596 IEEE GEOSCIENCE AND REMOTE SENSING LETTERS, VOL. 4, NO. 4, OCTOBER 2007 A Rapid and Automatic MRF-Based Clustering Method for SAR Images Gui-Song Xia, Chu He, and Hong Sun, Member, IEEE Abstract—This letter presents a precise and rapid clustering method for synthetic aperture radar (SAR) images by embedding a Markov random field (MRF) model in the clustering space and using graph cuts (GCs) to search the optimal clusters for the data. The proposed method is optimal in the sense of maximum a posteriori (MAP). It automatically works in a two-loop way: an outer loop and an inner loop. The outer loop determines the cluster number using a pseudolikelihood information criterion based on MRF modeling, and the inner loop is designed in a “hard” mem- bership expectation–maximization (EM) style: in the E step, with fixed parameters, the optimal data clusters are rapidly searched under the criterion of MAP by the GC; and in the M step, the parameters are estimated using current data clusters as “hard” membership obtained in the E step. The two steps are iterated until the inner loop converges. Experiments on both simulated and real SAR images test the performance of the algorithm. Index Terms—Graph cuts (GCs), image clustering, Markov random field (MRF) model, synthetic aperture radar (SAR). I. I NTRODUCTION W ITH MORE and more synthetic aperture radar (SAR) sensors being used, the volume of SAR images rapidly increases. To effectively make use of these huge image data, fast and unsupervised image analysis algorithms will be very helpful and crucial. Motivated by these, this letter suggests a clustering method for SAR images, which rapidly and automat- ically works. Clustering is a widely used approach for data analysis in feature space and can be applied to image segmentation, where it is also named unsupervised image segmentation. However, due to the assumption that pixels are spatial independent in the image space, the classical clustering methods [e.g., K-means and fuzzy c-mean (FCM)] and their variations [1] fail on SAR images, which have very low “SNR” because of their typical speckle signals. A Markov random field (MRF) model provides an effec- tive technique to impose local spatial information. Unsuper- vised MRF (USMRF)-based segmentation methods combine Manuscript received December 6, 2006; revised March 7, 2007. This work was supported in part by the National Nature Science Foundation of China under Project 60372057 and Project 4037605 and in part by the Open Research Fund of the State Key Laboratory of Information Engineering in Surveying, Mapping and Remote Sensing. The authors are with the Signal Processing Laboratory, Department of Communication Engineering, Electronic Information School, Wuhan Univer- sity, Wuhan 430079, China (e-mail: gsxia.lhi@gmail.com; hc@eis.whu.edu.cn; hongsun@whu.edu.cn). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/LGRS.2007.903065 the local spatial information with the model-based cluster- ing approach [2]–[8] and can increase the segmentation pre- cision. However, the MRF-based methods always convert the segmentation problem to a combinational optimization task, which is computationally expensive, even by using some accelerating scheme [e.g., simulated annealing (SA)]. Thus, many MRF-based clustering methods are a tradeoff be- tween the accuracy and the computational complexity of the segmentation. Aiming at both improving the clustering accuracy and eas- ing the computational burdens, this letter suggests a cluster- ing method for SAR images by embedding an MRF model in the image space of the classical clustering methods, and using a recent multilevel graph cut (GC) [9]–[11] algorithm to effectively compute the optimal clusters for the data. The proposed algorithm works in a two-loop way: an outer loop and an inner loop. The outer loop determines the cluster number using a pseudolikelihood information criterion (PLIC) for MRF modeling. In addition, the inner loop is designed in a “hard” membership expectation–maximization (EM) style: in the E step, with fixed parameters, the optimal data clusters are rapidly searched under the criterion of maximum a posteriori (MAP) by the GC; and in the M step, the parameters are estimated using current data clusters obtained in the E step with “hard” cluster membership. The two steps are iterated until the two loops converge, respectively. To justify the efficiency of the proposed clustering approach, we compare it with traditional USMRF-based SAR image segmentation method and the clas- sical clustering method, i.e., K-means. The remainder of this letter is organized as follows. In Section II, the basics of the clustering criterion for SAR images are recalled and summarized. The multilevel GC algorithm is briefly described in Section III, and the proposed clustering method is presented in Section IV. In Section V, experimental results on real and simulated SAR images are presented and analyzed. Section VI gives our conclusion. II. CLUSTERING CRITERION FOR SAR I MAGES AND MRF In this section, first, with the assumption that the cluster number K is known, we recall the clustering criterion for SAR images. A SAR image on a rectangular pixel lattice S, contain- ing a set of pixels Y = {y s ,s ∈ S}, will be summarized into K clusters, with the kth cluster modeled by some parameter θ k . Thus, the entire set of clusters can be described by Θ= {θ k ,k =1, 2,...,K}, and every pixel y s will be assigned a cluster label x s ∈{1, 2,...,K}. Let X = {x s ,s ∈ S} denote the labeled image, and W =(X, Θ) denote a world state of the observed image Y . Therefore, the clustering is to pursue W , 1545-598X/$25.00 © 2007 IEEE Authorized licensed use limited to: IEEE Xplore. Downloaded on January 19, 2009 at 05:06 from IEEE Xplore. Restrictions apply.