Fuzzy-C-Means Clustering Based On The Gray And Spatial Feature For Image Segmentation

Accurate and robust image segmentation was identified as one of the most challenging issues facing PET quantification in oncological imaging. This difficulty is compounded by the low spatial resolution and high noise characteristics of PET images. The fuzzy C-means (FCM) clustering algorithm was largely used in various medical image segmentation approaches. However, the algorithm is sensitive to both noise and intensity heterogeneity since it does not take into account spatial contextual information. To overcome this limitation, a new fuzzy segmentation technique adapted to typical noisy and low resolution oncological PET data is proposed. PET images smoothed using a nonlinear anisotropic diffusion filter are added as a second input to the proposed FCM algorithm to incorporate spatial information (FCM-S). In addition, a methodology was developed to integrate the a trous wavelet transform in the standard FCM algorithm (FCM-SW) to allow handling of heterogeneous lesions' uptake. The algorithm was applied to the simulated data of the NCAT phantom, incorporating heterogeneous lesions in the lung and clinical PET/CT images of 21 patients presenting with histologically proven nonsmall-cell lung cancer (NSCLC) and 7 patients presenting with laryngeal squamous cell carcinoma (LSCC) to assess its performance for segmenting tumors with arbitrary size, shape, and tracer uptake. For NSCLC patients, the maximal tumor diameters measured from the macroscopic examination of the surgical specimen served as the ground truth for comparison with the maximum diameter estimated by the segmentation technique, whereas for LSCC patients, the 3D macroscopic tumor volume was considered as the ground truth for comparison with the corresponding PET-based volume. The proposed algorithm was also compared to the classical FCM segmentation technique. There is a good correlation (R2 = 0.942) between the actual maximal diameter of primary NSCLC tumors estimated using the proposed PET segmentation procedure and those measured from the macroscopic examination, and the regression line agreed well with the line of identity (slope = 1.08) for the group analysis of the clinical data. The standard FCM algorithm seems to underestimate actual maximal diameters of the clinical data, resulting in a mean error of -4.6 mm (relative error of -10.8 +/- 23.1%) for all data sets. The mean error of maximal diameter estimation was reduced to 0.1 mm (0.9 +/- 14.4%) using the proposed FCM-SW algorithm. Likewise, the mean relative error on the estimated volume for LSCC patients was reduced from 21.7 +/- 22.0% for FCM to 8.6 +/- 28.3% using the proposed FCM-SW technique. A novel unsupervised PET image segmentation technique that allows the quantification of lesions in the presence of heterogeneity of tracer uptake was developed and evaluated. The technique is being further refined and assessed in clinical setting to delineate treatment volumes for the purpose of PET-guided radiation therapy treatment planning but could find other applications in clinical oncology such as the assessment of response to treatment.

The clustering methods based on Fuzzy C-Means (FCM) are frequently used in image-segmentation. But the standard FCM algorithm has some defects, especially ignoring the pixel spatial information's influence on the classification result. For the sake of a more reasonable objective function, an improved FCM algorithm is proposed in this paper, which uses spatial information and S-function to determine the weight coefficients of the objective function. Experimental results show that the proposed algorithm has better performance than the standard FCM algorithm.

The fuzzy C-means (FCM) algorithm has got significant importance compared to other methods in medical image segmentation. In this paper, we propose a conditional spatial fuzzy C-means (csFCM) clustering algorithm to improve the robustness of the conventional FCM algorithm. This is achieved through the incorporation of conditioning effects imposed by some auxiliary variables and spatial information in the membership functions. By combining these two aspects, we are able to solve the problems of sensitivity to noisy data and inhomogeneity. The experimental results on several simulated and real-patient MRI brain images show that the csFCM method has superior performance on image segmentation than the FCM algorithm and some other FCM-based clustering algorithms.

Gold immunochromatographic strip (GICS) quantitative detective can provide more information than the qualitative or semiquantitative testing. In this paper, a fast color image segmentation method is presented to develop the quantitative detective of GICS. The image of GICS was acquired by Charge-coupled Device (CCD) image sensor, and segmented by fuzzy c-means (FCM) clustering algorithm based on color histogram in HSV color space. Maximin-distance algorithm was adopted to get the initial positions of centroids and cluster number to overcome the shortcoming that the FCM algorithm may produce local optimal results. For the segmented target image, a special characteristic parameter was constructed and calculated in HSV color space to achieve the quantitative interpretation of the GICS.

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.

Deep learning has been popular for a few years, and it shows great capability on unsupervised leaning of representation. Deep belief network consists of multi layers of restricted Boltzmann machine(RBM) and a deep auto-encoder, which uses a stack architecture learning feature layer by layer. The learning rule is that one deeper layer learns more complex representations, which are the high level features of the input data, from the representations learnt by the layer before. Fuzzy C-Means(FCM) is one of the most popular clustering algorithms, which allows one piece of data belong to several clusters. In this paper the authors propose a novel clustering model, and introduce a novel clustering technique(DBNOC) which combines deep belief network and fuzzy c-means. The main idea is that: first, it clusters with the high level representations learnt by stacked RBM to produce the initial cluster center, then it uses the fine-tune step including one center holding clustering algorithm and deep auto-encoder to optimize the cluster center and membership between input data and every cluster by cross iteration. The authors use FCM clustering algorithm to fulfill the model and do experiment on both low dimensional datasets and high dimensional datasets. The experiment results suggest that the proposed deep belief network oriented clustering method is better than the standard K-Means and FCM algorithm on the test datasets. Even on high dimensional datasets, the DBNOC clustering method show more generalization. What's more, the proposed model is suitable both in theoretical and practical.

Aiming at the problem that traditional fuzzy C-means (FCM) clustering algorithm is susceptible to noise in processing noisy images, a noisy image segmentation method based on FCM wavelet domain feature enhancement is proposed. Firstly, the noise image is decomposed by two-dimensional wavelet. Secondly, the edge enhancement of the approximate coefficient is carried out, and the artificial fish swarm (AFS) optimization algorithm is used to process the threshold value of the detail coefficient, and the processed coefficient is reconstructed by wavelet transform. Finally, the reconstructed image is segmented by FCM algorithm. Five typical gray-scale images are selected by adding Gaussian noise and Salt& pepper noise, respectively, and segmented by various methods. The peak signal-to-noise ratio (PSNR) and error rate (MR) of segmented images are used as performance indexes. Experimental results show that compared with traditional FCM clustering algorithm segmentation method, particle swarm optimization (PSO) segmentation method and other methods, the indexes of image segmentation by the proposed method is greatly improved. It can be seen that the proposed segmentation method retains the texture information of image edge well, and its anti-noise performance and segmentation performance are improved.

This paper presents a new technique for incorporating local membership information into the standard fuzzy C-means (FCM) clustering algorithm. In this technique, the objective consists of minimizing the classical FCM function with a unity fuzzifier exponent plus the Kullback-Leibler (KL) information distance acting as a fuzzification and regularization term. The KL distance is proposed to measure the proximity between cluster membership function of a pixel and an average of the cluster membership functions of immediate neighborhood pixels. Therefore, minimizing this KL distance biases the cluster membership of the pixel toward this smoothed membership function of the local neighborhoods. This can provide immunity against noise and results in clustered images with piecewise homogeneous regions. Results of clustering and segmentation of synthetic and real-world medical images are presented to compare the performance of the proposed local membership KL information based FCM (LMKLFCM) and the standard FCM, a local data information based FCM (LDFCM) and a type of local membership information based FCM (LMFCM) algorithms.

Fuzzy C-means (FCM) clustering algorithm tries to get the memberships of each sample to each Cluster by optimizing an objective function, and then assign each of the samples to an appropriate class. The Fuzzy C-means algorithm doesn’t fit for clusters with different sizes and different densities, and it is sensitive to noise and anomaly. We present two improved fuzzy c-means algorithms, Clusters-Independent Relative Density Weights based Fuzzy C-means (CIRDWFCM) and Clusters-Dependent Relative Density Weights based Fuzzy C-means (CDRDWFCM), according to the various roles of different samples in clustering. Several experiments of them are done on four datasets from UCI and UCR. Experimental results shows that this two presented algorithms can increase the similarity or decrease the iterations to some extent, and get better clustering results and improve the clustering quality.

In this study, the concepts of competitive agglomeration clustering algorithm is incorporated into fuzzy c-means (FCM) clustering algorithm for symbolic interval-values data. In the proposed approach, called as IFCMwUNC clustering algorithm, the problems of the unknown clusters number and the initialization of prototypes in the FCM clustering algorithm for symbolic interval-values data are overcome and discussed. Due to the competitive agglomeration clustering algorithm possess the advantages of the hierarchical clustering algorithm and the partitional clustering algorithm, IFCMwUNC clustering algorithm can be fast converges in a few iterations regardless of the initial number of clusters. Moreover, it is also converges to the same optimal partition regardless of its initialization. Experiments results show the merits and usefulness of IFCMwUNC clustering algorithm for the symbolic interval-values data.

The localization accuracy of a fingerprint-based localization system is dependent on several factors, one of which is the accuracy and efficiency at which the fingerprint database is clustered. Most highly efficient and accurate clustering algorithms have high time-dependent computational complexity (CC), which tends to limit their practical applicability. A technique that has yet to be explored is the sequential hybridization of multiple low-time CC clustering algorithms to produce a single moderate-time CC clustering algorithm with high localization accuracy. As a result, this paper proposes a clustering algorithm with a moderate time CC that is based on the sequential hybridization of the closest access point (CAP) and improved k-means clustering algorithms. The performance of the proposed sequential hybrid clustering algorithm is determined and compared to the modified affinity propagation clustering (m-APC), fuzzy c-mean (FCM), and 2-CAP algorithms presented in earlier research works using four experimentally generated and publicly available fingerprint databases. The performance metrics considered for the comparisons are the position root mean square error (RMSE) and clustering time based on big O notation. The simulation results show that the proposed sequential hybrid clustering algorithm has improved localization accuracy with position RMSEs of about 54%, 77%, and 52%, respectively, higher than those of the m-APC, FCM, and 2-CAP algorithms. In terms of clustering time, it is 99% and 79% faster than the m-APC and FCM algorithms, respectively, but 90% slower than the 2-CAP algorithm. The results have shown that it is possible to develop a clustering algorithm that has a moderate clustering time with very high localization accuracy through sequential hybridization of multiple clustering algorithms that have a low clustering time with poor localization accuracy. Doi: 10.28991/ESJ-2024-08-02-02 Full Text: PDF

Image segmentation plays an important role in machine vision, image recognition, and imaging applications. Based on the fuzzy c-means clustering algorithm, a kernel-distance-based intuitionistic fuzzy c-means clustering (KIFCM) algorithm is proposed. First, a fuzzy complement operator is used to generate the membership degree whereby the hesitation degree of intuitionistic fuzzy set is generated; second, a kernel-induced function is used to calculate the distance from each point to the cluster center instead of the Euclidean distance; third, a new objective function that includes the hesitation degree is established, and the optimization of the objective function results in new iterative expressions for the membership degree and the cluster center. The proposed KIFCM algorithm is compared with the fuzzy c-means clustering (FCM) algorithm, the kernel fuzzy c-means clustering (KFCM) algorithm, and the intuitionistic fuzzy c-means clustering (IFCM) algorithm in segmenting five images. The experimental results verify the effectiveness and superiority of our proposed KIFCM algorithm.

Dissolved gas analysis in transformer oil (DGA) is an important method for power transformer insulating diagnosis. Aiming at the problem that fuzzy C-means (FCM) clustering algorithm is likely to fall into local minimum point when being used for dissolved gas analysis, dynamic tunneling algorithm was introduced for its high global optimization performance. Then a FCM clustering algorithm was presented based on these two algorithms. On the basis of local minimum obtained by optimization searching of FCM algorithm, using dynamic tunneling process to search a lower energy valley, then the value was submitted to FCM algorithm for iterative optimization until global minimum point was found by repeating the process. Through the application of this algorithm for DGA in transformer oil, transformer fault diagnosis can be achieved. These tests for fault diagnosis of chromatography transformer oil and noise samples show that, the algorithm can cluster samples quickly and effectively and with high accuracy for diagnosis.

This paper presents a new modified fuzzy c-means (FCM) clustering algorithm that exploits bilateral symmetry information in image data. With the assumption of pixels that are located symmetrically tend to have similar intensity values; we compute the degree of symmetry for each pixel with respect to a global symmetry axis of the image. This information is integrated into the objective function of the standard FCM algorithm. Experimental results show the effectiveness of the approach. The method was further improved using neighbourhood information, and was compared with conventional fuzzy c-means algorithms.

Fast and robust fuzzy c-means clustering algorithms incorporating local information for image segmentation