An improved intuitionistic fuzzy c-means clustering algorithm incorporating local information for brain image segmentation

An Intuitionistic Fuzzy C-Means and Local Information-Based DCT Filtering for Fast Brain MRI Segmentation

Structural and photometric anomalies in the brain magnetic resonance images (MRIs) affect the segmentation performance. Moreover, a sudden change in intensity between two boundaries of the brain tissues makes it prone to data uncertainty, resulting in the misclassification of the pixels lying near the cluster boundaries. The discrete cosine transform (DCT) domain-based filtering is an effective way to deal with structural and photometric anomalies, while the intuitionistic fuzzy C-means (IFCM) clustering can handle the uncertainty using the intuitionistic fuzzy set (IFS) theory. In this background, we propose two novel approaches, namely, the DCT-based intuitionistic fuzzy C-means (DCT-IFCM) and the DCT-based local information IFCM (DCT-LIFCM), which effectively deal with the Rician and Gaussian noises and also handle the data uncertainty problem to provide high segmentation accuracy. The DCT-IFCM approach performs the histogram-based segmentation, while the DCT-LIFCM uses the pixel-wise computation to include the spatial information. Although the DCT-LIFCM delivers slightly better performance than the DCT-IFCM, the latter is very fast in providing equally high segmentation accuracy. An exhaustive performance analysis is provided to demonstrate the superior performance of the proposed algorithms compared with the state-of-the-art algorithms, including those based on the DCT-based filtering approach and the IFS theory.

A novel group decision making method based on CoCoSo and interval-valued Q-rung orthopair fuzzy sets

Interval-valued q-rung orthopair fuzzy set (IVq-ROFS) is a powerful tool for dealing with uncertainty. In this paper, we first propose a new method for aggregating multiple IVq-ROFSs, which is easier to understand and implement in the multi-attribute group decision making process compared to current aggregation operators. Secondly, this paper introduces a new fuzzy entropy with parameters based on IVq-ROFS, which is highly flexible due to its adjustable parameters. Based on this, the IVq-ROFS-based attribute weight calculation method is proposed to obtain the objective weights of the attributes, which is more reasonable and objective than the existing methods. Then, for the dimensional differences between the three compromise scores in the original Combined Compromise Solution (CoCoSo) method, the enhanced compromise scores are proposed. These scores are obtained by normalizing the three dependent compromise scores, ensuring that they fall within the same range. Finally, a novel CoCoSo mothed on IVq-ROFS using the proposed fuzzy entropy and enhanced compromise scores is presented. The proposed method is highly adaptable and scalable, not limited to IVq-ROFS. The excellent performance and robustness of the proposed method are verified in sepsis diagnosis applications.

Micro-segmentation of retinal image lesions in diabetic retinopathy using energy-based fuzzy C-Means clustering (EFM-FCM)

Diabetic retinopathy (DR) is a prevalent cause of global visual impairment, contributing to approximately 4.8% of blindness cases worldwide as reported by the World Health Organization (WHO). The condition is characterized by pathological abnormalities in the retinal layer, including microaneurysms, vitreous hemorrhages, and exudates. Microscopic analysis of retinal images is crucial in diagnosing and treating DR. This article proposes a novel method for early DR screening using segmentation and unsupervised learning techniques. The approach integrates a neural network energy-based model into the Fuzzy C-Means (FCM) algorithm to enhance convergence criteria, aiming to improve the accuracy and efficiency of automated DR screening tools. The evaluation of results includes the primary dataset from the Shiva Netralaya Centre, IDRiD, and DIARETDB1. The performance of the proposed method is compared against FCM, EFCM, FLICM, and M-FLICM techniques, utilizing metrics such as accuracy in noiseless and noisy conditions and average execution time. The results showcase auspicious performance on both primary and secondary datasets, achieving accuracy rates of 99.03% in noiseless conditions and 93.13% in noisy images, with an average execution time of 16.1 s. The proposed method holds significant potential in medical image analysis and could pave the way for future advancements in automated DR diagnosis and management. RESEARCH HIGHLIGHTS: A novel approach is proposed in the article, integrating a neural network energy-based model into the FCM algorithm to enhance the convergence criteria and the accuracy of automated DR screening tools. By leveraging the microscopic characteristics of retinal images, the proposed method significantly improves the accuracy of lesion segmentation, facilitating early detection and monitoring of DR. The evaluation of the method's performance includes primary datasets from reputable sources such as the Shiva Netralaya Centre, IDRiD, and DIARETDB1, demonstrating its effectiveness in comparison to other techniques (FCM, EFCM, FLICM, and M-FLICM) in terms of accuracy in both noiseless and noisy conditions. It achieves impressive accuracy rates of 99.03% in noiseless conditions and 93.13% in noisy images, with an average execution time of 16.1 s.

Fuzzy clustering for the within-season estimation of cotton phenology

Crop phenology is crucial information for crop yield estimation and agricultural management. Traditionally, phenology has been observed from the ground; however Earth observation, weather and soil data have been used to capture the physiological growth of crops. In this work, we propose a new approach for the within-season phenology estimation for cotton at the field level. For this, we exploit a variety of Earth observation vegetation indices (derived from Sentinel-2) and numerical simulations of atmospheric and soil parameters. Our method is unsupervised to address the ever-present problem of sparse and scarce ground truth data that makes most supervised alternatives impractical in real-world scenarios. We applied fuzzy c-means clustering to identify the principal phenological stages of cotton and then used the cluster membership weights to further predict the transitional phases between adjacent stages. In order to evaluate our models, we collected 1,285 crop growth ground observations in Orchomenos, Greece. We introduced a new collection protocol, assigning up to two phenology labels that represent the primary and secondary growth stage in the field and thus indicate when stages are transitioning. Our model was tested against a baseline model that allowed to isolate the random agreement and evaluate its true competence. The results showed that our model considerably outperforms the baseline one, which is promising considering the unsupervised nature of the approach. The limitations and the relevant future work are thoroughly discussed. The ground observations are formatted in an ready-to-use dataset and will be available at https://github.com/Agri-Hub/cotton-phenology-dataset upon publication.

Robust intuitionistic fuzzy clustering with bias field estimation for noisy image segmentation

The concept of intuitionistic fuzzy set has been found to be highly useful to handle vagueness in data. Based on intuitionistic fuzzy set theory, intuitionistic fuzzy clustering algorithms are proposed and play an important role in image segmentation. However, due to the influence of initialization and the presence of noise in the image, intuitionistic fuzzy clustering algorithm cannot acquire the satisfying performance when applied to segment images corrupted by noise. In order to solve above problems, a robust intuitionistic fuzzy clustering with bias field estimation (RIFCB) is proposed for noisy image segmentation in this paper. Firstly, a noise robust intuitionistic fuzzy set is constructed to represent the image by using the neighboring information of pixels. Then, initial cluster centers in RIFCB are adaptively determined by utilizing the frequency statistics of gray level in the image. In addition, in order to offset the information loss of the image when constructing the intuitionistic fuzzy set of the image, a new objective function incorporating a bias field is designed in RIFCB. Based on the new initialization strategy, the intuitionistic fuzzy set representation, and the incorporation of bias field, the proposed method preserves the image details and is insensitive to noise. Experimental results on some Berkeley images show that the proposed method achieves satisfactory segmentation results on images corrupted by different kinds of noise in contrast to conventional fuzzy clustering algorithms.

Clustering Optimization for Triple-Frequency Combined Observations of BDS-3 Based on Improved PSO-FCM Algorithm

The triple-frequency linear combination method can provide combinations with different characteristics and is one of the important methods to improve the performance of navigation services. Due to the large number of combinations and different combination performances, combinatorial clustering optimization is very important, and the efficiency of manual screening is very low. Firstly, based on the basic model, the objective equations are derived. Secondly, based on the fuzzy c-means (FCM) algorithm, three improved PSO-FCM algorithms are proposed, namely the S-PSO-FCM algorithm, L-PSO-FCM algorithm, and LOG-PSO-FCM algorithm. Thirdly, according to the different combination characteristics, the two datasets whose combined coefficients sum to 0 and 1 are emphatically discussed. Finally, the effectiveness of the improved PSO-FCM algorithms is studied based on the public dataset and the measured BeiDou-3 navigation satellite system (BDS-3) data of short baseline, long baseline, and ultra-long baseline. The results show that the performance of the proposed algorithm is better than that of the FCM algorithm, especially in short baseline and long baseline cases.

A Fuzzy Consensus Clustering Algorithm for MRI Brain Tissue Segmentation

Brain tissue segmentation is an important component of the clinical diagnosis of brain diseases using multi-modal magnetic resonance imaging (MR). Brain tissue segmentation has been developed by many unsupervised methods in the literature. The most commonly used unsupervised methods are K-Means, Expectation-Maximization, and Fuzzy Clustering. Fuzzy clustering methods offer considerable benefits compared with the aforementioned methods as they are capable of handling brain images that are complex, largely uncertain, and imprecise. However, this approach suffers from the intrinsic noise and intensity inhomogeneity (IIH) in the data resulting from the acquisition process. To resolve these issues, we propose a fuzzy consensus clustering algorithm that defines a membership function resulting from a voting schema to cluster the pixels. In particular, we first pre-process the MRI data and employ several segmentation techniques based on traditional fuzzy sets and intuitionistic sets. Then, we adopted a voting schema to fuse the results of the applied clustering methods. Finally, to evaluate the proposed method, we used the well-known performance measures (boundary measure, overlap measure, and volume measure) on two publicly available datasets (OASIS and IBSR18). The experimental results show the superior performance of the proposed method in comparison with the recent state of the art. The performance of the proposed method is also presented using a real-world Autism Spectrum Disorder Detection problem with better accuracy compared to other existing methods.

Point Tracking Technology of Sports Image Sequence Marks Based on Fuzzy Clustering Algorithm

Fuzzy clustering algorithms have received widespread attention in various fields. Point tracking technology has significant application importance in sports image data analysis. In order to solve the problem of limited tracking performance caused by the fuzzy and rough division of moving image edges, this paper proposes a point tracking technology based on a fuzzy clustering algorithm, which is used for the point tracking of moving image sequence signs. This article analyzes the development status of sports image sequence analysis and processing technology and introduces some basic theories about fuzzy clustering algorithms. On the basis of the fuzzy clustering algorithm, the positioning and tracking of the marker points of the moving image sequence are studied. A series of experiments have proved that the fuzzy clustering algorithm can improve the recognition rate of the landmark points of the moving image. For the detection and tracking of moving targets, the fuzzy clustering algorithm can reach the limit faster under the same number of iterations, and the image noise can be reduced to 60% of the original by 5 iterations. This has excellent development value in application.

Adaptive Feature Weights Based Double-Layer Multi-Objective Method for SAR Image Segmentation

The recently proposed multi-objective clustering methods convert the segmentation problem to a multi-objective optimization problem by extracting multiple features from an image to be segmented as clustering data. However, most of these methods fail to consider the impacts of different features on segmentation results when calculating the similarity using the Euclidean distance. In this paper, feature domination is defined to segment the image efficiently, and then an adaptive feature weights based double-layer multi-objective method (AFWDLMO) for image segmentation is presented. The proposed method mainly contains two layers: a weight determination layer and a clustering layer. In the weight determination layer, AFWDLMO adaptively identifies the dominant feature of an image to be segmented and specifies its optimal weight through differential evolution. In the clustering layer, multi-objective clustering functions are established and optimized based on the acquired optimal weight, and a set of solutions with high segmentation accuracy is found. The segmentation results on several texture images and SAR images show that the proposed method is better than several existing state-of-the-art segmentation algorithms.

E-Commerce Precision Marketing and Consumer Behavior Models Based on IoT Clustering Algorithm

This article aims to study e-commerce precision models and consumer behavior models based on clustering algorithms, and at the same time conduct detailed research on the Gaussian mixture distribution algorithm, consumer behavior and model construction, and precision marketing strategies in the clustering algorithm. First, a lot of analysis and demonstration of precision marketing strategies and the construction of consumer behavior models are carried out, and then the clustering algorithm-based electronic some experiments were carried out on the application of commercial precision marketing methods and consumer behavior models. The experimental results show that the precision marketing method using the clustering algorithm is more in line with the development of modern e-commerce. The application of the algorithm in the precision marketing methods of enterprises and consumer behavior models has promoted the vigorous development of enterprises, making the sales volume of enterprises reach 9.8 %.

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.

Pythagorean fuzzy time series model based on Pythagorean fuzzy c-means and improved Markov weighted in the prediction of the new COVID-19 cases

Time series is an extremely important branch of prediction, and the research on it plays an important guiding role in production and life. To get more realistic prediction results, scholars have explored the combination of fuzzy theory and time series. Although some results have been achieved so far, there are still gaps in the combination of n-Pythagorean fuzzy sets and time series. In this paper, a pioneering n-Pythagorean fuzzy time series model (n-PFTS) and its forecasting method (n-IMWPFCM) are proposed to employ a n-Pythagorean fuzzy c-means clustering method (n-PFCM) to overcome the subjectivity of directly assigning membership and non-membership values, thus improving the accuracy of the partition the universe of discourse. A novel improved Markov prediction method is exploited to enhance the prediction accuracy of the model. The proposed prediction method is applied to the yearly University of Alabama enrollments data and the new COVID-19 cases data. The results show that compared with the traditional fuzzy time series forecasting method, the proposed method has better forecasting accuracy. Meanwhile, it has the characteristics of low computational complexity and high interpretability and demonstrates the superiority of this model from a realistic perspective.

Self-Learning Network-based segmentation for real-time brain M.R. images through HARIS

In recent years in medical imaging technology, the advancement for medical diagnosis, the initial assessment of the ailment, and the abnormality have become challenging for radiologists. Magnetic resonance imaging is one such predominant technology used extensively for the initial evaluation of ailments. The primary goal is to mechanizean approach that can accurately assess the damaged region of the human brain throughan automated segmentation process that requires minimal training and can learn by itself from the previous experimental outcomes. It is computationally more efficient than other supervised learning strategies such as CNN deep learning models. As a result, the process of investigation and statistical analysis of the abnormality would be made much more comfortable and convenient. The proposed approach's performance seems to be much better compared to its counterparts, with an accuracy of 77% with minimal training of the model. Furthermore, the performance of the proposed training model is evaluated through various performance evaluation metrics like sensitivity, specificity, the Jaccard Similarity Index, and the Matthews correlation coefficient, where the proposed model is productive with minimal training.

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.

Rough Hypercuboid Based Generalized and Robust IT2 Fuzzy C-Means Algorithm

One of the important issues in pattern recognition and machine learning is how to find natural groups present in a dataset. In this regard, this paper presents a novel clustering algorithm, called rough hypercuboid-based interval type-2 fuzzy c -means (RIT2FCM). It judiciously integrates the merits of the rough hypercuboid approach, c -means algorithm, and interval type-2 fuzzy set, to address the uncertainty associated with real-life datasets. Using the concept of hypercuboid equivalence partition matrix (HEM) of rough hypercuboid approach, the lower approximation and boundary region of each cluster are implicitly defined, without using any prespecified threshold parameter. The interval-valued fuzzifier is applied to address the uncertainty coupled with different parameters of rough-fuzzy clustering algorithms, where the determination of the appropriate value of fuzzifier is a difficult task. An analytical formulation on the convergence analysis of the proposed RIT2FCM algorithm, along with a theoretical bound of its fuzzifier, is also introduced. The efficacy of the proposed RIT2FCM method is extensively compared with that of several existing clustering algorithms, using some cluster validity and classification rate indices on various real-life datasets. The proposed algorithm performs better than the state-of-the-art c -means algorithms in 92.59% cases, with respect to different cluster validity indices, in lesser computation time.

Intuitionistic Fuzzy C-Means Algorithm Based on Membership Information Transfer-Ring and Similarity Measurement

The fuzzy C-means clustering (FCM) algorithm is used widely in medical image segmentation and suitable for segmenting brain tumors. Therefore, an intuitionistic fuzzy C-means algorithm based on membership information transferring and similarity measurements (IFCM-MS) is proposed to segment brain tumor magnetic resonance images (MRI) in this paper. The original FCM lacks spatial information, which leads to a high noise sensitivity. To address this issue, the membership information transfer model is adopted to the IFCM-MS. Specifically, neighborhood information and the similarity of adjacent iterations are incorporated into the clustering process. Besides, FCM uses simple distance measurements to calculate the membership degree, which causes an unsatisfactory result. So, a similarity measurement method is designed in the IFCM-MS to improve the membership calculation, in which gray information and distance information are fused adaptively. In addition, the complex structure of the brain results in MRIs with uncertainty boundary tissues. To overcome this problem, an intuitive fuzzy attribute is embedded into the IFCM-MS. Experiments performed on real brain tumor images demonstrate that our IFCM-MS has low noise sensitivity and high segmentation accuracy.

A new weighted fuzzy C-means clustering approach considering between-cluster separability

Fuzzy C-means clustering algorithm (FCM) is an effective approach for clustering. However, in most existing FCM type frameworks, only in-cluster compactness is taken into account, whereas the between-cluster separability is overlooked. In this paper, to enhance the clustering, by incorporating the feature weighting and data weighting method, we put forward a new weighted fuzzy C-means clustering approach considering between-cluster separability, in which for achieving good compactness and separability, making the in-cluster distances as small as possible and making the between-cluster distances as large as possible, the in-cluster distances and between-cluster distances are taken into account; To achieve the optimal clustering result, the iterative formulas of the feature weights, membership degrees, data weights and cluster centers are obtained by maximizing the in-cluster compactness and the between-cluster separability. Experiments on real-world datasets were carried out, the results showed that the new approach could obtain promising performance.

Noise robust hybrid algorithm for segmenting image with unequal cluster sizes based on chaotic crow search and improved fuzzy c-means

Adding spatial penalty to fuzzy C-means (FCM) model is an important way to reduce the influence of noise in image segmentation. However, these improved algorithms easily cause segmentation failures when the image has the characteristics of unequal cluster sizes. Besides, they often fall into local optimal solutions if the initial cluster centers are improper. This paper presents a noise robust hybrid algorithm for segmenting image with unequal cluster sizes based on chaotic crow search algorithm and improved fuzzy c-means to overcome the above defects. Firstly, each size of clusters is integrated into the objective function of noise detecting fuzzy c-means algorithm (NDFCM), which can reduces the contribution of larger clusters to objective function and then the new membership degree and cluster centers are deduced. Secondly, a new expression called compactness, representing the pixel distribution of each cluster, is introduced into the iteration process of clustering. Thirdly, we use two- paths to seek the optimal solutions in each step of iteration: one path is produced by the chaotic crow search algorithm and the other is originated by gradient method. Furthermore, the better solutions of the two-paths go to next generation until the end of the iteration. Finally, the experiments on the synthetic and non–destructive testing (NDT) images show that the proposed algorithm behaves well in noise robustness and segmentation performance.

An Intensity Variation Pattern Analysis Based Machine Learning Classifier for MRI Brain Tumor Detection

BACKGROUND

An accurate detection of tumor from the Magnetic Resonance Images (MRIs) is a critical and demanding task in medical image processing, due to the varying shape and structure of brain. So, different segmentation approaches such as manual, semi-automatic, and fully automatic are developed in the traditional works. Among them, the fully automatic segmentation techniques are increasingly used by the medical experts for an efficient disease diagnosis. But, it has the limitations of over segmentation, increased complexity, and time consumption.

OBJECTIVE

In order to solve these problems, this paper aims to develop an efficient segmentation and classification system by incorporating a novel image processing techniques.

METHODS

Here, the Distribution based Adaptive Median Filtering (DMAF) technique is employed for preprocessing the image. Then, skull removal is performed to extract the tumor portion from the filtered image. Further, the Neighborhood Differential Edge Detection (NDED) technique is implemented to cluster the tumor affected pixels, and it is segmented by the use of Intensity Variation Pattern Analysis (IVPA) technique. Finally, the normal and abnormal images are classified by using the Weighted Machine Learning (WML) technique.

RESULTS

During experiments, the results of the existing and proposed segmentation and classification techniques are evaluated based on different performance measures. To prove the superiority of the proposed technique, it is compared with the existing techniques.

CONCLUSION

From the analysis, it is observed that the proposed IVPA-WML techniques provide the better results compared than the existing techniques.

SDResU-Net: Separable and Dilated Residual U-Net for MRI Brain Tumor Segmentation

BACKGROUND

Glioma is one of the most common and aggressive primary brain tumors that endanger human health. Tumors segmentation is a key step in assisting the diagnosis and treatment of cancer disease. However, it is a relatively challenging task to precisely segment tumors considering characteristics of brain tumors and the device noise. Recently, with the breakthrough development of deep learning, brain tumor segmentation methods based on fully convolutional neural network (FCN) have illuminated brilliant performance and attracted more and more attention.

METHODS

In this work, we propose a novel FCN based network called SDResU-Net for brain tumor segmentation, which simultaneously embeds dilated convolution and separable convolution into residual U-Net architecture. SDResU-Net introduces dilated block into a residual U-Net architecture, which largely expends the receptive field and gains better local and global feature descriptions capacity. Meanwhile, to fully utilize the channel and region information of MRI brain images, we separate the internal and inter-slice structures of the improved residual U-Net by employing separable convolution operator. The proposed SDResU-Net captures more pixel-level details and spatial information, which provides a considerable alternative for the automatic and accurate segmentation of brain tumors.

RESULTS AND CONCLUSION

The proposed SDResU-Net is extensively evaluated on two public MRI brain image datasets, i.e., BraTS 2017 and BraTS 2018. Compared with its counterparts and stateof- the-arts, SDResU-Net gains superior performance on both datasets, showing its effectiveness. In addition, cross-validation results on two datasets illuminate its satisfying generalization ability.

Bit Reduced FCM with Block Fuzzy Transforms for Massive Image Segmentation

A novel bit reduced fuzzy clustering method applied to segment high resolution massive images is proposed. The image is decomposed in blocks and compressed by using the fuzzy transform method, then adjoint pixels with same gray level are binned and the fuzzy c-means algorithm is applied on the bins to segment the image. This method has the advantage to be applied to massive images as the compressed image can be stored in memory and the runtime to segment the image are reduced. Comparison tests are performed with respect to the fuzzy c-means algorithm to segment high resolution images; the results shown that for not very high compression the results are comparable with the ones obtained applying to the fuzzy c-means algorithm on the source image and the runtimes are reduced by about an eighth with respect to the runtimes of fuzzy c-means.

Intuitionistic based segmentation of thyroid nodules in ultrasound images

Accurate delineation of thyroid nodules in ultrasound images is vital for computer-aided diagnosis. Most segmentation methods are semi-automated for thyroid nodules and require manual intervention, which increases the processing time and errors. We propose an automated intuitionistic fuzzy active contour method (IFACM) that integrates intuitionistic fuzzy clustering with an active contour for thyroid nodule segmentation using ultrasound images. Intuitionistic fuzzy clustering is used for the initialization of an active contour and estimation of the parameters required to automatically control the curve evolution. The IFACM was tested extensively on both artificial and real ultrasound images. The IFACM obtained a higher value of true positive (95.1% ± 2.86%), overlap metric (93.1 ± 2.95%), and dice coefficient (90.90 ± 3.08), indicating that the boundary delineated by the IFACM fits best to true nodules. Moreover, it obtained a lower value of false positive (04.1% ± 3.24%) and Hausdorff distance (0.50 ± 0.21 in pixels), further verifying the higher similarity of shape and boundary, respectively. According to the significance test, the results of the proposed method were more significant than those of the other segmentation methods. The main benefit of the IFACM is the automatic identification of nodules on the basis of image characteristics, which eliminates manual intervention. In all the experiments, all initial contours were automatically defined closer to the boundaries of the nodule, which is a benefit of the IFACM. Moreover, this method can segment multiple nodules in a single image efficiently.

Hybrid Fuzzy Clustering Method Based on FCM and Enhanced Logarithmical PSO (ELPSO)

Fuzzy c-means (FCM) is one of the best-known clustering methods to organize the wide variety of datasets automatically and acquire accurate classification, but it has a tendency to fall into local minima. For overcoming these weaknesses, some methods that hybridize PSO and FCM for clustering have been proposed in the literature, and it is demonstrated that these hybrid methods have an improved accuracy over traditional partition clustering approaches, whereas PSO-based clustering methods have poor execution time in comparison to partitional clustering techniques, and the current PSO algorithms require tuning a range of parameters before they are able to find good solutions. Therefore, this paper introduces a hybrid method for fuzzy clustering, named FCM-ELPSO, which aim to deal with these shortcomings. It combines FCM with an improved version of PSO, called ELPSO, which adopts a new enhanced logarithmic inertia weight strategy to provide better balance between exploration and exploitation. This new hybrid method uses PBM(F) index and the objective function value as cluster validity indexes to evaluate the clustering effect. To verify the effectiveness of the algorithm, two types of experiments are performed, including PSO clustering and hybrid clustering. Experiments show that the proposed approach significantly improves convergence speed and the clustering effect.

(T, S)-Based Single-Valued Neutrosophic Number Equivalence Matrix and Clustering Method

Fuzzy clustering is widely used in business, biology, geography, coding for the internet and more. A single-valued neutrosophic set is a generalized fuzzy set, and its clustering algorithm has attracted more and more attention. An equivalence matrix is a common tool in clustering algorithms. At present, there exist no results constructing a single-valued neutrosophic number equivalence matrix using t-norm and t-conorm. First, the concept of a ( T , S ) -based composition matrix is defined in this paper, where ( T , S ) is a dual pair of triangular modules. Then, a ( T , S ) -based single-valued neutrosophic number equivalence matrix is given. A λ -cutting matrix of single-valued neutrosophic number matrix is also introduced. Moreover, their related properties are studied. Finally, an example and comparison experiment are given to illustrate the effectiveness and superiority of our proposed clustering algorithm.