Fast fuzzy clustering

This paper presents a multistage random sampling fuzzy c-means based clustering algorithm, which significantly reduces the computation time required to partition a data set into c classes. A series of subsets of the full data set are used for classification in order to provide an approximation to the final cluster centers. The quality of the final partitions is equivalent to that of fuzzy c-means. The speed-up is normally a factor of 2-3 times, which is especially significant for high dimensional spaces and large data sets. Clustering has been used to generate fuzzy rules for control. In this paper, we show that the multistage random sampling fuzzy c-means based clustering algorithm can be effectively used to create fuzzy rules in the domain of magnetic resonance images where over 60,000 patterns and 3 features or attributes are common. >

There is always much difficult in the MR image segmentation. Although fuzzy c-means(FCM) clustering algorithm has been widely used in the field of image segmentation study, some inherent deficiencies of this algorithm especially the high cost of computation made the algorithm to be difficult widely used in practice. A novel algorithm, based on kernel fuzzy c-means (KFCM) clustering algorithm and the k-nearest neighbor (KNN) algorithm, is proposed to improve the performance of MR image segmentation. In this algorithm, the statistical gray level histogram of image is used in KFCM algorithm to speed up the algorithm. Furthermore, the spatial information of image is also considered by k-nearest neighbor algorithm based on kernel methods. With kernel methods each pixel of image is mapped into a high-dimensional feature space where FCM algorithm and KNN algorithm are carried out. Experiments show that the proposed algorithm is effective and efficient in image segmentation.

Possiblistic-Fuzzy C-Means Clustering Approach for the Segmentation of Satellite Images in HSL Color Space

In this paper, a new method is proposed to decrease sensitiveness to motion noise and uncertainty in magnetic resonance imaging (MRI) segmentation especially when only one brain image is available. The method is approached with considering spatial neighborhood information by fusing the information of pixels with their neighbors with Dempster–Shafer (DS) theory. The basic probability assignment (BPA) of each single hypothesis is obtained from the membership function of applying fuzzy c-means (FCM) clustering to the gray levels of the MRI. Then multiple hypotheses are generated according to the single hypothesis. Then we update the objective pixel’s BPA by fusing the BPA of the objective pixel and those of its neighbors to get the final result. Some examples in MRI segmentation are demonstrated at the end of the paper, in which our method is compared with some previous methods. The results show that the proposed method is more effective than other methods in motion-blurred MRI segmentation.

Unsupervised fuzzy methods are proposed for segmentation of 3D Magnetic Resonance images of the brain. Fuzzy c-means (FCM) has shown promising results for segmentation of single slices. FCM has been investigated for volume segmentations, both by combining results of single slices and by segmenting the full volume. Different strategies and initializations have been tried. In particular, two approaches have been used: (1) a method by which, iteratively, the furthest sample is split off to form a new cluster center, and (2) the traditional FCM in which the membership grade matrix is initialized in some way. Results have been compared with volume segmentations by k-means and with two supervised methods, k-nearest neighbors and region growing. Results of individual segmentations are presented as well as comparisons on the application of the different methods to a number of tumor patient data sets.

Abstract—This research presents an integrated framework for satellite image retrieval, segmentation, and visualization, utilizing Python-based algorithms and geospatial data processing methods. It incorporates Google Maps-based image acquisition, a Tkinter-powered interactive GUI, and the U-Net segmentation model to efficiently process satellite imagery. Satellite image segmentation, powered by U-Net, plays a vital role in geospatial analysis, enabling automated classification and extraction of key features from high-resolution imagery. The framework facilitates seamless high-resolution map generation, segmentation, and an- alytical visualization through interactive tools like bar graphs and pie charts. By leveraging U-Net’s robust architecture, this implementation enhances segmentation accuracy and supports applications in urban planning, environmental monitoring, and disaster management. Through the automation of retrieval, processing, and visualization of satellite imagery, this research advances geospatial intelligence and provides a scalable solution for efficient image segmentation workflows. Keywords—Satellite Image Segmentation, Land Cover Classi- fication, Remote Sensing, Image Processing, Semantic Segmen- tation, Deep Learning Models, Convolutional Neural Networks (CNNs), U-Net Architecture, Geospatial Analysis, Land Use Analysis

Use of a fuzzy granulation–degranulation criterion for assessing cluster validity

Automatic segmentation of Magnetic Resonance Images (MRI) for tissue classification becomes more challenging when the image is corrupted with noise and intensity non-uniformity (INU). Several fuzzy clustering based statistical retrospective methods exist for simultaneous correction and segmentation of images but most of them fail to be robust in presence of noise, outliers and INU artifacts. In this paper, a hybridization of rough c-means and spatial fuzzy c-means clustering is presented whose objective function has been modified to accommodate INU field as well. While the membership function of fuzzy sets enables efficient handling of overlapping partitions, the concept of lower and upper approximations of rough sets deals with uncertainty, vagueness, and incompleteness in class definition. The experiments conducted on brain MR images show promising results in terms of segmentation accuracy and class separability. The usefulness of proposed algorithm is also investigated on high field MR images. The proposed algorithm Rough-Theoretic Bias-Corrected Fuzzy C-Means Algorithm (R-BCFCM) has significant performance improvement over other similar methods from rough-fuzzy family and can be employed for MRI corrupted with high intensity non-uniformity and noise.

Surgical robots are gaining increasing popularity because of their capability to improve the precision of pedicle screw placement. However, current surgical robots rely on unimodal computed tomography (CT) images as baseline images, limiting their visualization to vertebral bone structures and excluding soft tissue structures such as intervertebral discs and nerves. This inherent limitation significantly restricts the applicability of surgical robots. To address this issue and further enhance the safety and accuracy of robot-assisted pedicle screw placement, this study will develop a software system for surgical robots based on multimodal image fusion. Such a system can extend the application range of surgical robots, such as surgical channel establishment, nerve decompression, and other related operations. Initially, imaging data of the patients included in the study are collected. Professional workstations are employed to establish, train, validate, and optimize algorithms for vertebral bone segmentation in CT and magnetic resonance (MR) images, intervertebral disc segmentation in MR images, nerve segmentation in MR images, and registration fusion of CT and MR images. Subsequently, a spine application model containing independent modules for vertebrae, intervertebral discs, and nerves is constructed, and a software system for surgical robots based on multimodal image fusion is designed. Finally, the software system is clinically validated. We will develop a software system based on multimodal image fusion for surgical robots, which can be applied to surgical access establishment, nerve decompression, and other operations not only for robot-assisted nail placement. The development of this software system is important. First, it can improve the accuracy of pedicle screw placement, percutaneous vertebroplasty, percutaneous kyphoplasty, and other surgeries. Second, it can reduce the number of fluoroscopies, shorten the operation time, and reduce surgical complications. In addition, it would be helpful to expand the application range of surgical robots by providing key imaging data for surgical robots to realize surgical channel establishment, nerve decompression, and other operations.

The region clustering of a magnetic resonance imaging (MRI) image is more complicate than a computed topography (CT) image because a MRI image composes of three components such as Tl -weighted, T2-weighted, and proton density (PD) in each layer. However, the MRI images provide more detail than the CT images. Therefore, we propose a technique of the region clustering of MRI image by using fuzzy c-means (PCM). The fuzzy c-means algorithm is an iterative operation, that is very time-consuming and makes the algorithm impractical for using in image segmentation. To cope with this problem, the discrete curve evolution (DCE) technique is applied to find the actual cluster center to refine the initial value of the fuzzy c-means algorithm, which reduces the convergence time. In experimental results, the proposed technique provides the same segmentation accuracy as the fuzzy c-means technique. Moreover, this technique takes lower computational time comparing to the previous method.

Segmentation of brain magnetic resonance imaging (MRI) data plays an important role in the computer-aided diagnosis and neuroscience research. Fuzzy c-means (FCM) clustering algorithm is one of the most usually used techniques for brain MRI image segmentation because of its fuzzy nature. However, the conventional FCM method fails to carry out segmentation well enough due to intensity inhomogeneity in MRI data. To overcome this issue, we propose an improved algorithm based on FCM clustering for segmentation of brain MRI data. Specifically, we modify the conventional FCM algorithm to allow for intensity inhomogeneity by introducing the regularization of the neighborhood influence and bias field. Results show that our proposed algorithm obtains reasonable segmentation of white matter (WM), gray matter (GM), and cerebrospinal fluid (CSF) from MRI data, which is superior to the expectation-maximization (EM) and conventional FCM methods.

Fuzzy c-means (FCM) is a popular clustering method for image segmentation. However, FCM has difficulties in handling artifacts in brain magnetic resonance imaging (MRI), especially when it comes to bias field and noise. We propose a novel multiple-surface-approximation-based FCM with interval membership method for simultaneous bias correction and segmentation of Brain MRI. First, multiple surface representation of bias field is embedded into FCM to estimate and correct bias field. Then memberships of the improved FCM are extended to intervals. After the extension, clustering centers of different MR brain tissues could be solved more properly by the proposed method. Moreover, the proposed method is less sensitive to noise by introducing effects of neighboring pixels. Experiments conducted on artificial images and synthetic and real clinical Brain MRI show that the proposed method is effective and obtains better results of both bias field correction and segmentation than comparing methods.

Image segmentation plays a preliminary and indispensable step in medical image processing. Image segmentation plays a crucial role in many medical imaging applications. In this paper, we present a novel algorithm called image Filtering spatial Kernel Fuzzy C-Means(FKFCM) for fuzzy segmentation of magnetic resonance imaging (MRI)data. The algorithm is realized by modifying the objective function in the conventional Fuzzy C-Means (FCM) algorithm using a kernel-induced distance metric, a spatial penalty on the membership functions and then using the image filtering method to correct the image. The algorithm results are compared with standard FCM, Kerneled Fuzzy C-Means (KFCM) and Spatial Fuzzy C-Means(SFCM). The performance of the proposed segmentation algorithm FKFCM provides satisfactory results compared with other algorithms.

Improved evidential fuzzy c-means method

Brain stroke is the major second leading cause of death for the people above the age of 60 and fifth leading cause in people aged 15–59. Automatic ischemic stroke lesion segmentation of Magnetic Resonance Images (MRI) is an important task since manual identification by medical experts is time-consuming. In this work, the Diffusion Weighted (DW) brain MR images of ISLES 2015 challenge dataset and Radiopaedia are pre-processed based on hybrid contrast enhancement and filtering technique. The skull is stripped by thresholding techniques along with mathematical morphology procedure. Later the identification of ischemic stroke lesion is performed by maximum entropy-based and Fuzzy C Means (FCM) thresholding. The segmented results are compared with expert’s ground truth and the performance is analyzed by means of similarity indices. It is observed that FCM performs better in identifying multiple and minute stroke lesion in MR images. There is nearly 98% close match between FCM segmented results and the ground truth scribed by the experts. Thus the proposed automated work flow helps in assisting the clinicians to identify the ischemic stroke lesion in DW modality of brain MR images.