Hanqiang Liu

A novel fuzzy clustering algorithm with non local adaptive spatial constraint for image segmentation

Generalized fuzzy c-means clustering algorithm with improved fuzzy partitions (GIFP_FCM) is a novel fuzzy clustering algorithm. However when GIFP_FCM is applied to image segmentation, it is sensitive to noise in the image because of ignoring the spatial information contained in the pixels. In order to solve this problem, a novel fuzzy clustering algorithm with non local adaptive spatial constraint (FCA_NLASC) is proposed in this paper. In the proposed method, a novel non local adaptive spatial constraint term is introduced to modify the objective function of GIFP_FCM. The characteristic of this technique is that the adaptive spatial parameter for each pixel is designed to make the non local spatial information of each pixel playing a different role in guiding the noisy image segmentation. Segmentation experiments on synthetic and real images, especially magnetic resonance (MR) images, are performed to assess the performance of an FCA_NLASC in comparison with GIFP_FCM and fuzzy c-means clustering algorithms with local spatial constraint. Experimental results show that the proposed method is robust to noise in the image and more effective than the comparative algorithms.

Spectral clustering with eigenvector selection based on entropy ranking

Ng-Jordan-Weiss (NJW) method is one of the most widely used spectral clustering algorithms. For a K clustering problem, this method partitions data using the largest K eigenvectors of the normalized affinity matrix derived from the dataset. It has been demonstrated that the spectral relaxation solution of K-way grouping is located on the subspace of the largest K eigenvectors. However, we find from a lot of experiments that the top K eigenvectors cannot always detect the structure of the data for real pattern recognition problems. So it is necessary to select eigenvectors for spectral clustering. We propose an eigenvector selection method based on entropy ranking for spectral clustering (ESBER). In this method, first all the eigenvectors are ranked according to their importance on clustering, and then a suitable eigenvector combination is obtained from the ranking list. In this paper, we propose two strategies to select eigenvectors in the ranking list of eigenvectors. One is directly adopting the first K eigenvectors in the ranking list. Different to the largest K eigenvectors of NJW method, these K eigenvectors are the most important eigenvectors among all the eigenvectors. The other eigenvector selection strategy is to search a suitable eigenvector combination among the first Km (Km>K) eigenvectors in the ranking list. The eigenvector combination obtained by this strategy can reflect the structure of the original data and lead to a satisfying spectral clustering result. Furthermore, we also present computational complexity reduction strategies for ESBER method to deal with large-scale datasets. We have performed experiments on UCI benchmark datasets, MNIST handwritten digits datasets, and Brodatz texture datasets, adopting NJW method for a baseline comparison. The experimental results show that ESBER method is more robust than NJW method. Especially, ESBER method with the latter eigenvector selection strategy can obtain satisfying clustering results in most cases.

Fuzzy c-means clustering with non local spatial information for noisy image segmentation

As an effective image segmentation method, the standard fuzzy c-means (FCM) clustering algorithm is very sensitive to noise in images. Several modified FCM algorithms, using local spatial information, can overcome this problem to some degree. However, when the noise level in the image is high, these algorithms still cannot obtain satisfactory segmentation performance. In this paper, we introduce a non local spatial constraint term into the objective function of FCM and propose a fuzzy cmeans clustering algorithm with non local spatial information (FCM_NLS). FCM_NLS can deal more effectively with the image noise and preserve geometrical edges in the image. Performance evaluation experiments on synthetic and real images, especially magnetic resonance (MR) images, show that FCM_NLS is more robust than both the standard FCM and the modified FCM algorithms using local spatial information for noisy image segmentation.

A multiobjective spatial fuzzy clustering algorithm for image segmentation

Multiobjective spatial fuzzy clustering for image segmentation is proposed.The non-local spatial information of an image is introduced into fitness functions.The final solution is chosen by a cluster index with non-local spatial information.The proposed method can automatically evolve the number of clusters.Experiments on noisy images demonstrate the superiority of the proposed method. This article describes a multiobjective spatial fuzzy clustering algorithm for image segmentation. To obtain satisfactory segmentation performance for noisy images, the proposed method introduces the non-local spatial information derived from the image into fitness functions which respectively consider the global fuzzy compactness and fuzzy separation among the clusters. After producing the set of non-dominated solutions, the final clustering solution is chosen by a cluster validity index utilizing the non-local spatial information. Moreover, to automatically evolve the number of clusters in the proposed method, a real-coded variable string length technique is used to encode the cluster centers in the chromosomes. The proposed method is applied to synthetic and real images contaminated by noise and compared with k-means, fuzzy c-means, two fuzzy c-means clustering algorithms with spatial information and a multiobjective variable string length genetic fuzzy clustering algorithm. The experimental results show that the proposed method behaves well in evolving the number of clusters and obtaining satisfactory performance on noisy image segmentation.

Non-local spatial spectral clustering for image segmentation

As one of widely used clustering algorithms, spectral clustering clusters data using the eigenvectors of the Laplacian matrix derived from a dataset and has been successfully applied to image segmentation. However, spectral clustering algorithms are sensitive to noise and other imaging artifacts because of not taking into account the spatial information of the pixels in the image. In this paper, a novel non-local spatial spectral clustering algorithm for image segmentation is presented. In the proposed method, the objective function of weighted kernel k-means algorithm is firstly modified by incorporating the non-local spatial constraint term. Then the equivalence between the objective functions of normalized cut and weighted kernel k-means with non-local spatial constraints is given and a novel non-local spatial matrix is constructed to replace the normalized Laplacian matrix. Finally, spectral clustering techniques are applied to this matrix to obtain the final segmentation result. The novel algorithm is performed on synthetic and real images, especially magnetic resonance (MR) images, and compared with the traditional spectral clustering algorithms and segmentation algorithms with spatial information. Experimental results demonstrate that the proposed algorithm is robust to noise in the image and obtains more effective performance than the comparison algorithms.

Fuzzy spectral clustering with robust spatial information for image segmentation

In recent years, spectral clustering has become one of the most popular clustering algorithms in areas of pattern analysis and recognition. This algorithm uses the eigenvalues and eigenvectors of a normalized similarity matrix to partition the data, and is simple to implement. However, when the image is corrupted by noise, spectral clustering cannot obtain satisfying segmentation performance. In order to overcome the noise sensitivity of the standard spectral clustering algorithm, a novel fuzzy spectral clustering algorithm with robust spatial information for image segmentation (FSC_RS) is proposed in this paper. Firstly, a non-local-weighted sum image of the original image is generated by utilizing the pixels with a similar configuration of each pixel. Then a robust gray-based fuzzy similarity measure is defined by using the fuzzy membership values among gray values in the new generated image. Thus, the similarity matrix obtained by this measure is only dependent on the number of the gray-levels and can be easily stored. Finally, the spectral graph partitioning method can be applied to this similarity matrix to group the gray values of the new generated image and then the corresponding pixels in the image are reclassified to obtain the final segmentation result. Some segmentation experiments on synthetic and real images show that the proposed method outperforms traditional spectral clustering methods and spatial fuzzy clustering in efficiency and robustness.

Spectral clustering with fuzzy similarity measure

Spectral clustering algorithms have been successfully used in the field of pattern recognition and computer vision. The widely used similarity measure for spectral clustering is Gaussian kernel function which measures the similarity between data points. However, it is difficult for spectral clustering to choose the suitable scaling parameter in Gaussian kernel similarity measure. In this paper, utilizing the prototypes and partition matrix obtained by fuzzy c-means clustering algorithm, we develop a fuzzy similarity measure for spectral clustering (FSSC). Furthermore, we introduce the K-nearest neighbor sparse strategy into FSSC and apply the sparse FSSC to texture image segmentation. In our experiments, we firstly perform some experiments on artificial data to verify the efficiency of the proposed fuzzy similarity measure. Then we analyze the parameters sensitivity of our method. Finally, we take self-tuning spectral clustering and Nystrom methods for baseline comparisons, and apply these three methods to the synthetic texture and remote sensing image segmentation. The experimental results show that the proposed method is significantly effective and stable.

Spectral Clustering with Eigenvector Selection based on Ensemble Ranking

Ng-Jordan-Weiss (NJW) method is one of the most widely used spectral clustering algorithms. For a clustering problem with K clusters, this method clusters data using the largest K eigenvectors of the normalized affinity matrix derived from the data set. However, the top K eigenvectors are not always the most important eigenvectors for clustering. In this paper, we propose an eigenvector selection method based on an ensemble of multiple eigenvector rankings (ESEER) for spectral clustering. In ESEER method, first multiple rankings of eigenvectors are obtained by using the entropy metric, which is used to measure the importance of each eigenvector, next the multiple eigenvector rankings are aggregated into a single consensus one, then the first K eigenvectors in the consensus ranking list are adopted as the selected eigenvectors. We have performed experiments on artificial data sets, standard data sets of UCI repository and handwritten digits from MNIST database. The experimental results show that ESEER method is more effective than NJW method in some cases.

Local manifold spectral clustering with FCM data condensation

In this paper, a novel local manifold spectral clustering with fuzzy c-means (FCM) data condensation is presented. Firstly, a multilayer FCM data condensation method is performed on the original data to contain a condensation subset. Secondly, the spectral clustering algorithm based on the local manifold distance measure is used to realize the classification of the condensation subset. Finally, the nearest neighbor method is adopted to obtain the clustering result of the original data. Compared with the standard spectral clustering algorithm, the novel method is more robust and has the advantages of effectively dealing with the large scale data. In our experiments, we first analyze the performances of multilayer FCM data condensation and local manifold distance measure, then apply our method to solve image segmentation and the large Brodatz texture images classification. The experimental results show that the method is effective and extensible, and especially the runtime of this method is acceptable.

Intuitionistic fuzzy set approach to multi-objective evolutionary clustering with multiple spatial information for image segmentation

Abstract Intuitionistic fuzzy set is a useful tool to handle the uncertainty in data. In order to deal with the uncertainty in an image and meanwhile overcome the sensitivity to image noise, a multi-objective evolutionary intuitionistic fuzzy clustering algorithm with multiple image spatial information (MOEIFC-MSI) is proposed to perform image segmentation in this paper. The important innovations of the method are listed as follows: (1) an intuitionistic fuzzy set of the image is first constructed by using a generalized fuzzy complement function; (2) this intuitionistic fuzzy set of the image is then utilized to compute fitness functions and a fuzzy evaluation index for selecting the optimal solution; (3) two kinds of complementary image spatial information are also introduced into the fitness functions and the fuzzy evaluation index to make the proposed method robust to image noise; (4) a real-coded variable string length technique is utilized to encode the cluster centers to automatically determine the number of clusters. Experimental results on synthetic, Berkeley and magnetic resonance (MR) images show that the proposed method outperforms state-of-the-art methods in noise robustness and segmentation performance.