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Integration of synthetic aperture radar image segmentation method using Markov random ﬁeld on region adjacency graph G.-S. Xia, C. He and H. Sun Abstract: A novel approach to obtain precise segmentation of synthetic aperture radar (SAR) images using Markov random ﬁeld model on region adjacency graph (MRF-RAG) is presented. First, to form a RAG, the watershed algorithm is employed to obtain an initially over-segmented image. Then, a novel MRF is deﬁned over the RAG instead of pixels so that the erroneous segmen- tation caused by speckle in SAR images can be avoided and the number of conﬁgurations for the combinatorial optimisation can be reduced. Finally, a modiﬁcation method based on Gibbs sampler is proposed to correct edge errors, brought by the over-segmented algorithm, in the segmentations obtained by MRF-RAG. The experimental results both on simulated and real SAR images show that the proposed method can reduce the computational complexity greatly as well as increase the segmentation precision. 1 Introduction established on over-segmented regions, and then the regions are merged under the Markov context with some This paper addresses the problems of obtaining precise and measures on the tonal or texture characteristics. For fast segmentation of synthetic aperture radar (SAR) images instance, Saarinen [8] obtained the over-segmented and presents a novel approach by using Markov random regions of colour images using watershed algorithm and ﬁeld model on region adjacency graph (MRF-RAG). then merged the regions greedily by RAG processing Pixel-by-pixel MRF model-based method has been used according to some similarity; Sarkar et al. [6, 9] built successfully for image segmentation, by introducing RAG on the over-segmented optical satellite images, spatial information easily, in both supervised mode and deﬁned the region similarity on the input image and then unsupervised mode [1– 5]. However, there are two main used greedy method to merge the RAG under Markov problems in this method, when applied to SAR images. context; Tupin [11] applied RAG on optical images under First, because of the typical speckle signal of SAR Markov context and then fused this RAG with SAR image images, many erroneous pixels speckle the segmented to estimate an elevation model. Yu [12] used RAG to result, which reduces the segmentation precision. reﬁne and modify the polarimetric SAR image segmentation Secondly, the pixel-by-pixel MRF model-based approaches by merging the pre-segmented region greedily using polari- are themselves computationally intensive for the combina- metric statistics (e.g. Wishart model and the K distribution). torial optimisation to estimate the segmentation out of an In fact, in merging-based approaches, the algorithm is extremely large number of conﬁgurations [6]. simply a statistical region merging, and the merging To reduce the effects of the speckle signals in SAR threshold is selected experimentally, which is also a difﬁ- images, Yang has shown an approach based on region hier- cult problem. Otherwise, many of these methods are dealt archical model, recovering the erroneous segmentations with optical and multispectral images, and few can be caused by speckle using a special estimation scheme in the used for SAR images. In addition, the existing RAG-based hierarchical model [7]. However, when reducing the speck- methods usually adopt greedy approach (e.g. in [6, 8 – 10, les, it will also cause some over-smoothing. To conquer the 12]) to merge the regions, which result in local minimum drawback of the heavy computational burden, two different solution. kinds of approaches have been used. One of them uses multi- In this paper, we propose an integrated approach to resolution techniques [3, 4], which decompose the original reduce the computational complexity of the pixel-by-pixel image into an image pyramid, do segmentation process at MRF-based techniques and as well as improve the segmen- the coarsest resolution using MRF model-based method tation precision for SAR images. First, over-segmentations, and then propagate the segmentation at the coarsest resol- derived from watershed segmentation algorithm, as well as ution to the next-ﬁner one until the ﬁnest resolution is the original SAR images are taken as the inputs of the pro- reached. Another approach uses region-based techniques posed method to form a RAG. Then, a novel MRF is deﬁned [6, 8 – 11]: ﬁrst, a region adjacency graph (RAG) is on the RAG rather than on pixels, by which the resolution space of combinatorial optimisation problem is reduced, # The Institution of Engineering and Technology 2007 and so is the computational time. Moreover, Gamma distri- doi:10.1049/iet-rsn:20060128 bution for the marginal distribution of each class in the SAR Paper ﬁrst received 9th September and in revised form 19th November 2006 intensity image is employed. In this step, the local statistical The authors are with the Signal Processing Laboratory, Electronic Information characteristics of the regions are introduced and the energy School, Wuhan University, Wuhan 430079, Hubei, People’s Republic of China of the MRF model is computed. After that, the SAR image E-mail: guisong_xia@163.com; hc@eis.whu.edu.cn; hongsun@whu.edu.cn segmentation is an optimal labelling problem of the RAG 348 IET Radar Sonar Navig., 2007, 1, (5), pp. 348 –353 under the Bayesian framework. The criterion used for only if obtaining the optimal segmentation is maximum a posteriori (MAP) probability, and the simulated annealing (SA) algor- P(X ¼ x) . 0, 8x [ F ithm – a global energy minimisation method – is adopted to P(Xi ¼ xi jXj ¼ xj , 8Sj = Si ) solve the combinatorial optimisation problem. Moreover, a modiﬁcation method based on Gibbs sampler (MGS) is pro- ¼ P(Xi ¼ xi jXj ¼ xj , Sj [ N (Si )) (2) posed ﬁnally to correct the edge errors, brought by the initial over-segmented algorithm. With the Hamersley-Clifford equivalence theorem, the The remainder of the paper is organised as follows. In MRF can be represented by Gibbs distribution as Section 2, the framework of MRF over RAG is simply ( ) recalled. In Section 3, a novel MRF-RAG is deﬁned on 1 1 X SAR images in detail. Section 4 gives the modiﬁcation P(X ¼ x) ¼ exp{ À U (x)} ¼ exp À Vc (x) (3) Z Z method and the proposed segmentation scheme. Section 5 c[C presents and analyses the experimental results on simulated and real SAR images. Finally, Section 6 concludes the where Z is the normalisation constant of Gibbs distribution, C paper. is the deﬁned clique system of Si shown in Fig. 1b, U(x) is the energy function and Vc is the clique potential over clique c. The segmentation based on MRF-RAG deﬁnes and 2 MRF-RAG framework selects good likelihood term and clique function on the RAG and then takes an optimisation step to obtain the In this section, we recall the framework of the MRF model optimal segments. over RAG on the assumption that there is an over- segmented image. 3 MRF-RAG model deﬁnition on SAR image 2.1 Graph deﬁnition The segmentation approach based on MRF model is usually under the Bayesian framework. Here, it is assumed that at It is assumed that the image is initially over-segmented into each node Si , 1 i Q of the RAG there are ni obser- a set of Q disjoint regions, denoted by S¼ fS1 , S2 , . . . , SQg. vations on a variable Yi , describing the pixel grey in the A RAG of the over-segmented image is deﬁned as follows. region Si . Using the Baye’s rule, the posterior probability Each region corresponds to a node Si , 1 i Q of the graph distribution of X given Y is G. The relationship between two different regions is deﬁned P(Y ¼ yjX ¼ x)P(X ¼ x) by their adjacency as edges of the graph, denoted by E. P(X ¼ xjY ¼ y) ¼ (4) Then the graph G is G¼ (S, E). An example of RAG is P(Y ¼ y) shown in Fig. 1a, with the dashed line denoting the edges When the image is designed, P(Y ¼ y) is constant and (4) of the over-segmentation. can be written as 2.2 MRF model on RAG P(X ¼ xjY ¼ y) / P(Y ¼ yjX ¼ x)P(X ¼ x) (5) Let G ¼ (S, E) be the RAG. We deﬁne a neighbourhood The ﬁrst term in the right-hand-side of (5) is a likelihood term system on G denoted by N as N ¼ fN(Si): 1 i Qg, and the second one is a prior term, which can be called a where N(Si) is a set of regions in S which are neighbours regularisation term in MRF model. We will show below of Si . Let X ¼ fXi: 1 i Qg denote any family of how to deﬁne these two terms in the MRF-RAG model. random variable, representing the labels of the region Si in S. Each Xi is a discrete value variable taking value in 3.1 Likelihood term the discrete ﬁnite set L ¼ fl1 , l2 , . . . , lKg of labels, where K is the number of classes in the image. The likelihood term describes the probability of region Si Let F be the set of all conﬁgurations with its observation Yi at the given region label x. Due to the independent assumption of the pixels in a region, in F ¼ {x ¼ (x1 , x2 , . . . , xQ ): xi [ L, 1 i Q} (1) the view of probability theory, the conditional probability of Y given class label x should be written as a product and let the event fX1 ¼ x1 , . . . , XQ ¼ xQg abbreviated as fX ¼ xg represent a special conﬁguration in F. Then X is a Y Q YY Q MRF with respect to its neighbourhood system N if and P(Y ¼ yjX ¼ x) ﬃ P(Yi ¼ yi jX ¼ xi ) ﬃ i¼1 i¼1 v[Yi P(vjX ¼ xi ) (6) As Gamma distribution is a usual and effective distribution for SAR images, here also we adopt this distribution to describe the image model. So (6) can be rewritten as YY Q MM MÀ1 Mv P(Y ¼ yjX ¼ x) ﬃ v exp À (7) i¼1 v[Yi G(M)sM x sx Fig. 1 Example of RAG where sx is the parameter of the Gamma distribution of a RAG class label x, and M is the number of looks of the SAR b Neighbourhood and clique system of RAG image. IET Radar Sonar Navig., Vol. 1, No. 5, October 2007 349 3.2 Regularisation term So according to MAP criterion, the estimation of x given Y is Different regions in the over-segmented image should have b ¼ arg max P(X ¼ xjY ¼ y) X a rather similar characteristic to be merged to form an x optimal segmentation. This knowledge is introduced in ( XQ X the deﬁnition of the clique potential of the RAG. Here, in ¼ arg min {Ts(Si , Sj ) þ bi u(xSi , xSj )}: order to reduce the computational complexity, only the pair- x i¼1 Sj [N (Si ) wise cliques (shown in Fig. 1b) are considered. For each pair of adjacent regions Si and Sj , the pooled X ) Mv v variance is deﬁned as [13] þ log v þ À M log (13) v[Y sx sx ! i ni var{Si } þ nj var{Sj } 1 1 var{Si þ Sj } ¼ þ (8) ni þ nj À 2 ni nj 4 Segmentation scheme based on MRF model where varfSig, varfSjg and varfSi þ Sjg are the variances and ni and nj are the number of pixels in each region. Let Si be After deﬁning the MRF-RAG model on SAR images, we the mean of Si , then the normalised difference detail the proposed segmentation schemes in Sections 4.1– 4.3. .qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ t ; jS i À S j j var{Si þ Sj } (9) 4.1 Over-segmentation of the SAR image is a test statistic of the Student t test for ni 2 nj 2 2 degrees of freedom. By noting the t test value by Tt(Si , Sj), we deﬁne The over-segmentation algorithm used here is a modiﬁed the clique potential of the RAG as morphological watershed segmentation algorithm [14] using basin dynamic watershed transformation to segment Vc (xSi , xSj ) ¼ Tt(Si , Sj ) þ bi u(xSi , xSj ) (10) the SAR images. First, a statistical gradient of the SAR image, which can be viewed as a hilly area with many where u(i, t) ¼ 21 for t ¼ i, and u(i, t) ¼ 1 otherwise. xSi is basins, is obtained using the ratio of averages edge detector the label on region Si , and bi is the region size ratio par- [15] instead of the morphological edge detectors prior to ameter, deﬁned as bi ¼ nj =(ni þ nj ). watershed transformation. Then the watershed transform- The ﬁrst term of the clique potential in (10) describes the ation algorithm with a suitable basin dynamic threshold is similarity between two regions in the observation image and adopted to process the statistical gradient image to obtain the second term gives a prior similarity on the label image. segmentation of the SAR image. This approach has a Using (3), we write the prior term as good performance on SAR images, providing over- 8 9 segmentation with only some errors on edges. More detail 1 < X X Q = information on the watershed segmentation algorithm for P(X ¼ x) ¼ exp À Ts(Si , Sj ) þ bi u(xSi , xSj ) SAR image can be found in [14, 15]. An example of the Z : i¼1 S [N (S ) ; j i region edge of over-segmented image is shown in Fig. 3c. (11) After deﬁning the likelihood term and the regularisation 4.2 MRF-RAG-based segmentation term by (5), (7) and (11), we obtain the posterior distri- bution of x given S, as When the over-segmented image is obtained, together with the original SAR image, they form a RAG. As described in 1 Section 3, we deﬁne a MRF over the RAG of the over- P(X ¼ xjY ¼ y) / exp Z segmentation, using (6)– (12). Then, the MRF-RAG-based ( ( segmentation method is adopted to estimate the optimal XQ X n o À Ts(Si , Sj ) þ bi u(xSi , xSj ) conﬁguration X by (13). In this paper, we adopt the SA i¼1 Sj [N (Si ) algorithm, a global method for combinatorial optimisation, to minimise the second term in (12). Compared with some X )) Mv v local optimisation method, the SA algorithm can converge þ log v þ À M log (12) to the global minimal solutions and provide a good v[Yi sx sx estimation. Table 1: Segmentation accuracy (%) for different classes of the simulated image in Fig. 3 by different methods Class 1 Class 2 Class 3 Class 4 Class 5 Methods Pixel Rag RagM Pixel Rag RagM Pixel Rag RagM Pixel Rag RagM Pixel Rag RagM Class 1 98.68 92.71 99.99 1.23 0 0.01 0.09 4.58 0 0 0.94 0 0 1.77 0 Class 2 2.48 0 0.04 95.89 95.54 99.73 1.36 1.87 0.20 0.21 1.73 0.04 0.07 0.86 0 Class 3 0.23 1.06 0.01 2.26 0.53 0.16 93.79 96.71 99.27 2.66 1.33 0.44 1.05 0.37 0.11 Class 4 0.02 0.19 0 0.57 0.23 0.04 3.48 0.94 0.45 92.05 98.36 99.25 3.89 0.28 0.26 Class 5 0.01 0.43 0 0.12 0.19 0.02 1.86 0.34 0.07 3.19 0.37 0.31 94.82 98.66 99.60 Error rate Pixel-by-pixel MRF: 5.45 MRF-RAG: 3.35 MRF-RAG þMGS: 0.43 Pixel ¼ traditional pixel-by-pixel MRF model method; Rag ¼ the proposed MRF-RAG model-based method before MGS; RagM ¼ the proposed MRF-RAG model-based method after MGS 350 IET Radar Sonar Navig., Vol. 1, No. 5, October 2007 4.3 Modiﬁcation based on Gibbs sampler By deﬁning a MRF-RAG model for the SAR image, we can obtain a good segmentation only through the MRF-RAG-based segmentation method (the segmentation performances on simulated image are shown in Table 1). The initial segmentation is crucial, since if there are some errors in the initial over-segmentation, these errors cannot be corrected during the MRF-RAG-based segmentation step. Actually, the modiﬁed watershed segmentation algor- ithm, the initial over-segment method adopted here, is very suitable in our case, because it usually causes over- segmentation but with few false segmentations except at the edges of the regions. To recover the erroneous segmen- tation at the edges of the regions, we propose a modiﬁcation approach MGS to modify the segmentation of the MRF-RAG-based method. Let bM be the ith modiﬁcation, and p(bM ) be the prior X (i) X (i) probability of X bM , which is a Gibbs distribution obtained (i) from Potts model over the second-order neighbourhoods. We obtain bM using MAP criterion as follows X (i) 8 > b, >X i¼0 > > > < (i) i=0 and bM isnot X (i) bM ¼ XM , b X (iþ1) edge pixel > > > > > argmax p Y jb(i) p b(i) , otherwise : XM XM X where p(Y jbM ) is the conditional distribution of Y given X (i) bM , which is also a Gamma distribution on SAR images. X (i) Here we use Gibbs sampler to implement the maximisation of the posterior probability in (14). It is known that the modiﬁcation step converged, if bM X (iþ1) has little difference with bM . Moreover, the modiﬁcation step will converge X (i) after a few iterations since a good estimation b is provided X by the MRF-RAG-based segmentation step. The ﬂowchart of the proposed segmentation scheme is shown in Fig. 2. 5 Experiments and analysis The proposed method is applied to a simulated SAR image and two real SAR images. In addition, we do some compari- son with the pixel-by-pixel MRF segmentation method on segmentation performance and computational complexity. Fig. 3a is a simulated three-dimensional SAR image with ﬁve classes and the mean reﬂectivities are [20 60 180 378 590]. Fig. 3b is a three-dimensional ERS-1/2 airborne SAR image, acquired from an agricultural crops scene in Fig. 3 Segmentations of the simulated and real SAR images a 256 Â 256 original images b 256 Â 256 original images c Edge map of the over segmentations obtained by the modiﬁed watershed algorithm d Edge map of the over segmentations obtained by the modiﬁed watershed algorithm e Proposed MRF-RAG model-based method before MGS f Proposed MRF-RAG model-based method before MGS g Proposed MRF-RAG model-based method after MGS h Proposed MRF-RAG model-based approach after MGS i Traditional pixel-by-pixel MRF model method j Traditional pixel-by-pixel MRF model method Parameters of the pixel-by-pixel MRF model method are 0.5 and 0.6 for the synthetic image and the real image, respectively; and 200 iter- ations of SA are taken to obtain the optimal segmentation for Fig. 2 Flowchart of the proposed segmentation scheme pixel-by-pixel MRF model method IET Radar Sonar Navig., Vol. 1, No. 5, October 2007 351 Fig. 4 Proposed MRF-RAG model and the traditional pixel-by-pixel model a 750 Â 1024 original images b Small cut of the original image (750 Â 1024) in the blue rectangle c Segmentations obtained by the proposed MRF-RAG model-based approach after MGS d Segmentations obtained by the proposed MRF-RAG model-based approach after MGS e Traditional pixel-by-pixel MRF model method f Traditional pixel-by-pixel MRF model method Parameters of the pixel-by-pixel MRF model method are 0.5 for the image 352 IET Radar Sonar Navig., Vol. 1, No. 5, October 2007 Table 2: Comparison of the computational time of label ﬁeld from the observed image data, involving deter- pixel-based MRF segmentation method and the mining a particular conﬁguration out of the conﬁgurations proposed MRF-RAG-based segmentation method with the size of L MÂN. However, in the MRF-RAG-based approach, if we over-segment the original image into Q Algorithm Pixel-based Proposed regions, the number of conﬁgurations will be L Q.). computational time MRF (h) method (min) In addition, as the MRG-RAG segmentation provides a good prior knowledge to the MGS, the MGS method Fig. 3a 3.5 12 implemented on the segmentation border can correct the Fig. 3b 3.1 10 edge errors, brought by the over-segmented algorithm, in Fig. 4 7.9 18 the segmentations obtained by MRF-RAG, and converges rapidly. Programming was done in Matlab and was run on Pentium-based personal computer (2.6 GHz) The experimental results both on simulated and real SAR images prove that the proposed method can reduce the com- putational complexity greatly as well as increase the seg- France (the SAR data are provided by ESA-CNES). Fig. 4a mentation precision. is a four-dimensional L-band polarimetric SAR image (HV channel), acquired from an agricultural land scene in Flevoland (The Netherlands) (the SAR data are provided 7 Acknowledgments by JPL). In order to implement the supervised segmentation, we select the training samplers from the original images, as The work is partially supported by the National Nature shown in Figs 3a, b and 4a. Science Foundation of China under projects Nos. In the modiﬁed watershed algorithm [14], the threshold 60372057 and 4037605. The author Gui-Song Xia would ﬁxes the rate of over- or under-segmentation. For different like to thank Yan-Li Guo for valuable discussion. The SAR images, a determinate algorithm for the threshold authors would like to thank the anonymous reviewers for selection does not exist and it is mainly selected experimen- good discussion and the ESA-CNES for providing SAR tally. In our experiment, to guarantee over-segmentation, images. the thresholds for watershed algorithm are 20 for Fig. 3a, 30 for Fig. 3b and 35 for Fig. 4a. Segmentations of the simulated SAR image (Fig. 3a) are 8 References shown in Fig. 3c, e, g and i. The detailed comparison on seg- mentation accuracy for different classes by two methods, 1 Geman, S., and Geman, D.: ‘Stochastic relaxation Gibbs distributions, pixel-by-pixel MRF-based method and the proposed inte- and the Bayesian restoration of images’, IEEE Trans. Pattern Anal. grated MRF-RAG-MGS-based approach, is shown in Mach. Intell., 1984, 6, (6), pp. 721–741 2 Manjunath, B.S., and Chellappa, R.: ‘Unsupervised texture Table 1. From Table 1, we can see that the proposed segmentation using Markov random ﬁelds’, IEEE Trans. Pattern method has better performances than the traditional Anal. Mach. Intell., 1991, 13, (5), pp. 478–482 pixel-by-pixel MRF-based method. 3 Krishnamachari, S., and Chellappa, R.: ‘Multiresolution Gauss– Segmentations of the real SAR images (Figs. 3a and Markov random ﬁeld models for texture segmentation’, IEEE Trans. Image Process., 1997, 6, (2), pp. 251– 267 Fig. 4a) are shown in Figs. 3d, f, h, j and Fig. 4, respectively. 4 Comer, M.L., and Delp, E.J.: ‘The EM/MPM algorithm for In addition, the computational time is shown in Table 2. segmentation of textured images: analysis and further experimental From Figs. 3, 4 and Table 1, we can see that the proposed results’, IEEE Trans. Image Process., 2000, 9, (10), pp. 1731–1744 segmentation algorithm with the MRF-RAG model pre- 5 Cao, Y., Sun, H., and Xu, X.: ‘An unsupervised segmentation method vents the block artefacts and reduces the effects of based on MPM for SAR images’, IEEE Geosci. Remote Sens. Lett., 2005, 2, (1), pp. 55–58 speckle, giving a precise segmentation. Moreover, after 6 Sarkar, A., Banerjee, A., Banerjee, N., Brahma, S., Kartikeyan, B., implementing the MGS, the segmentation precision Chakraborty, M., and Majumder, K.L.: ‘Land cover classiﬁcation in increases further. In contrast, the effects of speckle occur MRF context using Dempster-Shafer fusion for multisensor in the pixel-by-pixel MRF-based segmentation algorithm. imagery’, IEEE Trans. Image Process., 2005, 14, (5), pp. 634–645 In addition, Table 2 shows that with MRF-RAG-MGS 7 Yang, Y., Sun, H., and He, C.: ‘Supervised SAR image MPM segmentation based on region-based hierarchical model’, IEEE model, the computational time is reduced greatly. Geosci. Remote Sens. Lett., 2006, 3, (4), pp. 517– 521 Therefore we conclude that the proposed method has a 8 Saarinen, K.: ‘Color image segmentation by a watershed algorithm good segmentation performance for segmentation of homo- and region adjacency graph processing’. Proc. Int. Conf. on Image geneous zone scenes of SAR images, and can reduce the Processing, Austin, Texas, November 1994, pp. 1021– 1025 9 Sarkar, A., Biswas, M.K., and Sharmak, M.S.: ‘A simple unsupervised computational complexity greatly. MRF model based image segmentation approach’, IEEE Trans. Image Process., 2000, 9, (5), pp. 801–812 6 Conclusions 10 Kim, I.Y., and Yang, H.: ‘An integration scheme for image segmentation and labeling based on Markov random ﬁeld model’, A novel approach to obtain segmentation of SAR images IEEE Trans. Pattern Anal. Mach. Intell., 1996, 18, (1), pp. 69– 73 11 Tupin, F., and Roux, M.: ‘Markov random ﬁeld on region adjacency has been presented here based on the local statistical charac- graph for the fusion of SAR and optical data in radargrammetric teristics using MRF-RAG model and MGS. On one hand, by applications’, IEEE Trans. Geosci. Remote Sens., 2005, 43, (8), using good local statistical characteristics and suitable prior pp. 1920–1928 restrictions to form the region-based prior on the RAG, the 12 Yu, Y., and Acton, S.T.: ‘Polarimetric SAR image segmentation using texture partitioning and statistical analyses’. Proc. Int. Conf. on Image proposed method reduces the effects of speckle, thereby Processing, Vancouver, September 2000, pp. 677– 680 giving a precise segmentation. On the other hand, since 13 Oliver, C., and Quegan, S.: ‘Understanding synthetic aperture radar the MRF model is deﬁned on the RAG rather than on the images’ (Artech House, Boston, London, 1998), pp. 202– 205 pixels, the number of conﬁgurations used in combinatorial 14 Cao, Y.: ‘Study of the SAR image segmentation methods based on optimisation problem is reduced heavily and so is the com- watershed transformation and MRF models’, PhD thesis, Wuhan University, 2004 putational complexity (e.g. Let an image over M Â N lattice 15 Li, W., Benie, G.B., He, D.C., Wang, S.R., Ziou, D., and Gwyn, have L classes. Thus, under the pixel-by-pixel MRF frame- Q.H.J.: ‘Watershed-based hierarchical SAR image segmentation’, work, the segmentation goal is to estimate the hidden image Int. J. Remote Sens., 1999, 20, (17), pp. 3377–3390 IET Radar Sonar Navig., Vol. 1, No. 5, October 2007 353

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