Embedded Object Detection with Radar Echo Data by Means of Wavelet Analysis of MRA: Multi- Resolution Analysis

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1 (IJASA) Iteratioal Joural of Advaced omuter Sciece ad Alicatios, Vol., No.9, Embedded Obect Detectio with Radar Echo Data by Meas of Wavelet Aalysis of MRA: Multi- Resolutio Aalysis Kohei Arai Deartmet of Iformatio Sciece Saga Uiversity Saga ity, Jaa Abstract A method for embedded obect detectio with radar echo data by meas of wavelet aalysis of MRA: Multi- Resolutio Aalysis, i articular, three dimesioal wavelet trasformatios is roosed. I order to imrove embedded obect detectig caability, ot oly oe dimesioal radar echo data but also three dimesioal data are used. hrough a comariso betwee oe dimesioal edge detectio with Sobel oerator ad three dimesioal wavelet trasformatio based edge detectio, it is foud that the roosed method is suerior to the Sobel oerator based method Keywords-hree dimesioal wavelet trasformatio; Radar echo data; wavelet MRA; Edge detectio. I. INRODUION Measurig istrumet of Pulsed Radar for Udergroud obect detectios ad obect shae estimatios: PRU data is used to use for detectig embedded obects udergroud i geeral. he roblems of the PRU utilized embedded obect fidigs are () rage ad azimuth resolutio is ot good eough for small obect detectios, () oor resolutio of radar echo sigal receivers i the case that there is small differece of dielectric characteristics betwee embedded obects ad its surroudig materials. Other tha these, () multile reflectios from embedded obects ad surroudig materials are aother roblems together with () iterferece due to multile echo from embedded obects ad surroudig materials such as boudary layers, tiy stoes, etc. hrough huma ercetios with PRU radar echo data, i geeral, embedded obects are used to fid usually. herefore, it reuires huge exerieces ad kowledge for the erso i charge o huma ercetios. Meawhile, automatic detectios with differetiatio oerator of embedded obects from the radar echo data are used to attemt. he method for estimatio of the shae of embedded obects ad medium of material arameters from radar echo data is roosed []. Also the method utilizig filterig ad correlatio aalysis for oise removals is roosed together with the rerocessig of wavelet aalysis based method []. O the other had, the method for feature extractios i the freuecy domai which uses Fourier trasformatio is roosed. Meawhile, Hough trasformatio based method is roosed for extractio of embedded obects utilizig the well kow feature of which cylidrical shae of embedded obects show bi-olar fuctio of the curves theoretically []. he covetioal embedded obect fidig methods are based o the edge detectio algorithms utilizig the differetiatio oerator ad wavelet based Multi Resolutio Aalysis []: MRA. I the methods, radar echo data are treated as oe dimesioal data. Oe dimesioal differetial oerators ad MRA are used to use i the covetioal methods. Radar echo data are essetially three dimesioal data. herefore, it is ossible to imrove edge detectio erformaces by usig three dimesioal differetiatio oerators ad three dimesioal MRA. he followig sectio describes the roosed three dimesioal MRA for detectio of embedded obects with radar echo data followed by a comariso of edge detectio erformace betwee the covetioal oe dimesioal differetiatio oerators (he well-kow Sobel oerator i the aer) ad the roosed three dimesioal MRA. he coclusios ad some discussios are followed. II. PROPOSED MEHOD A. Pulsed Rdar for Udergroud Obect Detectios ad Obect Shae Estimatios Fig. shows the ricile of the ulsed radar for udergroud obect detectios ad obect shae estimatios. Radar echo data is the fuctio of time, f(t) at the ositio i cocer ad is scaed i two dimesioal groud surface, f(t:x,y). Figure. Pricile of the Pulsed Radar for Udergroud obect detectios. I the figure, the deth from the groud surface is exressed as followig euatio () P a g e

2 (IJASA) Iteratioal Joural of Advaced omuter Sciece ad Alicatios, Vol., No.9, V D r where V ad deotes, resectively, electric magetic wave roagatio seed of the udergroud ad the air. deotes time iterval of the ulse reeat cycle while deotes di-electric costat of the soils of the udergroud. ylidrical or sherical shaes of embedded obects i the udergroud show the edges as a arabolic fuctio i the ulsed radar echo image as show i Fig.. () Figure. Radar echo waveforms from cylidrical ad sherical shaes of embedded obects i the udergroud If the embedded obects are such cylidrical ad sherical shaes of obects, obect shaes ad three dimesioal locatio of the obect ca be estimated with a rior kowledge of the radar echo waveforms. It, however, is ot always aroriate of the assumtio of the obect shaes. For istace, there are some embedded cluster ies ad box tye of ies. It have to be estimated ad determied the obect shaes ad the three dimesioal locatios without such assumtio. B. he Proosed Method based o Wavelet Multi Resolutio Aalysis: MRA I order to estimate ad to determie the obect shaes ad the three dimesioal locatios, edges i the radar echo is extracted. I the covetioal method for edge detectio, oe dimesioal differetiatio i time domai is used to aly to the acuired radar echo. Also oe dimesioal wavelet trasformatio or Multi Resolutio Aalysis: MRA is alied to the radar echo data the iverse wavelet trasformatio or recostructio with high freuecy comoet is alied to the wavelet trasformed data thus edges are extracted, i geeral. Radar echo data, i essetial, is three dimesioal data. herefore, edge detectio erformace of the three dimesioal MRA or wavelet trasformatio based edge detectio method is suerior to the oe dimesioal methods. Namely, two dimesioally scaed radar echo sigals shows three dimesioal data. he three dimesioal MRA is alied to the three dimesioal radar echo data. After that, recostructio is made without low freuecy comoets results i three dimesioal edges are detected. It could be suerior to the covetioal oe dimesioal edge detectio with oe dimesioal differetiatio or differetial oerators. ε r. Daubechies base fuctio based Wavelet rasformatio Oe dimesioal wavelet trasformatio is exressed with the euatio (). F= f () where F, f deotes wavelet freuecy comoet ad radar echo sigal as a fuctio of time. deotes wavelet trasformatio matrix which is exressed as a bi-orthogoal fuctio based o base fuctios. ca be determied with a referece to the aedix. herefore, t =I. he f is coverted to F =(L,H ), F =L =(L,H ), F =L =(L,H ), ad F m =L m- =(L m,h m ). Also f is recostructed as - F m = - (L m,h m )=L m-,..., - F =L, - F =f. here are some based fuctios such as Haar, Daubechies, etc. hrough the exerimet with relimiary simulatio of radar echo data, Daubechies base fuctio is selected. Daubechies base fuctio is oe of bi-orthogoal fuctios. he F=(L,H ).where L, H deotes low ad high freuecy comoets, resectively. If iverse wavelet trasformatio is alied to the H comoet ad zero filled L comoet, the oe dimesioal edge (high freuecy comoet) ca be extracted. Oe dimesioal wavelet trasformatio ca be exaded to two dimesioal trasformatios easily. Namely, F=[[mfxy] t ] () where m deotes aother wavelet trasformatio matrix while fxy deotes two dimesioal scaed radar echo data. As the result, F=(LL,LH,HL,HH ) with four freuecy comoets i x ad y directios, LL,LH,HL,HH. If the two dimesioal iverse wavelet trasformatio is alied to the F with zero filled LL ad the other freuecy comoets, the two dimesioal edges are extracted. Pulsed radar echo data is exressed with three dimesioal data essetially, fxyz. x ad y directios are corresodig to the scaed directios of the groud surface while z directio is corresodig to time. he three dimesioal wavelet trasformatios are defied with the euatio (). F=[[m[lfxyz] t ] t ] () hus eight freuecy comoets are derived. he the three dimesioal iverse wavelet trasformatios is alied to F with zero filled LLL ad the other freuecy comoets results i three dimesioal edges are extracted. Daubechies base fuctio is defied as { α k} satisfyig the followig coditios, P a g e

3 (IJASA) Iteratioal Joural of Advaced omuter Sciece ad Alicatios, Vol., No.9, III. EXPERIMENS A. Data Used PRU of SIR- which is maufactured by GSSI: Geohysical Survey Systems, Ic. with the ceter freuecy of MHz is used to acuire the ulsed radar echo data of embedded obects of the road from the Kami-ozu to the Shimo-ozu, Kokura ward, Kita-Kyushu ity, i Jaa o d of Aril. Fig. shows the structure i the udergroud of this road. Groud surface (Road) Although huma ercetios with PRU radar echo data seems reliable, it takes huge exerieces ad kowledge. B. Attemt for Fidig Ukow Obects of ommo Use Boxes As it is metioed above, the commo use boxes are difficult to fid the locatio ad shaes (dimesios) through huma ercetios with PRU radar echo data. A attemt is made to estimate the locatio ad shaes of the commo use boxes with the roosed method. Fig. shows the PRU radar echo data (reflected echo sigals). Figure. ross sectio of the udergroud structure of the embedded obects. he embedded obects as show i able are foud from the udergroud of the road i cocer. ABLE. OBJES WHIH ARE EMBEDDED IN HE UNDERGROUND OF HE ROAD IN ONERN. DISANE DENOES HE DISANE FROM HE LEF END OF HE ROAD. DEPH SHOWS HE PREDIION RESULS WHILE DEPH DENOES HE AUAL DEPH OF HE EMBEDDED OBJES HROUGH HUMAN PEREPIONS WIH PRU RADAR EHO DAA. Obect No. Obect ame Distace(m) Deth(m) Deth(m) ables Pies... ommo use boxes.9 Ukow Ukow Old ies... ables ommo use boxes 9.-. Ukow Ukow Pies.. Locatio i cocer A Figure. Received scaed PRU radar echo data which corresods to cross sectio of the road. he to row umbers rages from to are corresodig to the embedded obects which are listed i the able. I the Fig., the locatios of two ukow embedded obects are idicated with locatio i cocer A ad B, resectively. It is hard to idetify by huma ercetios eve for the exertise ersos. O the other had, the other obects are recogizable ad are idetified the locatio ad the shaes. hree dimesioal reresetatios of PRU radar echo data is illustrated i Fig..hree dimesioal edges are detected with the roosed MRA based method. Namely, if the recostructio rocess is made without low freuecy comoet, LLL, the high freuecy comoet of edges ca be detected. hree dimesioal edges have much iformatio rather tha two dimesioal edges ad also rather tha oe dimesioal edge. B he commo use boxes iclude some ies ad cables for commoly used for the local govermets ad ublic agets ad the others. he distaces of the commo use boxes are kow while their deth is ukow. hese data are ot foud i the old list. Also it is difficult to estimate the deth ad dimesios of the commo use boxes because it is ot idetifiable i the PRU radar echo data as well. he cables ad ies are situated at the two locatios, resectively. heir dimesios are kow. he old ies are ot useable situatios. he deth ad the dimesios of the embedded obects derived from huma ercetios are coicidet to the redicted deth ad dimesios which are estimated from the record which is created at the costructio of the road. Figure. ocetual three dimesioal PRU of radar echo of the udergroud of the road.. Exerimetal Results Oe of the examles of the exerimetal results is show 9 P a g e

4 i Fig.. Fig. (a) ad (g) shows PRU radar echo data ad shows the locatio of embedded obects No. ad No.. I the figure, ot oly PRU radar echo but also oe dimesioal rofile i the directio of deth reeatedly. (IJASA) Iteratioal Joural of Advaced omuter Sciece ad Alicatios, Vol., No.9, (a) he locatio i cocer A i the PRU radar echo data (f)oe dimesioal rofile of the detected edges of the locatio A based o the roosed three dimesioal MRA based method with three dimesioal data of PRU radar echo data (g)he locatio B i the PRU radar echo data (b)oe dimesioal rofile at the locatio A i the deth directio (c)detected edges of the locatio A based o Sobel differetiatio oerator (h)oe dimesioal rofile of the locatio B i the deth directio (i) Detected edges of the locatio B by usig Sobel oerator (d)oe dimesioal rofile of the locatio A i the deth directio(edges are detected with Sobel differetiatio oerator) (e)detected edges of the locatio A based o the roosed three dimesioal MRA based method with three dimesioal data of PRU radar echo data () Oe dimesioal rofile of the locatio B of the detected edges with Soble oerator P a g e

5 (IJASA) Iteratioal Joural of Advaced omuter Sciece ad Alicatios, Vol., No.9, (k)detected edges of the locatio B based o three dimesioal MRA based method with three dimesioal PRU radar echo data (l)oe dimesioal rofile of the detected edges of the locatio B based o three dimesioal MRA based method with three dimesioal PRU radar echo data Figure. omarisos of the detected edges by Sobel oerator ad the roosed three dimesioal MRA based method D. Discussioss I the case of Sobel oerator, udesired edges are detected results i valuable ad desirable edges are hidde by the detected udesired edges. Meawhile, the roosed three dimesioal MRA based edge detectio method allows detectio of desirable edges deedig o freuecy comoets of edges. I this aer, although oe level, sigle stage of MRA is used, variety freuecy comoets of edges ca be detected by chagig the level. MRA does work as filter bak. Fig. (f), (i) shows the edges which are corresodig to the commo cable ad ies boxes with the roosed three dimesioal MRA based edge detectig method. he locatio at which the edges are detected is totally eual to the boxes locatios. Meawhile, the resultat images of Sobel oerator of the boxes does ot show clear edges which are corresodig to the boxes. IV. It may cocluded that ONLUSION () the roosed three dimesioal MRA based edge detectio is suerior to the covetioal edge detectio method with differetiatio oerator such as Sobel, Lalasia, etc. i terms of sesitivity to udesired edges, () he roosed three dimesioal MRA based edge detectio method is suerior to the oe dimesioal MRA based edge detectio method i terms of three dimesioal edge detectio, () Detected edges are coicidet to these of which the exertise ersos results, i articular, the edges which are difficult to detect such as the commo cable ad ie boxes i the exerimet of the roads. AKNOWLEDGEMEN he author would like to thak to GIS Kyushu o. Ltd. for rovidig the PRU radar data as well as the iformatio of the embedded obects i the udergroud of the road i cocer. Also the author would like to thak to oit research member of the cooerated research was made betwee GIS Kyushu o. Ltd. ad the Saga Uiversity. REFERENES [] aaka, et al., Surveillaces of the embedded obects by meas of time domai aalysis, Proceedigs of the th Worksho o the Udergroud Measuremets with Electro Magetic Waves, -, 999. [] ada, et al., Ivestigatio of characteristics with the oise removal method utilizig two dimesioal arabolic fuctio of wavelet for PRU radar data, Proceedigs of the th Worksho o the Udergroud Measuremets with Electro Magetic Waves, -, 999. [] Nagashima, et al., echology of embedded obect fidigs by meas of atter recogitio method i freuecy domais, Proceedigs of Sace Aeroautics Electroics Symosium, SANE--, 9 [] Yamauchi, H., Image rocessig methods for udergroud obect idetificatios with PRU radar images, Ritsumeika Uiversity Symosium o Image Processig ad Aalysis,.-,999. [] Arai, K. Fudametal heory of Wavelet Aalysis, Morikita Shua Publicig o. Ltd.,. APPENDIX (WAVELE RANSFORMAION MARIX) For istace, the th order of Daubechies base fuctio based with the suort legth of two ca be exressed with the euatio (A). [] x x (A) he th order of with the suort legth of four is also exressed with the euatio (A). Scalar data cosists eight umerical data, η to η is assumed. P a g e

6 (IJASA) Iteratioal Joural of Advaced omuter Sciece ad Alicatios, Vol., No.9, P a g e [] (A) i ad i i the euatios (A) ad (A) is also exressed with euatio (A) ad (A), resectively. [] [] I (A) [] [] I (A) hese euatio ca be exaded to the geeral suort legth of as show i euatio (A). ) su,,,...,( ),,,...,(su su ) ) ((su su [su] [su] r I r (A) herefore, the coefficiets of the Daubechies base fuctio ca be determied from the solutio of the euatio (A). AUHORS PROFILE Kohei ARAI Saga Uiversity Saga, Jaa Kohei Arai received a PhD from Niho Uiversity i 9. He was subseuetly aoited to the Uiversity of okyo, RS, ad the Jaa Aerosace Exloratio Agecy. He was aoited rofessor at Saga Uiversity i 99. He is also a aduct rofessor at the Uiversity of Arizoa ad is Vice hairma of ISU/OSPAR ommissio A.