X-SAR SpotLigh Images Feature Selection andWater Segmentation

Bruno Cafaro, Silvia Canale, Fiora Pirri“Sapienza” Universita di Roma

Department of Computer, Control, and Management Engineering “A. Ruberti”Roma, Italy

{cafaro,canale,pirri}@dis.uniroma1.it

Abstract—In this paper we address the feature selectionproblem for X-SAR images and further the segmentation ofspecific chosen classes. After defining a suitable feature spacefor X-SAR images we select the most significant ones via asupervised machine learning approach: the 1-norm SVM. Theselected features will be used for segmentation purposes, in orderto segment water areas from the background. We shall see thatthe most relevant features are based on texture elements. Sothe segmentation is texture based and achieved with variationalcalculus and level set methods. The work is mainly focused onurban park X-SAR SpotLight images, where lakes and riversare often present. The images are collected with the COSMO-SkyMed satellites constellation, equipped with a SAR sensor.

I. INTRODUCTION

SAR images are quite new products of the remote sensingindustry, especially when they are taken in the X band (f = 8-12 GHz). The resulting X-SAR images, when acquired inthe SpotLight mode, show high spatial resolution. This asset,together with the high penetration of the X band, guaranteeingall weather and day/night operability, makes this remote sens-ing product very attractive for several applications: environ-mental monitoring, riverfloods control, change detection. Forall these applications an effective understanding of backscat-tering mechanism is still on-going, and some examples canbe found in:[1], [2], [3]. For all these applications a firststep is that of defining a suitable feature space for X-SARimages, see for example [25], [26], and references therein.The feature space is composed of five main feature classes:edge maps, localized frequency maps, bounded frequencymaps, local statistics and textural maps. Starting from thisset of feature classes defined on the input space a resultingoutput feature space with dimension n × 76 is obtained,where n is the size of the samples collected over at least10 X-SAR images taken with both HH or V V polarizationand looking angle in a range between 30 and 50 degrees.Following the non linear programming based feature selection,explored in [4] and [5], we define an algorithm for selecting,among the whole feature set, the most significant supportsfor SVM-classification. Further, using the information gainedthrough the feature selection process, we introduce a specificsegmentation algorithm targeting water.

The paper is organized as follows. In section II we summa-rize the main properties of the X-SAR images, with particularattention to COSMO-SkyMed products, and we describe the

feature space. In section III we present the SVM basedfeature selection procedure, and, in section IV, we discussthe discriminative power of the reduced feature space. Thesegmentation problem is addressed in section V. In section VIexperiments and results on the proposed method are reported.We conclude in section VII addressing some comparison withthe literature and some possible future issues.

II. X-SAR IMAGES AND FEATURE SPACE

In the lasts decades one of the most promising ImagingSystem that has been developed is the Synthetic ApertureRadar (SAR). Its sensor is based on the detection of thebackscattered radiation of a microwave signal projected bya moving antenna. By the platform motion, the simulation ofa “long enough” antenna, in the same moving direction of theplatform, is performed. Long enough in this case refers to thespatial resolution that one wants to obtain in the azimuthaldirection:

δx =D

Laf(1)

here D is the distance between source and target, f is thefrequency of the signal and La is the length of the antenna.From the previous equation follows that on a space platform,such as the Italian satellites constellation COSMO-SkyMed(D ' 600 Km), the spatial resolution can be very high,given that the microwaves domain is: 0.3 GHz < f < 300MHz. Microwaves are chosen for their high penetrationtrough clouds and atmosphere, in order to guarantee allweather and day night coverage. In this paper we deal withSpotLight images at X band, acquired with both HH or V V

Fig. 1. Speckle collected over Madrid.

978-1-4577-1775-8/12/$26.00 ©2012 IEEE

polarizations, and looking angle in a range between 30 and 50degrees. Resulting images cover a square area of about 100km2, and are made of more than 20000× 20000 pixels withintensity values given in 16bits. Products delivered from theCOSMO-SkyMed ground segment are treated with GammaMAP filtering [11], for speckle reduction.

The high spatial resolution of X-SAR images is crucial fromthe point of view of the possible applications: in principleobjects of less than one meter could be detected. Instead, alsofor the presence of speckle noise, the resulting images are ofdifficult interpretation even for the human eyes, when a detailis extracted from the whole image. Speckle is a noise-likeeffect responsible of the degradation of SAR images and ariseswhen different parts of the same signal interfere in constructiveor destructive way [6] (respectively white or black pixels). TheSAR sensor detects the signal backscattered from a surface,that is a function of surface roughness and of the remotelysensed object dielectric constant. This induces the appearanceof new textures; for example over buildings, due to reflection,a great amount of speckle is collected (Fig. 1).

In order to obtain a complete feature set for the X-SARimage we apply several transformation functions mapping theoriginal image into a set of features images. Indeed, a featureis a function fj(u, v) : I(u, v) → Fj(u, v) applied to animage to enhance some object’s property, and resulting in thefeature image Fj . As gathered above we have defined fivemain sets of features mapping: edge maps, local statistics,localized frequency, bounded frequency and textural maps,that captures the local orientation of the texture elements. Werefer the readers , for the specific feature map, to: steerablepyramids [7], edge detectors [8], textural features [9], wavelets[10], Gabor wavelets [12]. The feature set F , according to thefunctions fj , is summarized in Table I.

The resulting feature space, H , is of dimension n × 76.This is defined for different water textures, and each point of

Edge fj = I ⊗ k k various kernel: Simoncelli, j=1,. . .Maps Convolution Laplace, Sobel, Prewitt . . . ,13

Local Mean Sliding Window j=14,. . .Statistics Variance [5× 5], [15× 15] . . . ,17

Textural fj = Gσ ⊗∇I G Gaussian j=18,. . .Maps Convolution ∇I Gradient of image I . . . ,28

Bounded Wavelete 1-D Ricker, Haar j=29,. . .Frequency Decomposition Daubechies ’Db6’ . . . ,40

Localized fj = I ⊗Gb(θ, sf) Gabor Filters Bank j=41,. . .Frequency Convolution 0 < θ < 2π, sf = 1, . . . , 6 . . . ,76

TABLE ISUMMARIZATION OF FEATURES DESCRIPTORS USED.

Fig. 2. Pixels classification and projection on GoogleEarth.

the image, and its transformations in feature space, belongs toR76. In this way we can characterize the different behaviorsof the signal and of the interaction of adjacent parts ofthe associated regions with water. The feature space can beconsidered complete in the sense of the characteristics thatobjects can have in the images, and also with respect to theinvariance property of objects in the scene as it are collectedfor vertical, horizontal and diagonal directions and on differentscales of the image.

The feature space indicated in Table I, is different fromthe one presented in [21], leading to an early classificationof basic land covers (Figure 2). Indeed we are interestedin analyzing the discriminative power of a complete set offeatures, considering even textural ones and local statistics.The results obtained in [21], for the feature selection process,are here exploited: features with little discriminative power arediscarded in this work, whilst features with a greater discrim-inative power are here studied more in details, consideringothers or new values for the feature parameters.

Before using the feature space for feature selection the inputspace is rescaled in the hyperspace R76.

~Hn(j) = ~Hn(j)

√76

max(H)+ 1 (2)

III. FEATURE SELECTION

In supervised machine learning problems, following dis-criminative methods, it is apparent that increasing the numberof features a more precise classification should result. Thisis true in general if the feature specifying the problem aresomehow already known, but it is no more true when the goalis not yet classification but the definition of a set of featuredescriptors. Therefore a set of features F is optimal if byadding one or more features F ∪ {f1, . . .} its discriminativepower remains unchanged.

To this aim we train a discriminative model on the baseset of features described in section II and we evaluate the

discrimination capability of selected features when used torepresent data in a classification model. These two goals areachieved simultaneously by the discriminative based approachillustrated in this section.

In [5] the importance of the reduced feature space for SVMclassification is addressed, and it is shown that wheneverthe selection is correctly addressed, the discriminative powerwith a feature space composed of about one third of thefeatures is reduced only of the 5%. It is important to note thatthis information tells us only which are the most significantfeatures in terms of classification. Our approach is based on[5] and it amounts to resolve the following problem:

minw,b,ξ 1Tmξs.t. wTxi − b+ ξi ≥ 1 xi ∈ A

wTxi − b− ξi ≤ 1 xi ∈ B||w||1 ≤ sξ ≥ 0m

(3)

that is a 1−norm SVM binary classifier [13]. In the previousequation w ∈ Rn is a real vector, b ∈ < is a scalar, and are theparameters characterizing the family of all possible classifier:

x(h,w, b) = sgn(wTx− b) (4)

where equation (4) is derived from the definition of thehyperplane:

π(w, b) = {x ∈ Rn|wTx− b = 0} (5)

that is orthogonal to direction w/||W ||q , and has a distancefrom the origin |b|/||W ||q , where || · ||q is the dual norm to`p-norm used to measure the distance [4]. Equation (4) arisesif we assume that all points in the half-space, defined by thedirection of w, are labeled with 1 and points in the remaininghalf-space are labeled with −1.

The separating hyperplanes are infinite, the optimal separat-ing hyperplane π∗(w, b), and the associated best classifier, canbe defined with two main criteria: the minimum error separa-bility and the minimum complexity separability. For a moredetailed explanation we refer the reader to the papers: [14],[15]. Indeed we want to highlight, here, the peculiar propertiescharacterizing the 1-norm and the 2-norm. In equation (3) the1-norm is adopted. In this formulation of the SVM problemwe find the optimal separating hyperplane by minimizing theloss function: J(w) = ||W ||1 [16]. This is because when wedeal with sparse scenarios, the loss penalty J(w) = ||w||1works better in selecting few non zero values in vector w; theridge penalty: J(w) = ||w||22 prefers typically solutions withseveral non zero coefficients [17].

IV. REDUCED FEATURE SPACE

In this section we discuss the discriminative power of thereduced feature space, by varying the parameter s, the param-eter controlling the structural complexity of the classifier, inequation (3), and identifying the best joint feature. We solvedproblem (3) for the four specified features space definitions,each of one relative to a class of water basins, with valuesof the parameter s lying in the range 2n, n = 5, . . . , 13.

s Sea Rivers Lakes Basinsℵ(π∗) = 7 ℵ(π∗) = 9 ℵ(π∗) = 15 ℵ(π∗) = 7

32 TR = 8.8 TR = 3.96 TR = 0 TR = 0.01TEST = 11.7 TEST = 5.43 TEST = 0 TEST = 0.52ℵ(π∗) = 8 ℵ(π∗) = 12 ℵ(π∗) = 12 ℵ(π∗) = 9

64 TR = 4.22 TR = 2.38 TR = 0 TR = 0TEST = 7.52 TEST = 2.71 TEST = 0 TEST = 0.04ℵ(π∗) = 14 ℵ(π∗) = 15 ℵ(π∗) = 12 ℵ(π∗) = 4

128 TR = 1.63 TR = 1.33 TR = 0 TR = 0TEST = 3.49 TEST = 1.41 TEST = 0 TEST = 0.12ℵ(π∗) = 21 ℵ(π∗) = 22 ℵ(π∗) = 12 ℵ(π∗) = 5

256 TR = 0.6 TR = 0.67 TR = 0 TR = 0TEST = 2.24 TEST = 0.68 TEST = 0 TEST = 0.34ℵ(π∗) = 37 ℵ(π∗) = 29 ℵ(π∗) = 12 ℵ(π∗) = 7

512 TR = 0.03 TR = 0.11 TR = 0 TR = 0TEST = 0.35 TEST = 0.07 TEST = 0 TEST = 0.44ℵ(π∗) = 36 ℵ(π∗) = 47 ℵ(π∗) = 12 ℵ(π∗) = 5

1024 TR = 0 TR = 0 TR = 0 TR = 0TEST = 0.37 TEST = 0.02 TEST = 0 TEST = 0.42ℵ(π∗) = 35 ℵ(π∗) = 39 ℵ(π∗) = 12 ℵ(π∗) = 4

2048 TR = 0 TR = 0 TR = 0 TR = 0TEST = 0.5 TEST = 0 TEST = 0 TEST = 0.42ℵ(π∗) = 35 ℵ(π∗) = 39 ℵ(π∗) = 12 ℵ(π∗) = 4

4096 TR = 0 TR = 0 TR = 0 TR = 0TEST = 0.5 TEST = 0 TEST = 0 TEST = 0.41ℵ(π∗) = 35 ℵ(π∗) = 39 ℵ(π∗) = 12 ℵ(π∗) = 4

8192 TR = 0 TR = 0 TR = 0 TR = 0TEST = 0.5 TEST = 0 TEST = 0 TEST = 0.4

TABLE IIRESULTS OF PROBLEM (3) FOR VARYING THE PARAMETER s. ℵ(π∗) IS

THE CARDINALITY OF S; TR AND TEST ARE TRAINING AND TEST SETMISCLASSIFICATION ERRORS

Classification of points in a specified class with respect to theother three (binary classifier) is obtained. At the same time,the optimal solution yields the reduced feature set given bythe support S(π) of π(w, b) with respect to the base featureset.

In Table II we summarize the results: by varying theparameter s thus a reduced feature space, specific for eachof the four water textures, is obtained. The cardinality ℵ(π∗)must be of about 50% of the original set to give an accurateclassifier for seas and rivers. Lakes and artificial basins showto have a more stable behavior, with a reduced feature spacecardinality of about 15 − 20% with respect to the originalcardinality. Selecting the appropriate values for parameter swe have the four reduced feature space summarized in TableIII.

It is important to note that the feature selected come from all

s ℵ(π∗) LC Hj FP % FN %256 21 Sea H1, H2, H4, H6, H7, H10, H11, 2.23 2.26

H12, H15, H16, H17, H18, H19, H20,H21, H22, H24, H26, H41, H59, H67

128 15 Rivers H1, H2, H4, H11, H12, H14, H15, H16, 1.02 1.54H17, H18, H19, H22, H26, H29, H70

64 12 Lakes H1, H2, H3, H10, H12, H13, H16, 0 0H17, H18, H20, H24, H26

64 9 Basins H1, H2, H5, H11, H13, H16, 0.04 0.03H17, H18, H19

TABLE IIIREDUCED FEATURE SPACE.

Fig. 3. Water segmentation for a low resolution X-SAR image. A pixel represents an area of 10× 10 m2. In white the segmented area.

the five main groups depicted in section II, except frequencymaps. However the previous results shows that localizedfrequency maps are the ones with less discriminative power.The joint feature set is obtained from the intersection betweenthe four subsets of reduced features, namely:

ˆJFS = {Hj |Hj ∈ S(π∗)S ∩ S(π∗)R ∩ S(π∗)L ∩ S(π∗)B}.(6)

Here the subscript refers to one of the four water tex-ture feature space. The resulting reduced feature space is

ˆJFS = {H1, H2, H16, H17, H18}, and is composed of: twoedge maps, local statistics based on variance, and a singlefeature from the textural maps. H1 and H2 come from theedge maps, and are the derivative calculated with Simoncellikernels; H16 is a the textural map, and is built as in Table I.H17 and H18 come from the local statistics. The importanceof textural maps in discriminating water, among others landcovers, is clearly proved, and this is the reason why we applya textural segmentation to X-SAR images to enhance waterwith respect to land, that here turns out as a background ofthe image.

V. WATER SEGMENTATION

Given the joint features from the reduced feature space, wecan now use it to segment the X-SAR high resolution images,identifying water, as well lakes, oceans, rivers, etc.

Segmentation is a crucial step in image analysis and threemain techniques are in higher demand: snakes and balloons,region growing, and energy minimization. The main differ-ence relies on the fact that energy minimization is a globaltechniques as opposed to the other two that are locally based.Indeed, Mumford and Shah [18] approach consists of findingthe minimum of a functional built by combining the length ofthe boundary, the gradient of the image, and the differencebetween the image and a smoothed version of the sameimage. Brox in [19] extended Mumford and Shah algorithmto multiple region segmentation. With respect to other energybased models Brox one is hard, but much accurate thanother and it is quite advantageous when combined with othermethods. Zhu and Yuille [20] introduced a method calledregion competition, that is based on the minimization of afunctional. The boundary of the region moves in the directionwhere an energy decreasing is guaranteed and adjacent regions

are merged if the merging decrease the energy, too. Themethod that we use here for texture segmentation is basedon Zhu and Yuille approach, given the selected joint features.The functional to be minimized is:

E[Γ, {αk}] =M∑k=1

{µ2

∮∂Rk

ds+ . . .

· · · − logP ({I(u,v) : (u, v) ∈ Rk}|αk) + λ}(7)

where Γ is the curve defining the region boundary, and Rk thek-th region. In the first step values for the parameters αk, arefound by maximum likelihood, and in the second step, fixedthe parameters, the following equation is solved:

d~v

dt= −δE[Γ, {αk}]

δ~v(8)

where ~v = (u, v) is the position vector of the boundarypixels, on the discretized grid, defined over each of the featuremapping. Both steps cause a decrease in the energy function,but do not change the number of regions. A second step isadded to check if adjacent regions merging also causes theenergy function to decrease. If this is the case then regionsare merged. The equation corresponding to (8), in this case,is:

d~v

dt=

∑k∈Q(~v)

[−µ

2cκ(~v) + logP (I(~v)|ακ)

]~nκ(~v) (9)

In equation (9) there are two main contributions to the levelset evolution: the smoothing force, due to the curvature cκ(~v),and the statistical force, based only on the statistics of asingle pixel, fitted using parameters αk. Both forces pointalong the normal ~nκ(~v). Q(~v) = {k|~v lies on Γκ}. The ksubscript here refers to region k. Segmentation using thismodel unfortunately gives very poor results on X-SAR images;and to improve the accuracy we have to evaluate the statisticsof a pixel in a sliding window of r × r pixels. So in thestatistical force we have the logarithm of the joint probabilityof the pixels inside the window.

Furthermore we have to take into account also the informa-tion gained from the feature selection process. The final modelis based on vector level set using the features images induced

Fig. 4. Water segmentation for high resolution X-SAR images, using textural features and beta distribution. In white the segmented area.

by the application of the joint features, as presented in TableI. The velocity is given by:

d~v

dt=

∑(u,v)∈Q(~v)

−µ2cκ(~v) + log

∏(u,v)∈Wx,y

P ( ~X(~v)|~αk)

~nκ(~v)(10)

in our case ~X is in R2, and W(x,y) is the sliding window.We have considered different distributions and in general wenoticed that distributions in X-SAR feature maps are skewed.So in case of a Beta distribution, the means and variancesof X1 and X2 (µ and ν) can be obtained from the marginaldistribution (see [27]) as follows:

µ1k =a1k

a1k + c1k, ν1k =

a1kc1k(a1k + c1k)2(a1k + c1k + 1)

(11)

µ2k =b2k

b2k + c2k, ν2k =

b2kc2k(b2k + c2k)2(b2k + c2k + 1)

(12)where the subscript pk refers to p-th dimension and k-thregion.

Note that for initialization, namely for choosing the pointswhere the energy minimization starts, we use a non parametricdistribution, namely a Parzen window, and the mean shiftmethods that in the end exploits the histogram of the texturemaps to define an initial distribution.

VI. EXPERIMENTS AND RESULTS

Experimental test have been made on both low and highresolution X-SAR images. In our algorithm the first step issolved using the Maximum Likelihood Estimator, that causesan energy decrease; the second step, the level set motion, issolved using a WENO5 approximation for the solution ofthe Partial Differential Equation, that gives a good level ofaccuracy, even if the time required for convergence is relevant.

Some results of segmentation of low resolution images aregiven in Figure 3, where a good result is obtained withoutthe need of having to use the textural features, but only thewindows of r×r, with r = 9 is considered. The image is takenin V V polarization, with a looking angle of about 38 degrees,and represents Stanley Park in Vancouver. It was acquired

in SpotLight mode, but was rescaled to 110 to obtain a low

resolution image.Two results obtained for high resolution images, when

considering the textural features, on an area over Melbourne,are illustrated in Figure 4 and 5, where the X-SAR, thecorrespondent optical, and the segmented area are reported.The SpotLight images were acquired in March 2009, witha looking angle of about 33 degrees and V V polarization.Results are encouraging: for the image in Figure 4 we have1.6% of pixels not recognized as water (false negatives), and1% of pixels wrongly recognized as water (false positives); forthe image in Figure 5 we have 5.8% of pixels not recognized aswater (false negatives), and 1,6% of pixels wrongly recognizedas water (false positives). The comparison is made using amanually selected mask over the water area. To build thetextural feature image we first compute the derivative of theimage in both direction, so obtaining the image gradient: ∇I;and after we perform a convolution with a gaussian smoothingfilter having a dimension of 30 × 30, mean and variancerespectively 2 and 1.6.

VII. CONCLUSIONS

In this paper we adopted a segmentation method based onthe minimization of an energy functional, with an additionalstep for adjacent regions merging and proved that this methodis suitable for X-SAR images water segmentation. The analysiswas made using textural features, selected from a set offeature descriptors, via a 1-norm SVM classifier. The resultsdepicted in section IV showed that the textural feature builtstarting from the first order derivative of the image has a greatdiscriminative power, as it is present in the set coming fromthe intersection of all the features selected and characterizingthe water.

In our work the spatial resolution of the images is still lessthan one meter, with respect to other works. For examplein [22] water is extracted defining a set of Gray Level Co-occurrence Matrix (GLCM) based features; or in [24] theauthors achieve water segmentation by solving the classicallevel set evolution equation; or in [23] using a sequence of

Fig. 5. Water segmentation for high resolution X-SAR images, using textural features and beta distribution. In white the segmented area.

morphological operations. It runs out that our model is moresuitable for small artificial basins or riverfloods as well.

For future research the definition of an appropriate method-ology for the exploitation of reduced feature space, and ofits goodness, has still to be developed, but feature selectioncan be easily performed also among new defined featurespaces. Actually the main problem to be addressed for agood exploitation of X-SAR images is the derivation of arobust generative model for classification, based on new X-SAR tuned features descriptors. This work is a preliminarypart for this kind of research.

ACKNOWLEDGMENT

The work reported in this paper has been supported by ASIwithin the COSMO-SkyMed Announcement of Opportunity(DC-OST-2009-116), SARFIRE Project 2288.

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