A New Classification Method Based on Cloude- Pottier Eigenvalue/eigenvector Decomposition

Transcription

1 A New Classfcaton Method Based on Cloude- Potter Egenvalue/egenvector Decomposton Cao Fang 1,,, Hong Wen 1, 1 Natonal Key Laboratory of Mcrowave Imagng echnology Insttute of Electroncs, Chnese Academy of Scences he Graduate School of Chnese Academy of Scences Bejng, P.R. Chna Abstract In ths paper, a new polarmetrc scatterng parameter, the averaged ntensty (I), s ntroduced to present the backscatter ntensty of fully polarmetrc SAR data. Accordng to the partcular analyss on the propertes of I, α angle and entropy H, the mappng rule of I-α-H feature space onto the Intensty-Hue-Saturaton (I-H-S) color space s proposed. We use the IHS transform nstead of segmentaton algorthm to fnsh the classfcaton. he mportant advantages of ths method are that the nformaton contaned n the I-α-H feature space s preserved wthout any loss n the resultng mage, and the executon tme s saved snce IHS transform s faster than most complcated segmentatons. he result shows that I has the addtonal nformaton whch s not contaned n α and H, and the classfcaton result s more readable than that of H/α/A. Keywords-averaged ntensty (I); Intensty-Alpha-Entropy (I-α- H) feature space; Intensty-Hue-Saturaton (I-H-S) color space; Intensty Hue Saturaton (HIS) transform; Cloude-Potter decomposton; unsupervsed classfcaton; polarmetrc SAR I. INRODUCION Many methods are developed for classfcaton of fully polarmetrc SAR data, one of whch, the Cloude-Potter decomposton [1], has ganed great popularty. he most mportant advantages of ths decomposton are that t s capable of coverng the whole range of scatterng mechansm and automatcally bass nvarant. hs decomposton s based on the egenvalue/egenvector calculaton of the coherency matrx of fully polarmetrc SAR data. From ths decomposton, a set of feature parameters can be extracted, whch contan the polarmetrc scatterng nformaton wthn the SAR data. A feature space can be formed usng ths parameter set. hen the specfc processng technque, such as segmentaton, can be appled to the feature space to obtan the classfcaton result. here are two stckng ponts need to be consdered. One s the way to choose the feature space, the other s the process appled to the space. In general, dfferent parameter presents dfferent nformaton. here are three most commonly used feature parameters H/α/A, whch present entropy, scatterng angle and ansotropy respectvely. In recent years, much research has been done on the use of dfferent segmentaton approaches to mprove the classfcaton performance. Despte the great mprovement of segmentaton algorthm, the resultng mage doesn t provde a suffcent resoluton compared wth the sngle channel ampltude mages. here may be two reasons. One s H/α/A only contan the nformaton of the three scatterng mechansms wth relatve values and gnore the nformaton of backscatter ntenstes wth absolute values, the other s the segmentaton processng loses too much nformaton to mantan the performance. hus t would help to use new parameter to present the ntensty nformaton and to propose a more desrable processng technque to replace the segmentaton. hs s precsely the am of ths paper. Some prevous research has already done for ths. For examples, Hellmann chooses the frst egenvalue (λ 1 ) [], and Kmura the total power (SPAN) [] to present the backscatter ntensty. From the expermental results, t shows that the mage of λ 1 s too nosy and the mage of SPAN doesn t have the same geometry as those of H/α. Besdes, snce they all use hyper-box to perform the segmentaton, the results are not apparently mproved compared wth the methods usng advanced segmentaton algorthms. In ths paper, we use the averaged ntensty I combned wth the Intensty Hue Saturaton (IHS) transform [4] to get a very good classfcaton result. In the secton II, the Cloude-Potter decomposton s outlned as the basc theorem of ths paper. hen the averaged ntensty I s extracted and ts characterstcs are descrbed n detal. In the secton IV and secton V, we form the I-α-H feature space and llustrate ts smlarty wth the I-H-S color space. hen the mappng rule between the I-α-H feature space and the I-H-S color space s nterpreted. In the secton VI, the whole procedure of ths classfcaton s analyzed. Fnally, the concluson s gven wth some dscusson on the characterstcs of ths classfcaton method. II. CLOUDE-POIER DECOMPOSIION Due to the recprocty theorem [1], the scatterng matrx [S] s gven by Svv S x S = (1) S x Shh, where the frst ndex denotes the receved polarzaton and the second denotes the transmtted polarzaton. [S] can be expressed as a vector usng Paul bass (C) Brtsh Crown Copyrght 005

2 Report Documentaton Page Form Approved OMB No Publc reportng burden for the collecton of nformaton s estmated to average 1 hour per response, ncludng the tme for revewng nstructons, searchng exstng data sources, gatherng and mantanng the data needed, and completng and revewng the collecton of nformaton. Send comments regardng ths burden estmate or any other aspect of ths collecton of nformaton, ncludng suggestons for reducng ths burden, to Washngton Headquarters Servces, Drectorate for Informaton Operatons and Reports, 115 Jefferson Davs Hghway, Sute 104, Arlngton VA Respondents should be aware that notwthstandng any other provson of law, no person shall be subject to a penalty for falng to comply wth a collecton of nformaton f t does not dsplay a currently vald OMB control number. 1. REPOR DAE 5 JUL 005. REPOR YPE N/A. DAES COVERED - 4. ILE AND SUBILE A New Classfcaton Method Based on Cloude-Potter Egenvalue/egenvector Decomposton 5a. CONRAC NUMBER 5b. GRAN NUMBER 5c. PROGRAM ELEMEN NUMBER 6. AUHOR(S) 5d. PROJEC NUMBER 5e. ASK NUMBER 5f. WORK UNI NUMBER 7. PERFORMING ORGANIZAION NAME(S) AND ADDRESS(ES) Natonal Key Laboratory of Mcrowave Imagng echnology Bejng, P.R. Chna 8. PERFORMING ORGANIZAION REPOR NUMBER 9. SPONSORING/MONIORING AGENCY NAME(S) AND ADDRESS(ES) 10. SPONSOR/MONIOR S ACRONYM(S) 1. DISRIBUION/AVAILABILIY SAEMEN Approved for publc release, dstrbuton unlmted 11. SPONSOR/MONIOR S REPOR NUMBER(S) 1. SUPPLEMENARY NOES See also ADM001850, 005 IEEE Internatonal Geoscence and Remote Sensng Symposum Proceedngs (5th) (IGARSS 005) Held n Seoul, Korea on 5-9 July ABSRAC 15. SUBJEC ERMS 16. SECURIY CLASSIFICAION OF: 17. LIMIAION OF ABSRAC UU a. REPOR unclassfed b. ABSRAC unclassfed c. HIS PAGE unclassfed 18. NUMBER OF PAGES 4 19a. NAME OF RESPONSIBLE PERSON Standard Form 98 (Rev. 8-98) Prescrbed by ANSI Std Z9-18

3 1 k = [ Svv + Shh, Svv Shh,S x ] () hen the coherency matrx [] has the form = kk (), where denotes ensemble averagng. Snce [] s a hermtan, postve, sem-defnte matrx, t can always be appled an egenvalue analyss. hus [] can be decomposed nto three parts 1e1 e1 + λe e + e = λ λ e (4), where λ are the real egenvalues of [] whch follow λ 1 λ λ 0, and e are the correspondng orthonormal egenvectors wrtten as δ γ e = [cosα,snα cos β e,snα sn β e ]. (5) Each part n (4) presents a scatterng contrbuton, and the amount of the contrbuton s gven by λ whle the type of scatterng s gven by e. he probablty of each scatterng mechansm s expressed as λ p =. (6) λ he three most wdely used parameters are descrbed n the followng. Entropy H = p log p (7) = 1 α angle α = p 1α 1 + pα + pα (8) Ansotropy p p A = (9) p + p he physcal nterpretatons and other detals of these three parameters can be found n [1]. From the classfcaton results, t can be seen that nether H/α/A nor H/α provdes a satsfactory nterclass resoluton. III. HE AVERAGED INENSIY o avod ths, frstly, a new parameter wth better performance s needed. For the approach descrbed n ths paper, we ntroduce the averaged ntensty I to reform the commonly used H-α-A feature space. hs parameter s based on the Cloude-Potter decomposton and gven by I = λ + (10) 1 p1 + λ p λ p, where λ are the ntenstes of the three scatterng mechansms, and p are the correspondng weghtng coeffcents whch present the probabltes. In order to make the gray mage I more readable, the logarthm s taken by default. he parameter I contans the ntensty and probablty nformaton of the whole three scatterng mechansms n (4). Moreover, (10) can be seen as a fuson method of the three channels fully polarmetrc SAR data. he major characterstcs of I are descrbed n the followng. Polarmetrc roll nvarance Speckle reducton nherently Fuson of the ntensty nformaton of the three scatterng mechansms correspondng to the three parts n (4) Contanng the probablty nformaton of the three scatterng mechansms Havng the same geometrc characterstcs as H/α/A Havng better nterclass resoluton than H/α/A Independence on H/α n physcal concepton Dependence on the de-specklng algorthm used to calculate the coherency matrx [] No addtonal computaton burden hs analyss ndcates that the averaged ntensty I shall be useful to extract nformaton from polarmetrc SAR data. he expermental result shows that I s partcularly ft for mantanng the whole three channels ntensty, t has addtonal nformaton whch s not contaned n α and H, and t shows a good speckle reducton performance wth suffcent resoluton (t relates to the de-specklng algorthm). IV. I-α-H FEAURE SPACE Based on the descrpton n secton III, we extend the H-α feature space usng the averaged ntensty I (Fg. 1). Choosng I/α/H to form the feature space s due to the specal propertes of I/α/H as shown n the secton V. Besdes, another reason s that n practce, α and H are seen to be more valuable than A to dstngush dfferent scatterng mechansms. In Fg. 1, the D box presents the I-α-H feature space. he base of the box s the well known D H-α plane, whch presents the mportant propertes of the three scatterng mechansms n (4). he vertcal axs s the averaged ntensty I. o smplfy the presentaton, the values of I are normalzed to the nterval 0~1. Fgure 1. I-α-H feature space

4 In the next sectons, we shall dscuss the relatonshp between the I-α-H feature space and the Intensty Hue Saturaton (I-H-S) color space. o avod confuson, we shall use the low case f to present the I-α-H feature space, and c to I- H-S color space. V. MAPPING OF I-α-H FEAURE SPACE ONO I-H-S COLOR SPACE We fnd out that accordng to physcal conceptons, the I-α- H feature space s nternally dentcal wth the I-H-S color space (ab. 1). A short vew of I-H-S color space s gven n APPENDIX A. More nformaton can be found n [4]. Here we focus on the physcal relatonshp between the I-α-H feature space and the I-H-S color space. From ab. 1, t s obvous that I f, α f, H f are assocated wth I c, H c, S c respectvely. Hence, t s reasonable to establsh the rule of mappng between the I-α-H feature space and the I-H-S color space. Accordng to the dmenson, there are transformaton functons needed. A. I f I c In scatterng theory, I f presents the backscatter ntensty wthn each pxel. In computer graphcs, I c s the ntensty of color of each pxel. As I f vares from 0 to 1 (the value s normalzed, see Sec. IV), the backscatter ntensty ncreases. Addtonally, as I c vares from 0 to 1, the brghtness ncreases. hus the transformaton between I f and I c s gven by I = I. (11) c B. α f H c he relatonshp between α f and H c s obvous because they all present some knds of type. α f presents the type of the scatterng mechansm. H c presents the type of a color of the spectrum, such as red, green, yellow, etc. Commonly, we prefer to set blue to water areas (odd bounce) and red to buldngs (even bounce) n the result mage. herefore, the strategy used n ths paper s that as α f vares from 0 to 90, the resultng color vares from blue, through cyan, green, yellow, to red (Fg. ). hs s a lttle dfferent from the defnton of H c (APPENDIX A). We need to adjust the range of the output varable H c, so the transformaton functon comes to be α H (1 f c = ) (1) 90, where the unt of α f s deg. It should be noted that (1) s not unchangeable, t can be modfed accordng to our needs. f Fgure. Interpretaton of α f C. H f S c ab. 1 shows that H f and S c all present some knds of degree. Note that when H f = 0, the pxel contans only one (pure) scatterng mechansm, and when H f = 1, the pxel contans three equal (mxed) scatterng components. hat s to say, 0 presents the pure state, 1 the totally mpure state. hs descrpton s just opposte to that of S c (APPENDIX A), so the relatonshp between H f and S c s gven by S = H. (1) c 1 f Usng (11)-(1), we can easly map the I-α-H feature space onto the I-H-S color space. Next, the IHS transform (APPENDIX B) can be appled to convert the I-H-S color space to the R-G-B color space, so the fnal result of ths classfcaton s obtaned. VI. CLASSIFICAION On the whole, the classfcaton method gven n ths paper conssts of three steps (Fg. ). Calculaton of I f /α f /H f usng (7), (8), and (10), Converson from I f /α f /H f to I c /H c /S c usng (11)-(1), Usng IHS transform to obtan the RGB resultng mage. Snce α f covers the whole range of scatterng mechansm, ths method s not lke the usual classfcaton methods whch separate the data nto a lmted number of classes (each class presents one specfc scatterng mechansm), but some general prncples stll can be gven, whch are shown n the followng accordng to the mappng rule used n ths paper. ABLE I. I-α-H FEAURE SPACE AND I-H-S COLOR SPACE I-α-H Feature Space I-H-S Color Space Component Descrpton Component Descrpton I f backscatter ntensty I c ntensty of color α f scatterng type H c type of color H f degree of randomness S c degree of purty Fgure. he proposed method for polarmetrc SAR classsfcaton

5 Pxels wth low I f, low α f and low H f present smooth areas, such as water, the color of whch shown n the fnal mage s dark blue. Pxels wth hgh I f, hgh α f and low H f present buldngs and man made structures, the color of whch s brght red. Pxels wth hgh H f present forest. Snce hgh H f leads to low S c (APPENDIX A), the color n the fnal mage s gray. hs method has at least fve advantages. It mantans the whole advantages of Cloude-Potter Decomposton, such as coverng the whole range of scatterng mechansm and roll nvarance. It ncludes the ntensty nformaton wthout addtonal computaton burden. It doesn t have any nformaton loss durng the process of the transformaton from the I/α/H feature space nto the classfcaton result. It s fast snce no algorthm s needed to perform the segmentaton. It s unsupervsed. he expermental results are n accord wth ths analyss. It shows that ths I/α/H classfcaton provdes a much better performance than the common methods, especally for resoluton. Moreover, snce the IHS transform s faster than most currently used segmentaton algorthms, t saves executon tme. It s mportant to note that the nformaton contaned n I/α/H s preserved wthout any loss n the resultng mage. hat s to say, the losses are only produced durng the Cloude- Potter decomposton. We fnd out that the speckle reducton algorthm s a really crucal pont to optmze the performance. Durng our experment, Lee flter [5] s chosen to calculate the coherency matrx [], and the result shows t s good enough to satsfy our most applcaton needs. VII. CONCLUSION A new polarmetrc scatterng parameter, the averaged ntensty (I), has been proposed to present the backscatter ntensty of fully polarmetrc SAR data, and a new classfcaton method has been developed n successon based on the Cloude-Potter decomposton and the IHS transform theorem. hs method has no nformaton loss durng the process of converson from the feature space to the resultng mage, and t s fast snce no complex segmentaton algorthm s needed. Besdes, t s promsng to use ths method for further vsual classfcaton purpose. ACKNOWLEDGMEN Mss Cao Fang wshes to express her thanks to Mr. Zhou Qang, one of her colleagues, for hs knd and patent ntroducton of IHS transform. APPENDIX A. I-H-S Color Space Usually, color s descrbed by assgnng values to red, green and blue components, as gven by (R, G, B). Here (R, G, B) formed a color space. here are other color spaces e.g. the I-H- S color space (whch s also called H-S-I or H-S-V color space). he I-H-S color space s defned as the way humans thnk about colour. I, H, S are ntensty, hue, saturaton respectvely. he defntons of I, H, S used n ths paper are gven n the followng. More nformaton can be found n [4]. 1) Intensty (I) refers to the ntensty or brghtness of the lght wth a range of 0~1. When the lght s at ts fullest ntensty, the color becomes brght, at ts least ntensty, the color becomes dm. ) Hue (H) corresponds to the wavelength of lght contrbutng to a color wth a range of 0~1. As the hue vares from 0 to 1, the color vares from red, through yellow, green, cyan, blue and magenta, back to red. ) Saturaton (S) s the degree of purty of a color, whch presents the amount of whte lght mxed n the color. he range of t s 0~1. When the saturaton s 0, the color s only shades of gray. When the saturaton s 1, the color contans no whte lght (pure color). B. IHS ransform he Intensty Hue Saturaton (IHS) transform s used to convert from RGB color presentaton to IHS color presentaton, and vce versa. In geologcal applcatons, the IHS transform s demonstrated as a method to combne co-regstered mages from dfferent sources. Detals of the way to perform IHS transform are gven n [4]. REFERENCES [1] E. Potter, S.R. Cloude, A revew of target decomposton theorems n radar polarmetry, IEEE rans. Geosc. Remote Sensng, vol. 4, no., pp , Mar [] M. Hellmann, A new approach for nterpretaton of full polarmetrc SAR-data, n Proc. IGARSS 98, vol. 4, pp , July [] K. Kmura, Y. Yamaguch, and H. Yamada, P-SAR mage analyss usng polarmetrc scatterng parameters and total power, n Proc. IGARSS 0, vol. 1, pp , July 00. [4] K.R. Castleman, Dgtal Image Processng. Prentce Hall, Englewood Clffs, NJ, USA, 1996 (Sec. 1..4) [5] J.S. Lee, M.R. Grunes, and S.A. Mango, Speckle reducton n multpolarzaton, multfrequency SAR magery, IEEE rans. Geosc. Remote Sensng, vol. 9, pp , July 1991.