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

[ACCESS RESTRICTED TO THE UNIVERSITY OF MISSOURI AT AUTHOR'S REQUEST.] The possibilistic c-means (PCM) was developed as an extension of the fuzzy c-means (FCM) clustering algorithm by abandoning the membership sum-to-one constraint. In the PCM, each cluster is independent of the other clusters and can be processed separately. Because of this separability, the sequential possibilistic one-mean (SP1M) was proposed to find clusters sequentially by running the possibilistic one-mean (P1M) c times. One critical problem in both PCM and SP1M is how to determine the parameter [subscript]. The sequential possibilistic one-mean with adaptive eta (SP1M-AE) was developed to allow [subscript] to change during iterations. In this thesis, a new dynamic adaptation mechanism for the parameter [subscript] in each cluster is inserted into SP1M. The resultant algorithm, called the sequential possibilistic one-mean with dynamic eta (SP1M-DE) is shown to provide superior performance over PCM, SP1M, and SP1M-AE in determining correct clustering results. In this thesis, the family of the SP1M clustering algorithm is also extended to combine local spatial information in an image. The resultant algorithm, called sequential possibilistic local information one-mean (SPLI1M) is shown to have a better performance on image segmentation over the fuzzy local information c-means (FLICM), the possibilistic local information c-means (PLICM), and the family of SP1M without combing local spatial information in image.

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.

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.

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.

An image segmentation method based on optimized spatial texture information is proposed in this article. Spatial information, including the relative position of neighbouring pixels and texture features of the multiscale neighbourhood, is incorporated into the similarity measure of the fuzzy c-means (FCM) clustering algorithm, in which the Gaussian kernel is adopted to diminish the local incorrect segmentation. The FCM clustering is spatially adjusted and optimized by the particle swarm optimization (PSO) algorithm. The purpose of optimization is to obtain the appropriate control parameters influencing spatial information, which can improve segmentation results. Experimental results demonstrate that the proposed method achieves better segmentation performance and is capable of effectively segmenting synthetic images and synthetic aperture radar (SAR) images.

Fuzzy c-means (FCM) clustering algorithm has been widely used in automated image segmentation. However, the standard FCM algorithm is sensitive to noise because of taking no into account the gray and spatial information of pixel. The paper proposes an improved FCM algorithm for image segmentation. We use the degree of gray similarity and distribution statistics of the neighbor pixels to form a new membership function for clustering. Not only it is effective to remove the noise spots and reduce the spurious blobs, but also it is ease to correct the misclassified pixels. Experimental results on three types of image indicate that the propose algorithm is more accurate and robust than the standard FCM algorithm

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.

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.

As fuzzy c-means clustering (FCM) algorithm is
\nsensitive to noise, local spatial information is often introduced
\nto an objective function to improve the robustness of the FCM
\nalgorithm for image segmentation. However, the introduction of
\nlocal spatial information often leads to a high computational
\ncomplexity, arising out of an iterative calculation of the distance
\nbetween pixels within local spatial neighbors and clustering
\ncenters. To address this issue, an improved FCM algorithm
\nbased on morphological reconstruction and membership filtering
\n(FRFCM) that is significantly faster and more robust than FCM,
\nis proposed in this paper. Firstly, the local spatial information
\nof images is incorporated into FRFCM by introducing morphological
\nreconstruction operation to guarantee noise-immunity
\nand image detail-preservation. Secondly, the modification of
\nmembership partition, based on the distance between pixels
\nwithin local spatial neighbors and clustering centers, is replaced
\nby local membership filtering that depends only on the spatial
\nneighbors of membership partition. Compared to state-of-theart
\nalgorithms, the proposed FRFCM algorithm is simpler and
\nsignificantly faster, since it is unnecessary to compute the distance
\nbetween pixels within local spatial neighbors and clustering
\ncenters. In addition, it is efficient for noisy image segmentation
\nbecause membership filtering are able to improve membership
\npartition matrix efficiently. Experiments performed on synthetic
\nand real-world images demonstrate that the proposed algorithm
\nnot only achieves better results, but also requires less time than
\nstate-of-the-art algorithms for image segmentation.

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.

PurposeMulti-view fuzzy clustering algorithms are not widely used in image segmentation, and many of these algorithms are lacking in robustness. The purpose of this paper is to investigate a new algorithm that can segment the image better and retain as much detailed information about the image as possible when segmenting noisy images.Design/methodology/approachThe authors present a novel multi-view fuzzy c-means (FCM) clustering algorithm that includes an automatic view-weight learning mechanism. Firstly, this algorithm introduces a view-weight factor that can automatically adjust the weight of different views, thereby allowing each view to obtain the best possible weight. Secondly, the algorithm incorporates a weighted fuzzy factor, which serves to obtain local spatial information and local grayscale information to preserve image details as much as possible. Finally, in order to weaken the effects of noise and outliers in image segmentation, this algorithm employs the kernel distance measure instead of the Euclidean distance.FindingsThe authors added different kinds of noise to images and conducted a large number of experimental tests. The results show that the proposed algorithm performs better and is more accurate than previous multi-view fuzzy clustering algorithms in solving the problem of noisy image segmentation.Originality/valueMost of the existing multi-view clustering algorithms are for multi-view datasets, and the multi-view fuzzy clustering algorithms are unable to eliminate noise points and outliers when dealing with noisy images. The algorithm proposed in this paper has stronger noise immunity and can better preserve the details of the original image.

Clustering documents enable the user to have a good overall view of the information contained in the documents. Most classical clustering algorithms assign each data to exactly one cluster, thus forming a crisp partition of the given data, but fuzzy clustering allows for degrees of membership, to which a data belongs to different clusters. In this system, documents are clustered by using fuzzy c-means (FCM) clustering algorithm. FCM clustering is one of well-know unsupervised clustering techniques. However FCM algorithm requires the user to pre-define the number of clusters and different values of clusters corresponds to different fuzzy partitions. So the validation of clustering result is needed. PBM index and F-measure are used for cluster validity.

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.

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.

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.