IEEE GEOSCIENCE AND REMOTE SENSING LETTERS, VOL. 5, NO. 4, OCTOBER 2008 673 Unsupervised Classification of Hyperspectral-Image Data Using Fuzzy Approaches That Spatially Exploit Membership Relations Gökhan Bilgin, Student Member, IEEE, Sarp Ertürk, Member, IEEE, and Tülay Yıldırım, Member, IEEE Abstract—This letter presents unsupervised hyperspectral- image classification based on fuzzy-clustering algorithms that spa- tially exploit membership relations. Not only is the conventional fuzzy c-means approach used to demonstrate the advantage of using membership relations but also Gustafson–Kessel clustering, which uses an adaptive distance norm, is, for the first time, used for the segmentation of hyperspectral images. A novel approach to include spatial information in the segmentation process is achieved by making use of spatial relations of fuzzy-membership functions among neighbor pixels. Two- and three-dimensional Gaussian filtering of fuzzy-membership degrees is utilized for this purpose. A novel phase-correlation-based similarity measure is used to further enhance the performance of the proposed approach by taking spatial relations into account for pixels with similar spectral characteristics only. It is shown that the proposed approach pro- vides superior clustering performance for hyperspectral images. Index Terms—Fuzzy clustering, hyperspectral images, phase correlation, unsupervised classification, wavelet transform. I. I NTRODUCTION H YPERSPECTRAL imaging is an emerging technology in remote sensing. Hyperspectral-image data contain hun- dreds of contiguous narrow spectral bands from the visible to the infrared range of the electromagnetic spectrum [1]. Because of the high dimensionality of hyperspectral data, band selection and dimension reduction are important in hyperspectral-image processing. Many traditional feature- extraction and dimension-reduction techniques have been adapted in hyperspectral imaging, such as principal-component analysis [2] and independent-component analysis (ICA) [3]. Nonnegative matrix factorization which offers a decomposition solution for hyperspectral features was introduced in [4]. A projection-pursuit algorithm has been developed in [5], which enables more accurate estimation of feature-extraction parame- ters. In this letter, initially, linear wavelet feature extraction [6] which uses the 1-D discrete wavelet transform (DWT) for reducing dimensionality of hyperspectral data in the spectral domain for each pixel is utilized. Although, wavelet feature Manuscript received May 12, 2008. Current version published October 22, 2008. G. Bilgin and T. Yıldırım are with the Department of Electronics and Telecommunication Engineering, Yildiz Technical University, 34349 Istanbul, Turkey (e-mail: gokhanb@ce.yildiz.edu.tr; tulay@yildiz.edu.tr). S. Ertürk is with the Department of Electronics and Telecommunication Engineering, University of Kocaeli, 41040 Kocaeli, Turkey (e-mail: sarp@ ieee.org). Digital Object Identifier 10.1109/LGRS.2008.2002319 extraction is not a novelty introduced by this letter, it is utilized before the fuzzy-clustering approaches presented in this letter to reduce the computational complexity with a simple feature- extraction approach [7]. Unsupervised classification or clustering/segmentation of hyperspectral data enable easier analysis of the high- dimensional data. Automated clustering of hyperspectral im- ages based on histogram thresholding has been studied in [8]. A hyperspectral-image segmentation approach based on Gaussian mixture models has been presented in [9], and clustering of hyperspectral images using non-Gaussian mixture models is investigated in [10]. Hyperspectral-image segmentation using a multicomponent Markov chain model has been studied in [11]. Unsupervised hyperspectral-image segmentation using a neuro- fuzzy approach based on weighted incremental neural networks has been introduced in [12]. A new algorithm which is referred to as ICA mixture model has been developed in [13]. In particular, for hyperspectral images, fuzzy clustering of the data can be more realistic and convenient than hard clus- tering methods by the means of assigning a pixel to more than one cluster with a certain degree of membership. In this way, overlapping clusters can be obtained conveniently [14]. In this letter, it is aimed to segment hyperspectral images by applying fuzzy c-means (FCM) clustering as well as its extended version that is referred to as Gustafson–Kessel clustering (GKC). In the literature, spatial relations of spectral signatures of hyperspectral data have been investigated to improve the per- formance of segmentation using Markov random fields [15] and morphological image-processing approaches [16]. In this letter, a novel phase-correlation-based similarity measure is used to enhance the performance of fuzzy clustering by taking spatial relations into account for pixels with similar spectral characteristics only. Moreover, the utilization of 2-D and 3-D Gaussian filters to membership functions is demonstrated to enhance accuracy. II. UTILIZING FUZZY APPROACHES FOR HYPERSPECTRAL-I MAGE CLUSTERING In this letter, as a first step, the driving idea for using fuzzy- clustering approaches for hyperspectral data is the capability of obtaining fuzzy memberships; because in the feature space, there might be no sharp boundaries among clusters. In FCM and GKC, initially, the number of clusters (c) has to be determined for the n-dimensional hyperspectral data, such that 1 <c<N 1545-598X/$25.00 © 2008 IEEE Authorized licensed use limited to: ULAKBIM UASL - YILDIZ TEKNIK UNIVERSITESI. Downloaded on November 5, 2008 at 15:58 from IEEE Xplore. Restrictions apply.