Remote Sensing Classification Using Fuzzy C-means Clustering with Spatial Constraints Based on Markov Random Field

This paper proposes a new clustering algorithm which integrates Fuzzy C-means clustering with Markov random field (FCM). The density function of the first principal component which sufficiently reflects the class differences and is applied in determining of initial labels for FCM algorithm. Thus, the sensitivity to the random initial values can be avoided. Meanwhile, this algorithm takes into account the spatial correlation information of pixels. The experiments on the synthetic and QuickBird images show that the proposed method can achieve better classification accuracy and visual qualities than the general FCM algorithm. Keyword: Fuzzy c-means clustering, Markov random field, remote sensing classification, Kernel density function. Introduction Fuzzy C-Means clustering algorithm (FCM) was introduced by Ruspini [1969], developed by Dunn [1973], generalized by Bezdek [1981]. The FCM algorithm and its derivatives have been used successfully in many applications, such as pattern recognition, classification, data mining, and image segmentation. Compared with crisp or hard clustering methods [Pham et al., 1999] which force pixels to belong exclusively to one class, FCM is the fuzzy variant of K-means [Hartigan and Wong, 1979], which allows pixels to belong to multiple clusters with varying degrees of membership. Indeed, FCM is an improvement over K-means when the data set can not clearly subdivide into underlying partitions. Due to the iterative nature, it is very important for an FCM algorithm to choose a good set of initial cluster centers randomly. If a good set of initial cluster centers were chosen, the algorithm may take less iteration to find the actual cluster centers. The pixels on an image are highly correlated, i.e. the pixels in the HongLei et al. Fuzzy C-means clustering 306 immediate neighborhood possess nearly the same feature data. Therefore, the spatial relation of neighboring pixels is an important characteristic which can be of great aid in image classification. However, the standard FCM only considers the pixel’s spectral information, ignoring the spatial information in image context, which makes it very sensitive to noise, outliers, and other imaging artifacts. Recently, many researchers have proposed several modified techniques for the FCM algorithm in determining initial centers. Cheng et al. presented a multistage random sampling FCM algorithm to get initial cluster centers by using a series of the full data, which significantly reduced the computation time of partitioning a data set into C class [Cheng et al., 1996]. Hung et al. [2001] proposed a modified FCM called the partition simplification FCM in order to simplify the data set and find an initial candidate set of cluster as close as possible to the actual cluster centers. Kannan [2005] implemented the silhouette method based on cluster center initialization instead of random initialization to improve the segmentation efficiency of the FCM algorithm. Hiren et al. [2003] used the Fuzzy C-Medoids algorithm to select C representative cluster centers for FCM. Hou et al. [2005] inducted Genetic algorithm into FCM by using its searches and parallelism to solve the locality and the sensitivity of the initial condition of FCM. Kuang et al. [2006] proposed the Polynomial Fuzzy C-Mean (PFCM) based on the solving multinomial root to avoid selecting initial centers randomly. Yu et al. [2008] integrated Gustafson-Kessel and Gath-Geva algorithm into FCM to avoid falling into a local minimum. Yang et al. [2010] described a new strategy to determine the cluster number and initial cluster center according to the actual situation of intrusion detection data. Shamsi et al. [2011] developed a specific method by incorporating the spatial neighborhood information to calculate the initial cluster centers to improve the strength of the clusters. Megha et al. [2011] described a novel algorithm by incorporating distribution of the gray level information in the image and a new objective function which ensures better stability and compactness of clusters. To deal with the inhomogeneity problem, many algorithms have been proposed by adding correction steps before classifying the image or by modeling the image as the product of original image and a smooth varying multiplier field. Many researchers have incorporated spatial information into the original FCM algorithm to get better classification results. Tolias and Panas [1998a] proposed a fuzzy rule-based system to impose spatial continuity on FCM, and the other paper [Tolias and Panas, 1998b], they used a small positive constant to modify the membership of the center pixel in a 3×3 window. Pham et al. [1999] modified the objective function in the FCM algorithm to include a multiplier field containing the first-order and second-order information of the image. Similarly, Ahmed et al. [2000] proposed an algorithm to compensate for the intensity inhomogeneity and to label a pixel by considering its immediate neighborhood. Pham [2002] presented an approach to penalize the FCM objective function to constrain the behavior of the membership functions, similar to methods used in the regularization and Markov random field (MRF) theory [Li, 1995]. Chen et al. [2004] proposed a robust image segmentation using FCM with spatial constraints based on new kernelinduced distance measure. Lung et al. [2009] proposed a Generalized Spatial Fuzzy C-Means (GSFCM) algorithm that utilizes both given pixel attributes and the spatial local information which is weighted correspondingly to neighbor elements based on their distance attributes.