not least, the exponential coefficients are employed to control the results of segmentation details. As a result, our effective and highly accurate method exhibits high robustness on both simulated and real MR image segmentation, compared to the state-of-the-art algorithms.

Morphological Reconstruction-Based Image-Guided Fuzzy Clustering with a Novel Impact Factor

The guided filter is a novel explicit image filtering method, which implements a smoothing filter on “flat patch” regions and ensures edge preserving on “high variance” regions. Recently, the guided filter has been successfully incorporated into the process of fuzzy c-means (FCM) to boost the clustering results of noisy images. However, the adaptability of the existing guided filter-based FCM methods to different images is deteriorated, as the factor ε of the guided filter is fixed to a scalar. To solve this issue, this paper proposes a new guided filter-based FCM method (IFCM_GF), in which the guidance image of the guided filter is adjusted by a newly defined influence factor ρ. By dynamically changing the impact factor ρ, the IFCM_GF acquires excellent segmentation results on various noisy images. Furthermore, to promote the segmentation accuracy of images with heavy noise and simplify the selection of the influence factor ρ, we further propose a morphological reconstruction-based improved FCM clustering algorithm with guided filter (MRIFCM_GF). In this approach, the original noisy image is reconstructed by the morphological reconstruction (MR) before clustering, and the IFCM_GF is performed on the reconstructed image by utilizing the adjusted guidance image. Due to the efficiency of the MR to remove noise, the MRIFCM_GF achieves better segmentation results than the IFCM_GF on images with heavy noise and the selection of the influence factor for the MRIFCM_GF is simple. Experiments demonstrate the effectiveness of the presented methods.

A Novel Type-2 Fuzzy C-Means Clustering for Brain MR Image Segmentation

The fuzzy C -means (FCM) clustering procedure is an unsupervised form of grouping the homogenous pixels of an image in the feature space into clusters. A brain magnetic resonance (MR) image is affected by noise and intensity inhomogeneity (IIH) during the acquisition process. FCM has been used in MR brain tissue segmentation. However, it does not consider the neighboring pixels for computing the membership values, thereby misclassifying the noisy pixels. The inaccurate cluster centers obtained in FCM do not address the problem of IIH. A fixed value of the fuzzifier ( m ) used in FCM brings uncertainty in controlling the fuzziness of the extracted clusters. To resolve these issues, we suggest a novel type-2 adaptive weighted spatial FCM (AWSFCM) clustering algorithm for MR brain tissue segmentation. The idea of type-2 FCM applied to the problem on hand is new and is reported in this article. The application of the proposed technique to the problem of MR brain tissue segmentation replaces the fixed fuzzifier value with a fuzzy linguistic fuzzifier value ( M ). The introduction of the spatial information in the membership function reduces the misclassification of noisy pixels. Furthermore, the incorporation of adaptive weights into the cluster center update function improves the accuracy of the final cluster centers, thereby reducing the effect of IIH. The suggested algorithm is evaluated using T1-w, T2-w, and proton density (PD) brain MR image slices. The performance is justified in terms of qualitative and quantitative measures followed by statistical analysis. The outcomes demonstrate the superiority and robustness of the algorithm in comparison to the state-of-the-art methods. This article is useful for the cybernetics application.

Rule-Based Modeling With DBSCAN-Based Information Granules

Rule-based models are applicable to model the behavior of complex and nonlinear systems. Due to limited experience and randomness involving constructing information granules, an insufficient credible rules division could reduce the model's accuracy. This paper proposes a new rule-based modeling approach, which utilizes density-based spatial clustering of applications with noise (DBSCAN)-based information granules to construct the rules. First, bear in mind the advantages of density-based clustering, DBSCAN is proposed to generate data structures. Based on these data structures, two rule-based models are constructed: 1) models using DBSCAN clusters to construct granules and rules directly and 2) models generating subgranules in each DBSCAN cluster for rule formation. Experiments involving these two models are completed, and obtained results are compared with those generated with a traditional model involving fuzzy C -means-based granules. Numerical results show that the rule-based model, which builds rules from subgranules of DBSCAN structures, performs the best in analyzing system behaviors.

Fuzzy Clustering to Identify Clusters at Different Levels of Fuzziness: An Evolutionary Multiobjective Optimization Approach

Fuzzy clustering methods identify naturally occurring clusters in a dataset, where the extent to which different clusters are overlapped can differ. Most methods have a parameter to fix the level of fuzziness. However, the appropriate level of fuzziness depends on the application at hand. This paper presents an entropy c -means (ECM), a method of fuzzy clustering that simultaneously optimizes two contradictory objective functions, resulting in the creation of fuzzy clusters with different levels of fuzziness. This allows ECM to identify clusters with different degrees of overlap. ECM optimizes the two objective functions using two multiobjective optimization methods, nondominated sorting genetic algorithm II (NSGA-II) and multiobjective evolutionary algorithm based on decomposition (MOEA/D). We also propose a method to select a suitable tradeoff clustering from the Pareto front. Experiments on challenging synthetic datasets as well as real-world datasets show that ECM leads to better cluster detection compared to the conventional fuzzy clustering methods as well as previously used multiobjective methods for fuzzy clustering.

Granular Fuzzy Modeling Guided Through the Synergy of Granulating Output Space and Clustering Input Subspaces

As an augmentation of classic fuzzy models, granular fuzzy models (GFMs) have been applied to many fields being in rapport with experimental data, models, and users. However, most of the existing methods used to construct GFMs are based on the principle of optimal allocation of information granularity, which requires that a numeric model be provided in advance. In this paper, a straightforward and convincing modeling method is proposed to directly construct GFM on a basis of experimental data. The method first granulates the output space to form some interval information granules with distinct semantics and then uses them to partition the entire input space into a series of input subspaces. Subsequently, an initial GFM is emerged by using "If-Then" rules to relate with those interval information granules positioned in the output space and structures expressed in prototypes that are produced by clustering individual input subspaces. Further, the initial GFM is also refined by continuously migrating prototypes in individual input subspaces. The experimental studies using the synthetic dataset and several real-world datasets are reported. They offer a useful insight into the feasibility and effectiveness of the proposed modeling method and reveal the impact of parameters on the performance of the ensuing GFMs. An application example is also presented to exhibit the advantages of the resulting GFM.

Performance Evaluation of an Independent Time Optimized Infrastructure for Big Data Analytics that Maintains Symmetry

Traditional data analytics tools are designed to deal with the asymmetrical type of data i.e., structured, semi-structured, and unstructured. The diverse behavior of data produced by different sources requires the selection of suitable tools. The restriction of recourses to deal with a huge volume of data is a challenge for these tools, which affects the performances of the tool’s execution time. Therefore, in the present paper, we proposed a time optimization model, shares common HDFS (Hadoop Distributed File System) between three Name-node (Master Node), three Data-node, and one Client-node. These nodes work under the DeMilitarized zone (DMZ) to maintain symmetry. Machine learning jobs are explored from an independent platform to realize this model. In the first node (Name-node 1), Mahout is installed with all machine learning libraries through the maven repositories. The second node (Name-node 2), R connected to Hadoop, is running through the shiny-server. Splunk is configured in the third node (Name-node 3) and is used to analyze the logs. Experiments are performed between the proposed and legacy model to evaluate the response time, execution time, and throughput. K-means clustering, Navies Bayes, and recommender algorithms are run on three different data sets, i.e., movie rating, newsgroup, and Spam SMS data set, representing structured, semi-structured, and unstructured data, respectively. The selection of tools defines data independence, e.g., Newsgroup data set to run on Mahout as others cannot be compatible with this data. It is evident from the outcome of the data that the performance of the proposed model establishes the hypothesis that our model overcomes the limitation of the resources of the legacy model. In addition, the proposed model can process any kind of algorithm on different sets of data, which resides in its native formats.

Fuzzy Broad Learning System: A Novel Neuro-Fuzzy Model for Regression and Classification

A novel neuro-fuzzy model named fuzzy broad learning system (BLS) is proposed by merging the Takagi-Sugeno (TS) fuzzy system into BLS. The fuzzy BLS replaces the feature nodes of BLS with a group of TS fuzzy subsystems, and the input data are processed by each of them. Instead of aggregating the outputs of fuzzy rules produced by every fuzzy subsystem into one value immediately, all of them are sent to the enhancement layer for further nonlinear transformation to preserve the characteristic of inputs. The defuzzification outputs of all fuzzy subsystem and the outputs of enhancement layer are combined together to obtain the model output. The k -means method is employed to determine the centers of Gaussian membership functions in antecedent part and the number of fuzzy rules. The parameters that need to be calculated in a fuzzy BLS are the weights connecting the outputs of enhancement layer to model output and the randomly initialized coefficients of polynomials in consequent part in fuzzy subsystems, which can be calculated analytically. Therefore, fuzzy BLS retains the fast computational nature of BLS. The proposed fuzzy BLS is evaluated by some popular benchmarks for regression and classification, and compared with some state-of-the-art nonfuzzy and neuro-fuzzy approaches. The results indicate that fuzzy BLS outperforms other models involved. Moreover, fuzzy BLS shows advantages over neuro-fuzzy models regarding to the number of fuzzy rules and training time, which can ease the problem of rule explosion to some extent.

Enhanced Fuzzy-based Local Information Algorithm for Sonar Image Segmentation

The recent boost in undersea operations has led to the development of high-resolution sonar systems mounted on autonomous vehicles. These vehicles are used to scan the seafloor in search of different objects such as sunken ships, archaeological sites, and submerged mines. An important part of the detection operation is the segmentation of sonar images, where the object's highlight and shadow are distinguished from the seabed background. In this work, we focus on the automatic segmentation of sonar images. We present our enhanced fuzzybased with Kernel metric (EnFK) algorithm for the segmentation of sonar images which, in an attempt to improve segmentation accuracy, introduces two new fuzzy terms of local spatial and statistical information. Our algorithm includes a preliminary de-noising algorithm which, together with the original image, feeds into the segmentation procedure to avoid trapping to local minima and to improve convergence. The result is a segmentation procedure that specifically suits the intensity inhomogeneity and the complex seabed texture of sonar images. We tested our approach using simulated images, real sonar images, and sonar images that we created in two different sea experiments, using multibeam sonar and synthetic aperture sonar. The results show accurate segmentation performance that is far beyond the stateof-the-art results.

Intuitionistic Center-Free FCM Clustering for MR Brain Image Segmentation

In this paper, an intuitionistic center-free fuzzy c-means clustering method (ICFFCM) is proposed for magnetic resonance (MR) brain image segmentation. First, in order to suppress the effect of noise in MR brain images, a pixel-to-pixel similarity with spatial information is defined. Then, for the purpose of handling the vagueness in MR brain images as well as the uncertainty in clustering process, a pixel-to-cluster similarity measure is defined by employing the intuitionistic fuzzy membership function. These two similarities are used to modify the center-free FCM so that the ability of the method for MR brain image segmentation could be improved. Second, on the basis of the improved center-free FCM method, a local information term, which is also intuitionistic and center-free, is appended to the objective function. This generates the final proposed ICFFCM. The consideration of local information further enhances the robustness of ICFFCM to the noise in MR brain images. Experimental results on the simulated and real MR brain image datasets show that ICFFCM is effective and robust. Moreover, ICFFCM could outperform several fuzzy-clustering-based methods and could achieve comparable results to the standard published methods like statistical parametric mapping and FMRIB automated segmentation tool.

A two-stage filter for removing salt-and-pepper noise using noise detector based on characteristic difference parameter and adaptive directional mean filter

In this paper, a two-stage filter for removing salt-and-pepper noise using noise detector based on characteristic difference parameter and adaptive directional mean filter is proposed. The first stage firstly detects the noise corrupted pixels by combining characteristic difference parameter and gray level extreme, then develops an improved adaptive median filter to firstly restore them. The second stage introduces a restoration scheme to further restore the noise corrupted pixels, which firstly divides them into two types and then applies different restoration skills for the pixels based on the classification result. One type of pixels is restored by the mean filter and the other type of pixels is restored by the proposed adaptive directional mean filter. The new filter firstly adaptively selects the optimal filtering window and direction template, then replaces the gray level of noise corrupted pixel by the mean value of pixels on the optimal template. Experimental results show that the proposed filter outperforms many existing main filters in terms of noise suppression and detail preservation.

Uncertain Data Clustering in Distributed Peer-to-Peer Networks

Uncertain data clustering has been recognized as an essential task in the research of data mining. Many centralized clustering algorithms are extended by defining new distance or similarity measurements to tackle this issue. With the fast development of network applications, these centralized methods show their limitations in conducting data clustering in a large dynamic distributed peer-to-peer network due to the privacy and security concerns or the technical constraints brought by distributive environments. In this paper, we propose a novel distributed uncertain data clustering algorithm, in which the centralized global clustering solution is approximated by performing distributed clustering. To shorten the execution time, the reduction technique is then applied to transform the proposed method into its deterministic form by replacing each uncertain data object with its expected centroid. Finally, the attribute-weight-entropy regularization technique enhances the proposed distributed clustering method to achieve better results in data clustering and extract the essential features for cluster identification. The experiments on both synthetic and real-world data have shown the efficiency and superiority of the presented algorithm.

Improving Image Search through MKFCM Clustering Strategy-Based Re-ranking Measure

The main intention of this research is to develop a novel ranking measure for content-based image retrieval system. Owing to the achievement of data retrieval, most commercial search engines still utilize a text-based search approach for image search by utilizing encompassing textual information. As the text information is, in some cases, noisy and even inaccessible, the drawback of such a recovery strategy is to the extent that it cannot depict the contents of images precisely, subsequently hampering the execution of image search. In order to improve the performance of image search, we propose in this work a novel algorithm for improving image search through a multi-kernel fuzzy c-means (MKFCM) algorithm. In the initial step of our method, images are retrieved using four-level discrete wavelet transform-based features and the MKFCM clustering algorithm. Next, the retrieved images are analyzed using fuzzy c-means clustering methods, and the rank of the results is adjusted according to the distance of a cluster from a query. To improve the ranking performance, we combine the retrieved result and ranking result. At last, we obtain the ranked retrieved images. In addition, we analyze the effects of different clustering methods. The effectiveness of the proposed methodology is analyzed with the help of precision, recall, and F-measures.

KL Divergence-Based Fuzzy Cluster Ensemble for Image Segmentation

Ensemble clustering combines different basic partitions of a dataset into a more stable and robust one. Thus, cluster ensemble plays a significant role in applications like image segmentation. However, existing ensemble methods have a few demerits, including the lack of diversity of basic partitions and the low accuracy caused by data noise. In this paper, to get over these difficulties, we propose an efficient fuzzy cluster ensemble method based on Kullback-Leibler divergence or simply, the KL divergence. The data are first classified with distinct fuzzy clustering methods. Then, the soft clustering results are aggregated by a fuzzy KL divergence-based objective function. Moreover, for image segmentation problems, we utilize the local spatial information in the cluster ensemble algorithm to suppress the effect of noise. Experiment results reveal that the proposed methods outperform many other methods in synthetic and real image-segmentation problems.

Degree-Pruning Dynamic Programming Approaches to Central Time Series Minimizing Dynamic Time Warping Distance

The central time series crystallizes the common patterns of the set it represents. In this paper, we propose a global constrained degree-pruning dynamic programming (g(dp)2) approach to obtain the central time series through minimizing dynamic time warping (DTW) distance between two time series. The DTW matching path theory with global constraints is proved theoretically for our degree-pruning strategy, which is helpful to reduce the time complexity and computational cost. Our approach can achieve the optimal solution between two time series. An approximate method to the central time series of multiple time series [called as m_g(dp)2] is presented based on DTW barycenter averaging and our g(dp)2 approach by considering hierarchically merging strategy. As illustrated by the experimental results, our approaches provide better within-group sum of squares and robustness than other relevant algorithms.

Architecture-Driven Level Set Optimization: From Clustering to Subpixel Image Segmentation

Thanks to their effectiveness, active contour models (ACMs) are of great interest for computer vision scientists. The level set methods (LSMs) refer to the class of geometric active contours. Comparing with the other ACMs, in addition to subpixel accuracy, it has the intrinsic ability to automatically handle topological changes. Nevertheless, the LSMs are computationally expensive. A solution for their time consumption problem can be hardware acceleration using some massively parallel devices such as graphics processing units (GPUs). But the question is: which accuracy can we reach while still maintaining an adequate algorithm to massively parallel architecture? In this paper, we attempt to push back the compromise between, speed and accuracy, efficiency and effectiveness, to a higher level, comparing with state-of-the-art methods. To this end, we designed a novel architecture-aware hybrid central processing unit (CPU)-GPU LSM for image segmentation. The initialization step, using the well-known k -means algorithm, is fast although executed on a CPU, while the evolution equation of the active contour is inherently local and therefore suitable for GPU-based acceleration. The incorporation of local statistics in the level set evolution allowed our model to detect new boundaries which are not extracted by the used clustering algorithm. Comparing with some cutting-edge LSMs, the introduced model is faster, more accurate, less subject to giving local minima, and therefore suitable for automatic systems. Furthermore, it allows two-phase clustering algorithms to benefit from the numerous LSM advantages such as the ability to achieve robust and subpixel accurate segmentation results with smooth and closed contours. Intensive experiments demonstrate, objectively and subjectively, the good performance of the introduced framework both in terms of speed and accuracy.