Integration of synthetic aperture radar image segmentation method

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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
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IET Radar Sonar Navig., Vol. 1, No. 5, October 2007                                                                                          353