Relevant polarimetric parameters for surface characterization using SAR data

Transcription

1 Relevant polarmetrc parameters for surface characterzaton usng SAR data INTRODUCTION S. Allan, L. Ferro-Faml, E. Potter Unversty of Rennes I.E.T.R, UMR CNRS 664, Image and Remote Sensng Group Campus de Beauleu - Bat.C, 63 Avenue Général Leclerc CS 745, 354 Rennes Cedex, France Emal: sophe.allan@unv-rennes.fr The am of ths paper s to present a new relevant polarmetrc parameter for surface characterzaton usng SAR data. Ths novel parameter shall be called Egenvalue Relatve Dfference (ERD) n the followng. The frst part of ths work ntroduces the Integral Equaton Model (IEM) n order to characterze the polarmetrc behavour of backscattered sgnals from rough surfaces. In a second step, from the Cloude/Potter Egenvector/value based Polarmetrc decomposton theorem, polarmetrc descrptors senstve to surface parameters are presented. The partcular case of the parameter called ansotropy s studed n depth. In order to take nto account the reflexon symmetry hypothess consdered for natural surfaces, a new polarmetrc parameter, the ERD, s presented and compared to ansotropy. A frst valdaton step of the ERD parameter s led on scatterometrc data. Measurements were acqured at EMSL, JRC laboratory (Italy), for a large set of roughness, frequency and ncdence angle. Contrary to the ansotropy, the new descrptor, ERD, s strctly monotonous wth respect to the surface roughness. In a second valdaton step, ERD and ansotropy are analysed and compared on a polarmetrc SAR dataset acqured by the German Aerospace Center (DLR) E-SAR sensor, at L-band, over the Allng test ste n Germany. POLARIMETRIC SCATTERING MODEL Sol descrpton Sol s manly characterzed by ts roughness and ts mosture. A stochastc surface s defned by ts correlaton functon, ϕ xx (x,y) and correlaton length, L c, ts heght probablty densty functon and standard devaton, σ. The surface spectrum, whch conssts the Fourer transform of the n th power of the correlaton functon, s requred by the IEM. By consderng the gaussan surface, the n th order surface spectrum takes the form: W n ( k, k ) x y σ πl = n c k exp The delectrc constant, ε, s drectly functon of the sol mosture content. x L c k 4n y L c () Integral Equaton Model In order to characterze natural surfaces, the IEM s employed n the followng to derve backscatterng coeffcents for co-polarzed and cross-polarzed channels formulated n []. Ths model s wdely used due to ts large valdty doman and snce t has been valdated on large sets of expermental data. The cross-polarzed nformaton s derved from the multple scatterng formulaton takng nto account the coherent SAR ntegraton process nsde each resoluton cell. Ths model satsfes the reflecton symmetry assumpton (the correlaton between co- and cross-polarzed channels s assumed to be zero). The IEM output s a functon of the radar angle, the radar frequency, the surface spectrum, the correlaton length, L c, the surface root mean square (rms) heght, σ, and the sol delectrc constant, ε. It s mportant to hghlght that the surface rms heght s generally consdered as the most mportant surface roughness characterstc [] [3]. A synoptc of the Integral Equaton Model s gven n Fg..

2 Surface Parameters W n, L c, σ, ε Radar Parameters f, θ Polarmetrc Integral Equaton Model Backscatterng Coeffcents σ, σ hhvv, σ,σ vvhh, σ hvhv Fg.. IEM scatterng model The dfferent backscatterng coeffcents are gathered nto a sngle matrx representaton under the form of a coherency matrx, T, defned as follow: wth A + RB A + IB T = A IB A RB () 4C A = σ B = σ C = σ hhvv hvhv Usng the IEM model, the coherency matrx has fve non-null elements. In what t follows, ths model wll be employed to analyse the ansotropy and the ERD polarmetrc parameters varatons and dependences. + σ EIGENVECTOR/VALUE BASED POLARIMETRIC DECOMPOSITION THEOREM By transformng the scatterng matrx S, n the monostatc case, nto the complex target vector k p, the coherency matrx T s defned as follows: k T = k P P wth k P = [ S HH + SVV S HH SVV S HV ]T (4) An egenvector/egenvalue based decomposton theorem presented n [4] allows to splt the dstrbuted matrx, T, nto a weghted sum of three orthogonal untary matrces gven by: (3) T = V Σ V 3 3 = = = λ v v = λ T (5) where V and Σ represent the dstrbuted target egenvector and egenvalue matrces respectvely. The untary egenvectors are parametersed usng four angular varables: v = [cosα,snα cos β jγ jδ T e,snα sn β e ] (6) A statstcal analyss of the decomposton s consdered then n order to extract the mean scatterng mechansm. The three man parameters of ths decomposton are: α, the ndcator of the mean scatterng mechansm, entropy, H, whch ndcates the random behavour of the global scatterng and the ansotropy, A, whch represents the relatve mportance of the secondary mechansms. The followng study concentrates on the analyss of the later parameter.

3 From the ordered egenvalues n terms of sze, the ansotropy s defned as: λ λ 3 A = wth < λ + λ3 Ths parameter s usually used as a surface roughness descrptor [3]. EIGENVALUE RELATIVE DIFFERENCE Reflexon Symmetry < A (7) As t has been observed wth the IEM, n the case of a natural sol, the correlaton between co- and cross-polarzed channels s often neglected, ths phenomenon corresponds to the reflecton symmetry case hypothess. It s then possble to derve, from the coherency matrx T presented n (), the analytcal expressons of the egenvalues. The lteral expressons of the Non-Ordered n Sze ( nos ) egenvalues are [5]: wth λ λ λ nos nos 3nos = = = 4σ ( σ + σ ) + f ( σ, σ ) ( σ + σ ) f ( σ, σ ) hvhv (8) f ( σ, σ ) ( σ + σ ) + 4ρ hhvvσ σ = (9) Egenvalue Relatve Dfference From the nos egenvalues presented above, a new parameter called the Egenvalue Relatve Dfference and denoted by ERD s defned as: λ λ nos 3nos ERD = wth < ERD < () λ + λ nos 3nos Ths novel parameter s smlar to the ansotropy for small roughness values, but presents a dfferent behavour n hgh frequences. Ths parameter s very senstve to roughness and could be compared to the correlaton parameter ρ RRLL also developed for roughness retreval [][6]. Comparson wth Ansotropy Fg. shows the ansotropy and ERD varatons obtaned usng the IEM model versus for varous ε values, where k corresponds to the wave number. In ths llustraton case, the surface spectrum s consdered gaussan, the ncdent angle presents a value of 4 and the radar frequency s consdered to be.3 GHz. As t can be notced, these two parameters are very senstve to the surface roughness relatve to the frequency, whereas, the dependence on the delectrc constant s less mportant. On the one hand, for each ε value, one ansotropy value corresponds to two dfferent values of, ntroducng an ambguty for surface roughness extracton, whereas, on the other hand, the ERD has a monotonc behavour. The valdty doman of the ansotropy s lmted untl equals.5. The ERD presents the advantage to have a larger valdty doman and to be bjectve wth for each ε value.

4 .8 ε = 5 ε = ε = 5 ε = 5 ε = 35. ε = 5 ε = ε = 5 ε = 5 ε = 35 A ERD Fg.. Ansotropy and ERD values smulated wth the IEM model VALIDATION In order to valdate our theoretcal approach, the behavour of the ansotropy and the ERD are analysed on scatterometrc and SAR real datasets. Valdaton on JRC scatterometrc data Indoor scatterometrc measurements obtaned n the European Mcrowave Sgnature Laboratory (EMSL) anechoc chamber at JRC laboratory [7] are now consdered. Data were acqured n a monostatc mode n the frequency range from to 9 GHz at varous ncdence angles between and 5 and for 7 rotaton angles. The target conssts of a smooth sotropc surface wth a correlaton length of 6 cm and a surface rms heght of.4 cm. It s mportant to notce that the correlaton between the co- and the cross-polarzed channels s non-null. To buld our coherency matrx based on the reflexon symmetry hypothess, these correlatons are consdered equal to zero. The ansotropy and the ERD are respectvely plotted versus on the Fgs. 3 and 4. On these two fgures, the ansotropy has the same behavour, ndependently of the ncdent angle value, as observed for the ERD descrptor. As t has been obtaned wth the IEM model, the ansotropy decreases for small, correspondng to smaller frequences, and ncreases as ncreases, whereas, the ERD decreases always wth. These data permt to valdate the polarmetrc parameter varatons wth derved wth the IEM model..9.8 θ = θ =.7 A.5 θ = 3 θ = 4.4 θ = Fg. 3. Ansotropy versus from JRC data

5 .8.4. ERD θ = 5 θ = 4 θ = θ = θ = Fg. 4. ERD versus from JRC data Valdaton on Allng E-SAR data The second step of ths approach s to study the ERD and ansotropy varatons on real SAR data. The polarmetrc SAR dataset under analyss was acqured by the German Aerospace Center (DLR) E-SAR sensor, at L-band, over the Allng test ste n Germany. The consdered scene, represented n Fg. 5 -a-, s manly composed of agrcultural felds and forest. An urban area s located at the bottom left-hand corner of the mage, and an solated buldng can be observed n the top rght-hand part of the scene. On the Fgs. 5 -b- and -c-, the ERD and the ansotropy are represented. It s vsble that the ERD permts to dstngush varous feld areas, whereas they are not vsble wth the ansotropy. Ths s manly due to the hgh correlaton between the co- and cross-polarzed channels on these dataset, whch correspond to nose nformaton. - -a- -b- -c- Fg. 5. Images of the Allng ste at L band: -a- Span, -b- ERD, -c- Ansotropy

6 On Fg. 6, the selected area marked n Fg. 5 s analyzed. The felds,4 and 7 correspond to vegetated areas. Wthn them, the ERD s very hgh, whereas the ansotropy presents dfferent values. The ERD permts to detect vegetaton on these areas. Moreover, on felds and 3, the correspondng n-stu rms heght measurements are.4 cm and.9 cm respectvely, for the same correlaton length. The ERD decreases between these two felds, whch corresponds to the results obtaned wth the IEM model. Fnally, the ERD presents homogenous values for the same cultvated felds (harrowed or seedbed). Therefore, a classfcaton of the varous surfaces s possble a- -b- -c- Fg. 6. Images of the selected zone: -a- Span, -b- ERD, -c- Ansotropy CONCLUSION In ths paper, a new polarmetrc descrptor based on the reflexon symmetry hypothess: the Egenvalue Relatve Dfference (ERD) has been presented. Usng the IEM surface scatterng model, t has been demonstrated that ERD has a larger valdty doman than Ansotropy. Moreover t presents a larger dynamc range. From measured data, the ERD s shown relevant for surface characterzaton. In fact, the reflexon symmetry hypothess s assumed. Ths nformaton s consdered as nose on surface natural meda. In the case of the Allng SAR data, these correlatons are very hgh and so, the ansotropy s shown very nosy. For less nosy datasets the dfference between the ERD and the ansotropy wll be less remarkable. REFERENCES [] A. K. Fung, Z. L and K. S. Chen, "Backscatterng from a randomly rough delectrc surface", IEEE Trans. Geosc. Remote Sensng, vol. 3, no., pp , 99. [] S. Allan, L. Ferro-Faml and E. Potter, "Surface parameters retreval from polarmetrc and mult-frequency SAR data", Proc. IGARSS, July 3. [3] I. Hajnsek, "Inverson of Surface Parameters usng Polarmetrc SAR", Doctoral Thess Unverstät Jena, DLR - Scence Report, ISSN ,. [4] S. R. Cloude and E. Potter, "A Revew of Target Decomposton Theorems n Radar Polarmetry", IEEE Trans. Geosc. Remote Sensng, vol. 34, no., pp , 996. [6] J. J. van Zyl, "Applcaton of Cloude s target decomposton theorem to polarmetrc magng radar", SPIE, vol. 7, pp. 84-, 99. [5] F. Matta, T. Le Toan, J.-C. Souyrs, C. De Carols, N. Floury, F. Posa and N. G. Pasquarello, " The effect of surface roughness on multfrequency polarmetrc SAR data", IEEE Trans. Geosc. Remote Sensng, vol. 35, no. 4, pp , July 997. [7] G. Nest, EMSL Experment Report, Backscatterng from Rough Delectrc surfaces, July 998.