Segmentation of SAR Images Based on MarkovRandom Field Model

Ousseini Lankoande, Majeed M. Hayat, and Balu SanthanamElectrical & Computer Engineering Department, MSC01

1100, 1 University of New Mexico, Albuquerque, NM 87131-0001{lankoande, hayat, bsanthan}@ece.unm.edu

Abstract – In synthetic-aperture-radar (SAR) imaging,large volumes of data are normally processed and trans-ported over airborne or space-based platforms. The de-velopment of fast and robust algorithms for processing andanalysis of this type of data is therefore of great importance.It has been demonstrated recently that a Markov-random-field (MRF) model, based on the statistical properties of co-herent imaging, provides an ideal framework to describe thespatial correlation within SAR imagery in the presence ofspeckle noise, which is present in all SAR imagery. Whencombined with Gibbs-energy-minimization techniques, theMRF-framework has also led to the development of effectiveand efficient speckle-reducing image restoration algorithms.In this work, the convexity of the Gibbs energy function forSAR imagery is established thereby facilitating the devel-opment of a novel image-segmentation algorithm for speck-led SAR imagery. The segmentation algorithm is too basedon minimizing the Gibbs energy function, which is attainedwithout the need for computationally intensive global opti-mization techniques such as simulated annealing. A com-parative experimental analysis, using real SAR imagery, ofthe proposed segmentation algorithm against a statistical-thresholding approach is undertaken showing the advantageof the proposed approach in the presence of the specklenoise. Notably, unlike the thresholding technique, the pro-posed algorithm can be applied to speckled imagery directlywithout the need for preprocessing the imagery for speckle-noise reduction.

Keywords: Segmentation, Markov random field, syntheticaperture radar, speckle noise.

1 IntroductionThe segmentation of remotely sensed images, such as syn-

thetic aperture radar (SAR) imagery, is a key component inthe automatic analysis and interpretation of data [1]. Varioussegmentation methods have been proposed in the literature.Some of the most common are the edge detection [2, 3, 4, 5],the region growing [6], and the thresholding [7] techniques.

However, these approaches have well-known flaws. For ex-ample, the edge detection technique is very much dependentupon the placement of the initial edge or even knowledgeof its position in advance [8]. The region-growing approachis also user-dependent when it comes to growing and merg-ing neighboring small regions [8, 9]. Moreover, segmenta-tion based on thresholding of grey levels is often inappro-priate for SAR images because of the presence of specklenoise [10], which is present in all SAR imagery, and it doesnot exploit the spatial dependency inherent in speckled SARimagery. Real SAR images are corrupted with an inherentsignal-dependent phenomenon named speckle noise. Thespeckle noise is grainy in appearance and primarily due tothe phase fluctuations of the electromagnetic return signals.

In order to address these issues, the Markov-random-field(MRF) method has been investigated [9, 11, 12]. However, itis well known that the MRF-based segmentation approachoffers a good performance (by minimizing the associatedGibbs energy function) when the underling Gibbs energyfunction is convex [13, 14]. Additionally, the convexity ofthe energy function guarantees the stability with respect tothe input [15, 16, 17] and makes the solution of the opti-mization problem less sensitive to changes in parameters.We have lately developed a MRF model [18, 19], based onthe statistical properties of coherent imaging [20], and shownthat it provides an ideal framework for capturing the spatialcorrelation within SAR imagery in the presence of specklenoise. We have also shown that by utilizing Gibbs-energy-minimization techniques, the MRF-framework can lead toeffective and efficient speckle-reduction algorithms. In thiswork we propose a novel MRF-based segmentation algo-rithm that exploits the convexity of the Gibbs energy functionproposed in [18, 19]. The efficacy of the proposed segmenta-tion algorithm is demonstrated using real SAR imagery andthe performance is compared to that offered by a statisticalthresholding approach [21].

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2005 IEEE International Conference on Systems, Man and CyberneticsWaikoloa, Hawaii October 10-12, 2005

2 Proposed segmentation approach2.1 The Markov-random-field model

In this section we revisit germane aspects of the pro-posed first-order MRF model for speckled images intro-duced in [18, 19, 22]. The MRF model is representedby an undirected graph, G = (V,E), that has undirectededges drawn as lines. The set V of vertices of the graph is{Ik, Ik1 , Ik2 , Ik3 , Ik4} and E is the set of edges. Two typesof cliques are defined for the first-order neighborhood shownin Figure 1(a) and Figure 1(b): the single-cliques and thepair-cliques, as seen in Figure 1(c).

Ik k1

k2

k3

Ik4

I

I I

(a) Graph form of the first-orderneighborhood.

Ik k1

k2

k3

Ik4

II I

(b) Lattice form of the first-orderneighborhood.

Single-clique

Two types of pair-cliques

(c) Cliques.

Figure 1: Neighborhood and cliques.

The conditional probability density function (cpdf) of theintensity Ikj

at point kj given the value of the intensity Ikiat

point ki is given by Goodman in [20]. In this work we havesubstituted the global mean, 〈I〉, by (it)kj

, which representsthe true intensity image at point kj . Within the MRF context,the cpdf of the intensity of the center pixel, ik, given the fourneighbors ik1 , ik2 , ik3 and ik4 is derived and it is given by:

pIk|Ik1···4

(ik|ik1···4) ∝ exp

{−

4∑j=1

ln[B(ik, ikj )

]

−4∑

j=1

{ A(ik, ikj )

B(ik, ikj )+ ln

(I0

[C(ik, ikj )

B(ik, ikj )

])}− 3 ln

[pIk

(ik)]}

,(1)

where A(ik, ikj ) = |αrkkj|2ikj + ik, B(ik, ikj ) = (it)k

× (1 − |αrkkj|2), and C(ik, ikj ) = 2

√ikikj |αrkkj

|.I0[·] is a modified Bessel function of the first kind and zero-th order, and αrkikj

and rkikjare, respectively, the coherence

factor [20] and the Euclidian distance between the points ki

and kj , and (it)kjis the true intensity at point kj . The cpdf

obtained in (1) has the form

pIk|Ik1···4

(ik|ik1···4) ∝ exp{−U(ik, ik1···4)}, (2)

where U(ik, ik1···4) = VC1(ik) + VC2(ik, ik1···4) (3)

and VC1(ik) = 3 ln[p

Ik(ik)

]; VC2(ik, ik1···4) =

4∑j=1

{A(ik, ikj)

B(ik, ikj)− ln

[I0

[C(ik, ikj)

B(ik, ikj)]]

+ ln[B(ik, ikj

)]}

.

Therefore, using the Hammersley-Clifford theorem [23], wederived the energy function or cost function of the MRF tobe U(ik, ik1···4). The terms VC1(ik) and VC2(ik, ik1···4) are,respectively, the single-clique and the pair-clique potentialfunctions. The energy function will be utilized in the seg-mentation process.

2.2 Segmentation algorithmThroughout this paper, we assumed the knowledge of the

number of classes N . After initialization of the parametersαrkikj

and N , the image to be segmented is scanned and eachpixel ik is replacing with the class that provides the highestcpdf, i.e.,

(ik)seg = arg maxik∈CL

pIk|Ik1···4

(ik|ik1···4), where (4)

CL = {CL1, · · ·, CLN} is the set of classes of the image.The maximization in (4) can be rewritten in the form of min-imizing the derived cost function U(ik, ik1···4) given in (3):

(ik)seg = arg minik∈CL

U(ik, ik1···4) (5)

The proposed energy function, unlike other cost functionsused in MRF-based segmentation techniques [9, 24, 25], isconvex. This property is straightforward to show using thecomposition rules of convex functions discussed in [13, 14].As a consequence, the minimization is reached without needfor a lengthy and computationally intensive processing suchas the simulated annealing [26].

The proposed segmentation algorithm is described entirelyby the flowchart shown in Figure 2 and can be summarizedas follows. The first step constitutes the initialization stagewhere the coherence parameter and the number of classes areset. The next step is the segmentation stage: For each pixelk, the intensity, ik, is run over all possible grey-level val-ues and the one that yields the highest cpdf (given its neigh-bors) is chosen. The class (in CL) corresponding to the cpdf-maximizing grey level is then assigned to the kth pixel. Thisprocess is repeated for all pixels k in the image.

3 Experimental resultsIn this section, the proposed segmentation described in

Section 2.2 is tested on real SAR images [27] and com-pared to the segmentation based-thresholding approach re-ported in [7, 21, 28]. One major difficulty in the thresholdingapproach is the choice of optimal thresholds. In this paperwe use a method that maximizes the inter-cluster variance.It is a statistical intensity-histogram-peak picking approach,whose aim is to determine from the histogram the thresh-olds that maximizes the distance between the peaks obtained

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STOP and return the Segmented image

Step 2: Segmentation stage

M x N=image size

Step 3:

k k+1

pIk|Ik1...4(ik|ik1...4)= exp{-U(ik, ik1...4)}

k > M x N ?no

yes

Step 1: Initialization stageSet αrkkj

and N= number of classes

k=1 (First pixel of the image)

Compute

(ik)seg=arg max pIk|Ik1...4(ik|ik1...4)

ik (ik)seg ,

ik CL ={CL1...CLN}, the classes's set

ik CL

Update each pixelwith the most probable class

Figure 2: Flowchart of the proposed segmentation algorithm.

from the histogram. It is entirely based on the data and noparameter is introduced [28]. Two real SAR images are usedfor the segmentation process [27], which we label by SAR-1 and SAR-2, respectively. We will test each segmentationapproach using the speckled SAR images as well as the de-noised SAR images in order to see their respectively sensi-tivity to the speckle noise.

In the absence of the true statistics of the true images cor-responding to the SAR images to be segmented (which isoften the case when dealing with real SAR images), the as-sessment of the quality of the segmentation is based on visualinspection of the segmented images.

Figures 3 and 5 present the three-class segmentation ofSAR-1 and SAR-2 using the thresholding and the proposedsegmentation approaches. Figures 3(b) and 5(b) clearly il-lustrate the poor segmentation results using the threshold-ing method in the presence of speckle noise. This failureis attributable to the fact that the thresholding segmentationapproach does not take into account the spatial correlationwithin the image, especially in the speckle component. Theresults are shown in Figures 3(c) and 5(c) showing the per-formance advantage offered by the proposed algorithm overthe thresholding technique.

In order to improve the segmentation process, one can pre-cede it with a speckle removal process. Various speckle re-

duction algorithms such as the modified-Lee, the enhanced-Frost and the gamma MAP filters [29] have been proposedin the literature. In this work we used a filtering approachbased on simulated annealing [18, 19]. The filtered versionof SAR-1 and SAR-2 are presented in Figures 4(a) and 6(a),respectively. The results obtained are obviously improved asseen in Figures 4 and 6. In Figure 6(a) on the right side ofthe image, we can see three trees. In the segmentation usingthe thresholding approach these tree are not differentiatedfrom the ground. However, for the proposed segmentationapproach shown in Figure 5(c), the differentiation is made.

The current version of the proposed segmentation al-gorithm is computationally less efficient compared to thethresolding approach. However, this issue can be resolved byusing a fast gradient-descent algorithm to yield the maximumcpdf. This is possible because the cost function, U(·, ik1···4),is convex (the proof of convexity is reported elsewhere).

4 ConclusionIn this paper we proposed a novel MRF-based segmenta-

tion algorithm for SAR images based on minimizing a pro-posed convex Gibbs energy function, which is derived fromthe statistical properties of speckle noise [18, 19, 20]. Exper-imental comparison of the proposed segmentation algorithmagainst a common thresholding segmentation technique il-lustrates two desirable features of the proposed approach.First, unlike the thresholding technique, the proposed algo-rithm can effectively segment noisy SAR images. The pro-posed algorithm can therefore be applied to speckled im-agery directly without the need for preprocessing the im-agery for speckle-noise reduction. Second, the proposed al-gorithm has the ability to differentiate various targets withinan image, which make the resulting segmentation more re-liable than the thresholding technique. An extension of thiswork will focus on having an unsupervised segmentation ap-proach.

The authors wish to thank Dr. Armin Doerry at SandiaNational Laboratories for providing the SAR imagery usedin this work.

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(a)

(b)

(c)Figure 3: (a) Noisy SAR-1. (b) Three-class segmentation ofthe noisy SAR-1 using the thresholding approach. (c) Three-class segmentation of the noisy SAR-1 using the proposedapproach.

(a)

(b)

(c)Figure 4: (a) Denoised SAR-1. (b) Three-class segmentationof the denoised SAR-1 using the thresholding approach. (c)Three-class segmentation of the denoised SAR-1 using theproposed approach.

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(a)

(b)

(c)Figure 5: (a) Noisy SAR-2. (b) Three-class segmentation ofthe noisy SAR-2 using the thresholding approach. (c) Three-class segmentation of the noisy SAR-2 using the proposedapproach.

(a)

(b)

(c)Figure 6: (a) Denoised SAR-2. (b) Three-class segmentationof the denoised SAR-2 using the thresholding approach. (c)Three-class segmentation of the denoised SAR-2 using theproposed approach.

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