Novel polarimetric SAR speckle filtering algorithm based on mean shift

Journal of Systems Engineering and Electronics

Vol. 24, No. 2, April 2013, pp.222-233

Novel polarimetric SAR speckle ltering algorithmbased on mean shift

Bo Pang*, Shiqi Xing, Yongzhen Li, and Xuesong Wang

School of Electronic Science and Engineering, National University of Defense Technology, Changsha 410073, China

Abstract: For better interpretation of synthetic aperture radar(SAR) images, the speckle ltering is an important issue. In thearea of speckle ltering, the proper averaging of samples withsimilar scattering characteristics is of great importance. However,existing ltering algorithms are either lack of a similarity judgmentof scattering characteristics or using only intensity information forsimilarity judgment. A novel polarimetric SAR (PolSAR) speckleltering algorithm based on the mean shift theory is proposed. As

polarimetric covariance matrices or coherency matrices form Rie-mannian manifold, the pixels with similar scattering characteristicsgather closely and those with different scattering characteristicsseparate in this hyperspace. By using the range-spatial joint meanshift theory in Riemannian manifold, the pixels chosen for avera-ging are ensured to be close not only in scattering characteristicsbut also in the spatial domain. German Aerospace Center (DLR)L-Band Experiment SAR (E-SAR) data and East China ResearchInstitute of Electronic Engineering (ECRIEE) PolSAR data areused to demonstrate the ef ciency of the proposed algorithm. Theltering results of two commonly used speckle ltering algorithms,

re ned Lee ltering algorithm and intensity driven adaptive neigh-borhood (IDAN) ltering algorithm, are also presented for thecomparison purpose. Experiment results show that the proposedspeckle ltering algorithm achieves a good performance in termsof speckle ltering, edge protection as well as polarimetric charac-teristics preservation.

Keywords: speckle, ltering, mean shift, polarimetric syntheticaperture radar (PolSAR).

DOI: 10.1109/JSEE.2013.00029

1. Introduction

As the coherent nature of synthetic aperture radar (SAR)systems, the polarimetric SAR (PolSAR) data are oftencontaminated by the speckle noise. The speckle seriouslyreduces the performance of PolSAR image interpretation,e.g., image segmentation [1], classi cation [2,3], snow

Manuscript received February 23, 2012.*Corresponding author.This work was supported by the National Natural Science Foundation

of China (61101180) and the China Postdoctoral Science Foundation(20110490088).

mapping [4], soil moisture estimation [5,6], polarimetricinterferometry [7]. Therefore, in order to obtain satisfac-tory results, the speckle ltering is essential for most ap-plications.

Without loss of generality, the basic objective of Pol-SAR speckle ltering is to suppress the noise level whilepreserving the structure and polarimetric information con-tained in PolSAR images. In principle, the PolSAR speckleltering should include as many neighboring pixels which

have similar scattering characteristics with the pixel to beltered in averaging as possible. However, the dif culty

lies in how to exclude those pixels with different scatteringcharacteristics while including a large number of pixels inthe ltering window. A similarity judging procedure maybe introduced to ensure no distortion of polarimetric infor-mation.

During the last decades, various PolSAR speckle lte-ring algorithms have been proposed. The commonly usedboxcar lter replaces the center pixel by the mean valueof pixels in a square ltering window. Clearly, it hasthe de ciency of indiscriminate averaging of neighboringpixels, both similar and dissimilar scattering characteris-tics, which will cause the corruption of scattering charac-teristics and the blur of edges between different regions. Inorder to overcome the shortcomings induced by the squarewindow, [8] introduced a re ned Lee PolSAR lter whichutilized eight directional windows to locate the most ho-mogeneous area inside the considered neighborhood. Un-fortunately, the re ned Lee ltering has some intractabledisadvantages. Firstly, a compromise should be made be-tween image smoothness and detail preservation. Largerwindows provide a better speckle smoothing effect butmay smear more details. Smaller windows provide moreimage texture preservation but the ltered image willbe less smoothed. Secondly, the x size of the direc-tional neighborhoods will induce artifacts in the vicin-ity of thin details, and the purely spatial ltering will re-sult in a “patchy” look [9]. In the intensity driven adap-

Bo Pang et al.: Novel polarimetric SAR speckle ltering algorithm based on mean shift 223

tive neighborhood (IDAN) ltering algorithm proposed by[9], a similarity judgment is taken into account. How-ever, the judgment was driven exclusively by the in-tensity information, the polarimetic information includedin polarimetric covariance matrices or coherency matri-ces is not suf ciently exploited. Recently, the wavelettransform was studied and used as a powerful tool forSAR speckle ltering [10–14]. The typical outcomes ofthe wavelet theory are the hard and soft thresholdingalgorithms, which were rstly proposed in [15]. How-ever, wavelet-based ltering algorithms usually cause se-vere visual artifacts like the ringing effect and Gibbseffect and are still dif cult to preserve original edgesand discontinuities [16]. Besides that, the wavelet-basedltering algorithm used for PolSAR data has not been

reported.

In 1975, the mean shift algorithm was proposed in[17]. Firstly, it is used as a method for clustering [18–20]. Since the mean shift algorithm has edge preservationproperty and requires no assumptions on the statistics, itis introduced later to adaptive smoothing [21], image seg-mentation [21] of optical images. This paper extends themean shift to PolSAR image speckle ltering and proposesa novel PolSAR speckle ltering algorithm based on it. Byusing the proposed algorithm, better smoothing, edge pre-serving and scattering characteristics protection results areacquired.

The remainder of this paper is organized as follows. InSection 2, the theory of mean shift is introduced. Section3 is dedicated to present how to represent the coherencymatrix which is a Hermitian positive de nite as Rieman-nian manifold and how to use the mean shift algorithmin Riemannian manifold. Depending on the above men-tioned work, the novel PolSAR speckle ltering methodbased on the mean shift algorithm is proposed. In Section4, the performance of the proposed speckle lter is demon-strated using the experiment SAR (E-SAR) data as well asthe East China Research Institute of Electronic Enginee-ring (ECRIEE) PolSAR data. The results are comparedwith those which are obtained by using the re ned Lee l-ter and IDAN lter, as they are usually considered as stan-dard references for evaluating the PolSAR speckle lter byradar community. Section 5 contains some conclusions andperspectives.

2. Mean shift algorithm

The mean shift algorithm is essentially an adaptive gradi-ent ascent algorithm for mode seeking (i.e., the local max-imum of the density estimator). Given a point x, it willconverge to some mode by calculating the mean shift vec-

tor in an iterative way.

2.1 Procedure of mean shift algorithm

The procedure of the mean shift algorithm can be summa-rized as follows.2.1.1 Probability density estimationThe rst step of the mean shift algorithm is to achieveprobability density estimation based on kernel density esti-mation methods. Given n data points xi (i = 1, 2, . . . , n)in d-dimensional space Rd, the kernel density estimatorwith kernel K(x) and d× d bandwidth matrix H is givenby

f(x) =1n

n∑i=1

KH (x− xi) (1)

whereKH (x) = |H |−1/2K(H−1/2x). (2)

Generally, the bandwidth matrix H is chosen as

H = diag(h21, . . . , h

2d) or H = h2I. (3)

If the latter is chosen, the only one parameter which shouldbe provided is the bandwidth parameter h. Then the densityestimation at point x based on the kernel function K(x)can be derived as

fh,K(x) =1

nhd

n∑i=1

K

(x− xi

h

). (4)

Usually, the kernel function is expressed in a radially sym-metric form, namely,

K(x) = ck,dk(‖x‖2) (5)

where k(‖x‖2) is called the pro le of the kernel K(x),and ck,d is the normalization coef cient. Thus the densityestimator in (4) can be written as

fh,K(x) =ck,d

nhd

n∑i=1

k

(∥∥∥∥x− xi

h

∥∥∥∥2)

. (6)

De ne g(‖x‖2) = −k′(‖x‖2), the kernel function corre-sponding to pro le g(‖x‖2) is

G(x) = cg,dg(‖x‖2) (7)

where cg,d is the normalization coef cient. The kernelK(x) is called the shadow of G(x) [18].2.1.2 Mean shift vector calculationAccording to the above de nition, the gradient of fh,K(x)can be expressed as

∇fh,K(x) =2ck,d

nhd+2

n∑i=1

(xi − x)g

(∥∥∥∥x− xi

h

∥∥∥∥2)

=

2ck,d

nhd+2

[n∑

i=1

g

(∥∥∥∥x− xi

h

∥∥∥∥2)]

︸︷︷︸part 1

.

224 Journal of Systems Engineering and Electronics Vol. 24, No. 2, April 2013⎡⎢⎢⎢⎢⎣

n∑i=1

xig

(∥∥∥∥x− xi

h

∥∥∥∥2)

n∑i=1

g

(∥∥∥∥x− xi

h

∥∥∥∥2) − x

⎤⎥⎥⎥⎥⎦

︸︷︷︸part 2

=

2ck,d

h2cg,dfh,G(x)︸︷︷︸

part 1

mh,G(x)︸︷︷︸part 2

. (8)

Clearly, the two parts of (8) have speci c meanings, re-spectively. The rst part is the density estimator based onkernel G(x) multiplying a constant. The second part iscalled the mean shift vector.

According to (8), the mean shift vector can be trans-formed as

mh,G(x) =12h2 cg,d

ck,d

∇fh,K(x)

fh,G(x)(9)

which shows that the mean shift vector is equal to thegradient of the density estimator based on kernel functionK(x) normalized by the density estimator based on kernelfunction G(x). It has the same direction as∇fh,K(x). Ini-tialize y0 = x and denote yj (j = 1, 2, . . .) as the succes-sive vector in iteration, then the mean shift vector can beexpressed as

yj+1 − yj = mh,G(yj) (10)

which shows that the mean shift vector also represents aniteration step size. From (9) and (10), it can be seen thatwhen the iteration is close to the mode (where the probabi-lity density is larger), the step size becomes smaller, whichwill bene t the mode seeking procedure. However, whenthe iteration is far from the mode (where the probabilitydensity is smaller), the step size becomes larger, which willspeed up the iteration. That is why the mean shift algorithmis also known as an adaptive gradient ascent algorithm formode seeking.2.1.3 Mode seeking iterationSubstituting yj by yj+1 until the difference between yj

and yj+1 is small enough or the iteration time exceedsgiven number, then the point y0 = x will converge to themode that it belongs to.

2.2 Kernel function selection

The quality of the density estimator is affected by thechoice of kernel. However, two commonly used kernelfunctions, Epanechnikov kernel and normal kernel, cansatisfy the need.

The pro le of Epanechnikov kernel is

kE(x) ={

1− x, 0 � x � 10, x > 1

(11)

which yields the Epanechnikov kernel as

KE(x) = ck,dkE(‖x‖2) ={

ck,d(1− ‖x‖2), ‖x‖ � 10, otherwise

(12)

where ck,d =12c−1d (d + 2) is the normalization coef cient

to ensure∫Rd

KE(x)dx = 1, and cd is the volume of the

unit d-dimensional sphere: c1 = 2, c2 = π, c3 = 4π/3,etc [19].

Based on the Epanechnikov kernel, the density estima-tor can be written as

f(x) =1

nhd

n∑i=1

KE

(x− xi

h

)=

ck,d

nhd

n∑i=1

kE

(∥∥∥∥x− xi

h

∥∥∥∥2)

. (13)

Its gradient has the form

∇f(x) =2ck,d

nhd+2

n∑i=1

(x− xi)k′E

(∥∥∥∥x− xi

h

∥∥∥∥2)

. (14)

Since k′E(x) can be expressed as

k′E(x) ={−1, 0 � x � 1

0, x > 1, (15)

∇f(x) becomes

∇f(x) =2ck,d

nhd+2

n∑i=1

(xi − x). (16)

For other kernels, the similar relation exists. For example,for the pro le

kN = exp(−1

2x

), x � 0, (17)

its corresponding kernel function is a normal kernel

KN (x) = (2π)−d/2 exp(−1

2‖x‖2

)=

ck,d exp(−1

2‖x‖2

)(18)

where ck,d = (2π)−d/2 is the normalization constant.The above representation shows that the pro le function

has the properties [18]:(i) Nonnegative,(ii) Nonincreasing: k(a) � k(b) if a < b,


(iii) Piecewise continuous and∫∞0

k(r)dr <∞.

From aforementioned properties of these pro le func-tions, it can be noted that the contribution of a pixel willdecrease as the distance between it and the pixel to be l-tered increases. This can help us to preserve the textureproperty of the image in speckle ltering.

3. PolSAR speckle ltering algorithmbased on mean shift

The PolSAR collects the complex scattering matrix of atarget with quad-polarizations. By using pauli basis and

assuming reciprocal backscattering, the obtained coherentscattering vector k can be expressed as

k =1√2[SHH + SVV, SHH − SVV, 2SHV]T (19)

where superscript “T” denotes the matrix transpose,the subscript “HV” in SHV represents the horizontal-transmitting and vertical-receiving radar response, the sub-scripts “HH” and “VV” have similar meanings. Anothercomplete representation of polarimetric information is thecoherency matrix.

T = kkH =

⎡⎣ T11 T12 T13

T21 T22 T23

T31 T32 T33

⎤⎦ =

⎡⎣ |SHH + SVV|2/2 (SHH + SVV)(SHH − SVV)∗/2 (SHH + SVV)S∗HV

(SHH − SVV)(SHH + SVV)∗/2 |SHH − SVV|2/2 (SHH − SVV)S∗HV

(SHH + SVV)∗SHV (SHH − SVV)∗SHV 2|SHV|2

⎤⎦ . (20)

where the superscript * denotes conjugation.Although the mean shift algorithm is a robust approach

to feature space analyses, it requires that the feature vec-tors lie in Euclidean space originally [18]. In [22], it wasproven that the complex covariance and coherency matri-ces form the non-Euclidean space. Therefore, in order touse the mean shift algorithm for PolSAR data, some ex-tensions have to be done. The procedure of extension issummarized in Fig. 1.

As mentioned in Fig. 1, on one hand, some extensions ofthe mean shift algorithm itself have been done. In [23,24],the mean shift algorithm was extended to be used in analy-tical manifold. On the other hand, Hermitian positive def-inite matrices such as the coherency matrices were provento form a Riemannian manifold step by step. Firstly, [25]demonstrated that real symmetric positive de nite matri-ces can be treated as tensor, and tensor space can be rep-resented as a Riemannian manifold. Based on this work,[26] further claimed that Hermitian positive de nite ma-trices can be represented as a Riemannian manifold. Fi-nally, similar to the treatment in [23], the mean shift algo-rithm can be used in the Riemannian manifold, so it can beused for processing PolSAR data. In the Riemannian mani-fold, pixels with similar scattering characteristics gathertogether and those with dissimilar scattering characteris-tics separate. Therefore, by using the range-spatial jointmean shift algorithm in Riemannian manifold, the simila-

rity judgment of scattering characteristics is accomplishedduring the speckle ltering.

Based on the aforementioned discussion, the PolSARdata space is denoted as a Riemannian manifold M , andits tangent space TX M is the plane tangent to the surfaceof the manifold at point X . According to the form of thekernel density estimator in Riemannian manifold, (6) canbe expressed as

fh,K(X) =ck,d

nhd

n∑i=1

k

(dist2(X, Xi)

h2

)(21)

where dist(X, Xi) is the Riemannian distance betweentwo tensors X and Xi. In the Riemannian manifold, thesquare of Riemannian distance dist(X, Y ) is de ned as[25]

dist2(X , Y ) = ‖y‖2X

= ‖logX

Y ‖2X

=

‖X− 12 log

XY X− 1

2 ‖2I

= ‖lnX− 12 Y X− 1

2 ‖22 (22)

where y = logX

Y = X12 ln(X− 1

2 Y X− 12 )X

12 denotes

logarithm map which maps the point Y ∈ M to the tan-gent vector y ∈ TX M , ‖ · ‖2 denotes the Euclidean norm,‖·‖X and ‖·‖I are respectively the norm de ned in tangentspaces TX M and TIM .

The gradient of (21) has the form

226 Journal of Systems Engineering and Electronics Vol. 24, No. 2, April 2013

The mean shift algorithm can onlybe used in Euclidean space [18].

In [23] and [24], the mean shiftalgorithm was extended to analytical manifold.

Hermitian positive definite matrices form non-Eulicean space [22].

Reference [25] demonstrated that real symmetric positive definite matrices can be treated as tensors, and tensors space is represented as a Riemannian manifold.

Reference [26] claimed that Hermitian positive definite matrices can be represented as a Riemannianmanifold.

Similar to the treatment in [23], the mean shiftalgorithm can be used in Riemannianmanifold, so it can be used for processingPolSAR data.

Fig. 1 Procedure of mean shift algorithm used for PolSAR data

∇fh,K(X) =ck,d

nhd

n∑i=1

k′(

dist2(X, Xi)h2

)∇dist2(X, Xi)h2

=

cg,d

nhd

n∑i=1

g

(dist2(X, Xi)

h2

)ck,d/h2

cg,d

n∑i=1

g

(dist2(X, Xi)

h2

)(−

n∑i=1

∇dist2(X , Xi)g(

dist2(X, Xi)h2

))=

fh,G(X)ck,d

h2cg,d

⎛⎜⎜⎜⎜⎝−

n∑i=1

∇dist2(X, Xi)g(

dist2(X, Xi)h2

)n∑

i=1

g

(dist2(X, Xi)

h2

)⎞⎟⎟⎟⎟⎠ . (23)

As de ned above, fh,G(X) is the kernel density estimatorbased on kernel G(x).

According to the de nition of the Riemannian distancein (22), it can be derived that [25]

∇dist2(X, Xi) = ∇‖xi‖2X = −2xi = −2 logX

Xi

(24)which indicates that∇dist2(X, Xi) is a tangent vector in

TX M . Substituting (24) into (23) yields

∇fh,K(X) =

fh,G(X)2ck,d

h2cg,d

⎛⎜⎜⎜⎜⎝

n∑i=1

xig

(dist2(X, Xi)

h2

)n∑

i=1

g

(dist2(X, Xi)

h2

)⎞⎟⎟⎟⎟⎠ . (25)


By comparing (8) with (25), the mean shift vector in Rie-mannian manifold has the form as

mh,G(X) =

n∑i=1

xig

(dist2(X, Xi)

h2

)n∑

i=1

g

(dist2(X, Xi)

h2

) . (26)

Usually, the joint spatial-range domain is considered,i.e., pixel coordinates are added into the feature vector. Atthis time, the joint mean shift vector should be expressedas [21]

mh,G(X) =n∑

i=1

xig

(dist2(Xr, Xri)

h2r

)g

(dist2(Xs, Xsi)

h2s

)n∑

i=1

g

(dist2(Xr, Xri)

h2r

)g

(dist2(Xs, Xsi)

h2s

)(27)

where Xs is the spatial part and Xr is the range part ofthe feature vector, hs and hr are the kernel bandwidthsused in the spatial part and range part, respectively. In thearea of image segmentation, the joint domain is often re-quired, because if only a range domain is considered, the

image will be over-segmented in area with the low gra-dient value [27]. Similarly, in the area of speckle ltering,the joint domain is also needed because we should ensurethe pixels included in averaging not only having the samescattering characteristics but also being close to the pixelto be ltered in the spatial domain (coordinate).

Based on the aforementioned derivation, how to use themean shift algorithm with PolSAR data, which forms aRiemannian manifold, is represented here. Firstly, usingthe minimal representation, the coherency matrix is rep-resented as a vector Y r, in which both intensity and fullpolarimetric information are included [25].

Y r = [T11,√

2T12, T22,√

2T13,√

2T23, T33]. (28)

When the joint spatial-range domain is considered, thefeature vector should be expressed as

Y = [Y s|Y r] = [x y|Y r] (29)

where Y s is the coordinate information (position) of thepixel.

Denote Y 1 as the start point of iteration and Y j (j =2, 3, . . .) as the successive kernel center. The iteration inthe Riemannian manifold can be expressed as

Y j+1 = expY j(mh,G(Y j)) = Y

12j exp(Y − 1

2j mh,G(Y j)Y

− 12

j )Y12j =

Y12j exp

⎛⎜⎜⎜⎜⎝

n∑i=1

(Y − 12

j xiY− 1

2j )g

(dist2(Y rj , Xri)

h2r

)g

(dist2(Y sj , Xsi)

h2s

)n∑

i=1

g

(dist2(Y rj , Xri)

h2r

)g

(dist2(Y sj , Xsi)

h2s

)⎞⎟⎟⎟⎟⎠Y

12j =

Y12j exp

⎛⎜⎜⎜⎜⎝

n∑i=1

log(Y − 12

j XiY− 1

2j )g

(dist2(Y rj, Xri)

h2r

)g

(dist2(Y sj , Xsi)

h2s

)n∑

i=1

g

(dist2(Y rj , Xri)

h2r

)g

(dist2(Y sj , Xsi)

h2s

)⎞⎟⎟⎟⎟⎠Y

12j (30)

where expX

(y) = X12 exp(X− 1

2 yX− 12 )X

12 denotes

the exponential map which maps the tangent vector y ∈TX M to the point Y ∈ M , and exp(·) is the matrixexponential. Nevertheless, it is different from the imagesegmentation that only one iteration for the mean shift al-gorithm is needed in the application of PolSAR speckleltering. Otherwise, all the pixels with similar scattering

characteristics will converge to the same mode (i.e., the lo-cal maximum of the density estimator), which will smearthe texture of the image.

4. Evaluation of algorithm

In this section, the ltering results of the proposed algo-rithm are represented. The corresponding ltering resultsof re ned Lee and IDAN speckle ltering algorithms arealso listed for comparison.

Firstly, ECRIEE PolSAR data are used for demonstra-tion. The optical image and the original PolSAR image areshown in Fig. 2 and Fig. 3(a), respectively. Some regions inFig. 3(a) are marked with red rectangles in order to demon-


strate the advantages of the proposed algorithm. In Region1, a blue strip can be seen, it corresponds to a road. Region2 includes the schoolyard and two rows of point scatterersaround it. According to the optical image, point scatterersprobably correspond to fencing and street lamps around theschoolyard. Region 3 is the teaching and living area of theschool, with dormitory, teaching building, auditorium andsome other buildings situating in it. Different ltering re-sults of this image are shown in Fig. 3(b) – Fig. 3(d) andare discussed hereinafter.

(i) Re ned Lee lterFig. 3(b) shows the ltering result obtained by the re-

ned Lee lter. The image after ltering has a “patchy”look and some details of the image are deteriorated. Forexample, some point scatterers in Regions 2 and 3 disap-pear or become much weaker in the ltered image.

(ii) IDAN lterFig. 3(c) shows the ltering result obtained by the IDAN

lter. Besides the “patchy” look and smearing of pointscatterers in Regions 2 and 3, corruption of scattering cha-

Fig. 2 Optical image of a school in Linshui, Hainan province, Chinafrom Google Earth

racteristics is also shown in IDAN ltering. In Region 1,the original blue strip which corresponds to the surfacescattering mechanism has become red which means di-hedral scattering after ltering. The deterioration of thescattering mechanism will mislead the interpretation of theSAR image, which is quite unacceptable.

(a) Original image (b) Refined Lee filter (7 7 window size)

(c) IDAN filter (50 50 window size) (d) Proposed algorithm with hr= 2.6, hs=15

I

I I

1

2

3

P1 P2

Fig. 3 Color-coded PolSAR image of a school in Linshui, Hainan province, China (737× 517 pixels) with Pauli basis, i.e., red is |HH−VV|,green is |HV|, and blue is |HH + VV|


(iii) Proposed lter

Fig. 3(d) shows the image ltered by the proposed algo-rithm. It is glad to see that the disadvantages of re ned Leeand IDAN ltering are overcome. Firstly, the ltered ima-ge is rather smoothed in homogeneous areas such as theschoolyard, and no “patchy” look can be seen. As a result,the two goals which are represented as two blue threadsin the schoolyard are highlighted in the ltered image. Se-condly, the details of the image, such as the point scatte-rers in Region 2 and Region 3, are well protected. Thirdly,while the speckle noise is ltered in the homogeneous re-gions such as the schoolyard, the texture of the image isstill preserved. Therefore, it can be said that the image in-formation is well protected in images ltered by the pro-posed algorithm.

German Aerospace Center (DLR) L-band E-SAR dataare also used to demonstrate the superiority of the proposedalgorithm. From the optical image and the correspondingoriginal PolSAR image shown in Fig. 4 and Fig. 5(a) re-spectively, it can be seen that this test site includes someagriculture elds with different crops and some road across

them. From the ltering results in Fig. 5(b) – Fig. 5(d), itis undoubted that the proposed algorithm gives the mostsmoothed result. Meanwhile, the ltering result of Re-gion 1 in Fig. 5(a) argues that the edges of the image arewell preserved by using the proposed algorithm. However,edges in Region 1 are broadened and blurred by using re-ned Lee and IDAN lters.

Fig. 4 Optical image of the agriculture eld in OberpfaffenhofenTest Site Area, German

(a) Original image (b) Refined Lee filter (7 7 window size)

(c) IDAN filter (50 50 window size) (d) Proposed algorithm with hr= 2.6, hs=15

I

I I

1

Fig. 5 Color-coded PolSAR image of agriculture eld in Oberpfaffenhofen Test Site Area, German (401× 401 pixels) with Pauli basis, i.e.,red is |HH−VV|, green is |HV|, and blue is |HH + VV|


In addition to visual inspection, we try to evaluate theperformance of different speckle ltering algorithms quan-titatively in terms of equivalent number of looks (ENL) andedge preserving index (EPI).

ENL is used to evaluate the smoothing performance ofspeckle ltering methods. It is de ned as

ENL = μ2/σ2. (31)

ENL refers to the ratio of the square of mean value μ to thevariance σ2 of all pixels in homogeneous regions. Gene-rally, the higher the ENL, the better the homogeneous re-gion is smoothed.

EPI is used to evaluate the edge preserving performanceof speckle ltering methods. It is de ned as

EPI =∑√(ps(i, j)−ps(i+1, j))2+(ps(i, j)−ps(i, j+1))2∑√(p0(i, j)−p0(i+1, j))2+(p0(i, j)−p0(i, j+1))2

(32)EPI refers to the ratio of gradient between ltered andorigi-nal images, where (i, j) is the position of the edge pixel,ps and p0 are the pixel values of ltered and original ima-ges, respectively. Generally, the higher the EPI, the betterthe edge is preserved.

The ENL and EPI values are calculated in areas markedwith white rectangles in Fig. 3(d) and Fig. 5(d). Region Iin Fig. 3(d) is an area in the schoolyard, which is a ho-mogeneous region used for ENL calculation. Region II inFig. 3(d) is an area including part of the road in the upperpart of the image, which includes many edge points and issuitable for EPI calculation. Similarly, Region I in Fig. 5(d)is an area in the agriculture eld, which is a homogeneousregion suitable for ENL calculation. Region II in Fig. 5(d)is an area including part of the road in the lower part of theimage, which includes many edge points and is suitable forEPI calculation.

In Table 1, ENL and EPI are presented for differentspeckle ltering algorithms. As shown in Table 1, the pro-posed ltering algorithm has both the highest ENL and EPIvalues, which indicates the best speckle suppressing andedge preserving performance.

Table 1 Comparison of different speckle ltering methods in termsof ENL and EPI

E-SAR image ECRIEE SAR imageENL EPI ENL EPI

Original image 2.27 1 2.92 1Re ned Lee lter 9.18 1.97 11.27 1.26

IDAN lter 3.17 2.39 3.82 2.31Proposed algorithm 11.2 2.63 19.75 2.47

Fig. 6 and Fig. 7 show the edge detection results of theconstant false alarm rate (CFAR) edge detector proposedin [28]. It can be seen that edges are preserved better inimages ltered by the proposed algorithm (Fig. 6(c) andFig. 7(c)), in which the outline of the road, runway andbuildings are clean and continuous. Nevertheless, the edgedetection results of the image ltered by the re ned Leelter (Fig. 6(a) and Fig. 7(a)) show incontinuous the edges

(such as edges of schoolyard and runway) and the smearededges of point scatterers (such as the edges of point scat-terers around the schoolyard). The edge detection resultsof the image ltered by the IDAN lter (Fig. 6(b) andFig. 7(b)) show a noise like image. This is the demonstra-tion of the better edge preservation property of the pro-posed algorithm from another aspect.

From the above discussions, it can be concluded thatthe proposed algorithm has an outstanding performance inspeckle reduction and edge protection. Nevertheless, forthe speckle ltering of PolSAR images, another issue thatshould be concerned is whether the polarimetric scatteringcharacteristics of targets are preserved after ltering. Inorder to demonstrate the polarimetric scattering charac-teristics preserving ability of the proposed algorithm, two

(a) Refined Lee filter (b) IDAN filter (c) Proposed algorithm

Fig. 6 Edge detection results of E-SAR image using CFAR edge detector


(a) Refined Lee filter (b) IDAN filter (c) Proposed algorithm

Fig. 7 Edge detection results of ECRIEE PolSAR image using CFAR edge detector

strong point-like scatterers marked as P1 and P2 inFig. 3(a) are chosen. P1 is a blue point inside the school-yard, and P2 is a red point outside the schoolyard. Theo-retically, these strong scatterers should preserve their scat-tering characteristics after ltering.

Firstly, as the color of the PolSAR image is the di-rect representation of scattering characteristics, the quali-tative judgment can be done through observing the color ofthese scatterers. It can be seen that P1 and P2 retain blueand red in images ltered by the re ned Lee, IDAN andthe proposed algorithms, being the intuitive conviction ofthe polarimetic scattering characteristics preserving abilityof these ltering algorithms. Nevertheless, it seems that P1and P2 become weaker in images ltered by the re nedLee and IDAN lters. In this sense, we can say that theproposed algorithm outperforms the re ned Lee and IDANalgorithms. Secondly, in order to evaluate the performanceof different speckle ltering algorithms quantitatively, thepowerful tool for extracting polarimetric scattering charac-teristics — H/A/α decomposition [29] is used. Accordingto this theory, T 3 can be eigen-decomposed as

T 3 = U3ΣU−13 (33)

where Σ is a 3×3 diagonal matrix with eigenvalues λ1,λ2, λ3 of T 3 as its diagonal elements, U3 = [u1, u2, u3]is a 3×3 unitary matrix with u1, u2, u3, the three unitorthogonal eigenvectors. Usually, the eigenvector ui is pa-rameterized as

ui =

[cosαiejϕi, sin αi cosβiej(δi+ϕi), sin αi sin βiej(γi+ϕi)]T.

(34)

In this way, the dominant scattering characteristics canbe obtained as a mean unit target vector [30]

u0 = ejϕ[cos α, sin α cos βejδ, sin α sin βejγ ]T (35)

where

α =3∑

k=1

Pkαk, β =3∑

k=1

Pkβk

γ =3∑

k=1

Pkγk, δ =3∑

k=1

Pkδk (36)

Pk = λk/

3∑i=1

λi.

Hence, the dominant scattering characteristics are deter-mined by α, β, δ and γ. Nevertheless, as α is the only rollinvariance parameter among these four parameters, it is of-ten taken as the main parameter for identifying the domi-nant polarimetric scattering characteristics [31]. Ideally,the α value of strong scatterers should not exhibit signi -cant change after ltering. In this paper, the α values of P1and P2 are calculated and presented in Table 2. It can beseen that the image ltered by the proposed algorithm hasthe most proximal α value with the original image, whichdemonstrates the best polarimetric scattering characteris-tics preserving ability of the proposed algorithm quantita-tively.

Table 2 Comparison of different speckle ltering methods in termsof α value

P1 P2

Original image 0.116 2 0.918 2Re ned Lee 0.131 4 0.902 3

IDAN 0.125 9 0.906 4Proposed algorithm 0.108 1 0.922 4

There are two parameters hs and hr that should bechosen in the proposed speckle ltering algorithm. How-ever, they are not chosen simply by the trial-and-error pro-cedure, but chosen by the following instructions. Firstly,according to our experience, in order to acquire bettersmoothed images, the spatial width parameter hs shouldusually be set larger to include more pixels into averaging,


for example hs = 15 is used in our experiment. Mean-while, in order to preserve the sharp edge, the range widthparameter hr should not be too large to prevent avera-ging inhomogeneous pixels, for example hr = 2.6 is usedin our experiment. Secondly, if the initialized parametersare not suitable, there are some adjusting instructions tofollow. Generally, a further smoothed image could be ob-tained by increasing hr or hs. However, hr serves as thedominate parameter of these two parameters because hs isusually set as a large enough number to include as manyneighboring pixels as possible. Therefore, if some edgesare blurred in the ltered image, we should diminish hr

rst to exclude some inhomogeneous pixels from averag-ing. Likewise, if the ltered image is not enough smoothed,we should augment hr rst to include more pixels in aver-aging. Thirdly, the results of our experiments indicate thatfor two images with quite different characteristics (E-SARagriculture eld and ECRIEE SAR urban data), the opti-mal parameters are both chosen as hs = 15, hr = 2.6,which exhibits the robustness of the proposed speckle al-gorithm for parameter chosen.

5. Conclusions

Speckle ltering should use information from surroun-ding pixels that have similar scattering characteristics asthe pixel to be ltered. In this paper, a novel speckle lte-ring algorithm to PolSAR based on the mean shift al-gorithm is introduced. By considering the joint spatial-range domain in the mean shift algorithm, two demandsin speckle ltering are satis ed. The rst is to choose pix-els close to the pixel to be ltered. The second is that pixelsincluded in averaging should be similar in scattering char-acteristics. Afterward, the pixels which are close in jointdomains are selected for yielding the ltered values of po-larimetric coherency matrices.

The desirable characteristics of the proposed polarimet-ric speckle ltering algorithm are veri ed using DLR L-band E-SAR data and ECRIEE X-band PolSAR data. Thecriteria of comparison include speckle reduction capabi-lity, edge sharpness and preservation of scattering charac-teristics. The experimental results prove the effectivenessof the proposed algorithm. In images ltered by the pro-posed lter, the speckle noise is greatly reduced, while thecontours and ne details are preserved and the blurring ef-fect is avoided.

Acknowledgment

The author would like to thank European Space Agency(ESA) for providing L-band E-SAR data and ECRIEE forproviding X-band PolSAR data used in this paper.

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Biographies

Bo Pang was born in 1984. He received his B.E. andmaster degrees from the College of Electronic Sci-ence and Engineering, National University of De-fense Technology (NUDT), China, in 2007 and2009, respectively. He is currently a Ph.D. candidatein NUDT. His research interests are radar signal pro-cessing, synthetic aperture radar (SAR) image inter-pretation and SAR 3-dimensional imaging.E-mail: [email protected]

Shiqi Xing was born in 1984. He received hisB.E. degree in radar information processing from theCollege of Electronic Science and Engineering, Na-tional University of Defense Technology (NUDT),China, in 2006. He is currently a Ph.D. candidatein NUDT. His research interests are interferometricsynthetic aperture radar (InSAR), synthetic apertureradar (SAR) signal processing.E-mail: xingshiqi [email protected]

Yongzhen Li was born in 1977. He received hisB.E. and Ph.D. degrees from National University ofDefense Technology (NUDT) in 1999 and 2004, re-spectively. Currently, he is an associate professor inNUDT. His research interests are radar signal pro-cessing, radar polarimetry and target recognization.E-mail: [email protected]

Xuesong Wang was born in 1972. He received hisB.E. and Ph.D. degrees from the College of Elec-tronic Science and Engineering, National Universityof Defense Technology (NUDT), China, in 1994 and1999, respectively. Currently, he is a professor inNUDT. His research interests are radar signal pro-cessing, radar polarimetry and target recognition.E-mail: [email protected]

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Novel polarimetric SAR speckle filtering algorithm based on mean shift