Source. Object. Seabed. Shadow zone C

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1 YESIN PPROH TO OJET DETETION IN SIDESN SONR R alder, L M Linne and D R armichael Herio-Wa Universiy, Scoland and DR incleaves, England 1 INTRODUTION Source In his paper, we consider he problem of objec deecion agains a exured background, and in paricular he deecion of objecs in sidescan sonar. The daa se is a series of sidescan segmens consising of an unknown number of irregularly shaped objecs in unknown areas of exure. We aemp, hrough an invesigaion of he saisical and geomeric properies of he daa o idenify he regions of dieren exures and he locaions of he objecs simulaneously, he single poin saisics of he various exure classes being known. We consider objec deecion as a ayesian image resoraion ask and propose a model using Gibbs eld srucures o model he prior knowledge of objec placemen and a simplied model of image formaion. In addiion o providing a formal framework for inroducion of muliple sources of informaion, his echnique also allows he complexiy of modelling o be conrolled by specicaion of he whole model hrough a se of cooperaing submodels. The aim of he echnique is o provide a robus objec deecion sysem, bu also o develop a mehod for approaching he srucuring of complex problems. The use of Mone arlo Markov chain (mcmc) echniques, geomeric srucures and relevan parameerisaions are proposed as such a mehod, wih advanages in simpliciy of model specicaion and ease of implemenaion. 2 MODEL DEVELOPMENT 2.1 SONR Objec Formaion The deniion of \objec" depends on conex a geological objec migh have a signcianly dieren morphology han a pipeline inspecion objec. In his example, we are ineresed generically in discree objecs which prorude above he seabed, bu which are sill conneced o i. The siuaion is shown diagramaically in gure 1, where we assume ha a ray based approach o he sonar propagaion problem is appropriae (1). Due o he denser maerial of he objec (eiher rock, or man-made iems), he reurn from he fron surface (poin ) is much sronger han he background (here are also muliple reurns from jus in fron of he objec), and he sonar race Shadow zone Objec Seabed Figure 1: Geomery of expeced sonar objecs. expeced is as shown in gure 2. The sonar shadow (poins {) afer he objec due o he majoriy of he energy being reeced is a very useful marker for his ype of objec. We assume ha he objecs sough are essenially he same size and fairly homogenous in shape (he acual shape and size is made exible hrough he modelling mehodology used). Furher, we assume ha he surrounding seabed is a leas locally a, and ha he reurn can be approximaed hrough a exure model. The exures are assumed a priori knowledge, and he model is rained from represenaive examples exraced from an image no in he es se. Finally, we assume ha he objecs are disinc, so ha a guard band of exure is always observed around hem. This is essenially a modelling requiremen which allows he sysem o simulaneously esimae likely exure class and deec objecs. I also improves false posiive rejecion. 2.2 Model srucure We srucure he modelling process by simulaing he ayesian poserior disribuion. The variables of ineres are exure class and objec locaion on per pixel basis, which we model as random elds and respecively. When required, we denoe he pair X for simpliciy. We assume ha he wo elds do Figure 2: Typical sonar objec, showing srong main reurn plus shadow ail.

2 no inerac (ha is, he behaviour of objecs is independen of he sedimen (exure) ype) and hence he poserior is: P (; jy ) / P (Y j; )P ()P ( ) (1) where Y is he observed image. In he descripion of he model we use a generic index for simpliciy, so he pixel of ineres is Y wih realisaion y. To faciliae manipulaion and compuaion, we assume ha he disribuions have Gibbs form (6) and a Meropolis algorihm is used for simulaion (alhough here are many alernaives (7)). The neighbourhoods are specied graphically and are denoed generically as N i i j () wih jnj ()j elemens (excluding he pixel of ineres a ). The model is specied hrough geomeric sizes of he neighbourhoods and parameers of he poenial funcions. ll of hese are relaed o physical consans, and hence are simple o esimae from he observed daa. 2.3 Poenial Funcions The overall poenial funcion is a weighed sum of he likelihood? and prior componens: V = w w L V L + w V (a) + w V (c) (2) where V L is he likelihood poenial, V (a) is he eld (geomery) poenial, and V (c) is he eld (exure) poenial. The number of parameers used in he model is relaively large. However, mos of he parameers are esimaed eiher hrough very simple rs order saisics of he observed image or hrough physical measuremen of he geomery of he objecs sough. Parameer consrucion is described in secion 2.4. The likelihood poenial funcion combines a simple exure model wih a geomerical emplae for he expeced exen of he objec and shadow, gure 3. This gure also denes he neighbourhood areas used in consrucing he poenial funcion. The funcion: V L = 1 3 V jn y ()j + V S jn S Y ()j + V O jn O Y ()j (3) weighs each of he componens by he number of elemens in he relevan area, assuming ha he eec of each componen should be of equal imporance in he overall funcion. The background poenial componen, V (), implemens he exure model. We assume ha correlaion beween he pixels is small, and ha he sysem can be represened by iid samples from he univariae hisogram of he exure. This is ofen approximaely he case in sonar, paricularly in he verical direcion due o non-uniy aspec raio pixels (3). Taking logs for simpliciy and numerical sabiliy, he poenial is: V () =? ln f c (y i ) i 2 N Y () (4) where he exure pmfs, f i (j) are esimaed by he normal couned hisogram approach over a sample area. For sabiliy, we require ha ln f i (j) > (we use =?6); failure o limi he dynamic range can resul in one componen dominaing all of he calculaions unnaurally. The shadow poenial componen, V S () assumes ha he shadow is drawn from he same pmf as he surround, bu ha he mean is scaled down by a xed value: V S () =? maxf; ln f c ([1 + &a ]y i g i 2 N S Y () (5) where he maxfg funcion is used o ensure sabiliy as above. Finally, o avoid specifying a reurn disribuion for he objec, a poenial based on mean dierences is consruced. Le m O and m be sample mean esimaes over he objec and background neighbourhoods, respecively, and le m = m O? m. The poenial componen is hen given by equaion 6, V O () = ( s anh? 1 2 (jm j? ) a = 0? s anh? 1 2 (m? ) a = 1 (6) This shows ha similar means are expeced when here is no objec presen, and a signicanly higher objec mean should be observed when an objec is suspeced. The prior models describe some general feaures of he objec deecion problem and help mainly o consrain he reconsrucion o likely realisaions. The eld prior is based on a modied Derin and Ellio syle Gibbs eld (4), (? 4 j 2 N O() V (a) =? jn O()j a? 2? 1 aj? jn ()j? aj? 1 2 j 2 N () where he neighbourhood deniions are as shown in gure 4. This poenial encourages clusering wihin he inner neighbourhood (represening he observaion ha objecs are small clusers of pixels), and encourages separaion of models in he ouer annulus neighbourhood (since objecs should be disinc from each oher). The eld prior on he exure classes esimaed is based on he mulinomial disribuion (2). The main (7)

3 w H Shadow neighbourhood N S y hh ackground guardband Ny w S w T h T NO y Objec neighbourhood Figure 3: Likelihood geomeric emplae and neighbourhood deniion. Objec locaion N O Isolaion background N Figure 4: Geomeric prior srucure of (objec presence) eld. feaure of his poenial is ha i encourages clusering of like labels, and hence models he main informaion: ha exures end o appear in clusers. The prior is dened on a square neighbourhood cenre he pixel of ineres, N (), and we assume ha he exures are a priori equally likely. Le n c = 1+jN ()j be he number of elemens in he neighbourhood including he curren pixel, and le n i () be he local hisogram esimae over he neighbourhood. Then, afer simplicaion he mulinomial based model becomes: s c (ln n c!? n c log ) V (c) = P n c i=1 ln(n i() + I(c ; i))! w w 0 a h 0 h (8) where here are exure classes, and I(i; j) = ij is he indicaor funcion. The parameer s c is calculaed afer pilo runs o mach he dynamic range of he mulinomial prior poenial o he ohers used. 2.4 Parameer onsrucion The model is consruced o make specicaion of he parameers as simple as possible, and he parameers used on he daa se seleced are shown in able 1. The sizes of he various neighbourhoods are calculaed by exracing a se of objecs from he daa and compuing heir mean size. However, i would also be possible o simply x he sizes o any arbirary value if a paricular objec morphology was required. Indeed he parameer values do no need o be paricularly specic, as he model used is sucienly exible o deviae somewha from he values used in deecing objecs close o he norm. In a similar way, he parameers of he likelihood funcion are esimaed direcly from he daa by exracing example objecs. The shadow scale & is compued by esimaing means of he background Parameer Value N O() Y 5 5 N S Y () 21 5 N Y () N O() 5 5 N () N () 5 5 Parameer Value & s c 21.0 s 7.5 w 0.1 w 0.5 w L 1.0 w 10.0 Table 1: onsruced parameers for es daa se. and shadow, and he mean dierence is se o be roughly equal o he observed objec o background mean dierence. The value of is slighly more arbirary (i conrols he degree of spread of mean dierence before all greaer dierences are considered simply \big", and have he same poenial). In his case, = 1:0 is found o give reasonable performance. The specicaion of balancing parameers s c and s is more complex, since hey are essenially modelling parameers inroduced o allow comparison of disparae poenials. The uning mehod used is o run he sampler for one pass and capure he dynamic range of he oher poenials; he paramers are compued o approximaely mach he appropriae dynamic ranges, resuling in equal weighing. s wih he oher parameers, absoluely accurae maching is no required since he sampling srucure of he model allows errors o be correced on fuure passes. The weighs in he overall poenial are chosen o re- ec subjecive belief on he imporance of he various componens of he model, empered by pilo runs of he sampler o judge he eecs. In his case, i was found ha he likelihood funcion mos reliably deeced he objecs, and hence is weighed more heavily; he value for w is reasonably vague, and he small value for w simply ensures ha noise spikes from he likelihood are removed on average. The overall weigh is, like he balance parameers, essenially a modelling choice. The value conrols he average Meropolis swap rae; oo high a value resuls in slow movemen, while oo low a value resuls in a grea deal of noise being inroduced a each sage. In heory, any value will work, bu judicious experi-

4 menaion in pilo runs of he sampler can sele on a value which balances he wo exremes. 2.5 Iniialisaion Process s wih all mcmc echniques, he iniial saring values for he elds should be irrelevan; he induced Markov chain should be allowed o sele for a suf- cien lengh of ime o \forge" he iniial sae. However, a reasonable iniial esimae of eld conens, while no guaraneeing faser convergence of he sampler, may help in pracice. In his example, he eld is iniialised by a crude meric based on he full model, and he eld is iniialised by a single pass of he iid exure model using maximum likelihood esimaion of exure class. Figure 5: Single exure deecion. 3 EXMPLE DETETIONS 3.1 Experimenal Technique The daa se used in his experimen were absraced from a survey carried ou in a major river esuary using a high frequency sidescan sysem. The daa examples are all from he por channel of he owsh (i.e., shadows appear on he lef of he objec), bu his is simply coincidence. For each example, he elds were iniialised as described above; he sampler was hen run for 23 ieraions and he eld was accumulaed over he las 20 passes (he delay before accumulaion allows for seling of he sampler). The accumulaed image was hresholded so ha objecs remaining had a leas a 25% probabiliy of being rue posiives, and he resul was edge deeced and overlaid on he original images. The hreshold for binarisaion is no criical, alhough some experimenaion is usually required o avoid loss of smaller objecs. 3.2 Deeced Objecs The deeced objecs in gures 5{8 show ypical examples from he daa se. ll of he obvious objecs in he daase are deeced, and here are few false posives. paricular feaure is ha many of he objecs are no of he expeced size or shape, bu are sill reliably deeced. This is due o a combinaion of he exibiliy of he poenials used and uning o general properies of he daase, raher han o specic values exraced from he daase. The hree arrowed false posiives are all caused by areas of he image which are sucienly close o he descripion of an objec o confuse he likelihood funcion, and sucienly far from oher objecs no o be rejeced by he eld prior. However, all of hem are of he order of one or wo pixels in size Figure 6: Deecion wih anchor scars. (roughly 10 cm wih his sonar), and herefore could be readily rejeced by reuning he algorihm o look for slighly bigger objecs. 4 DISUSSION The model developed has been shown o be eecive, wih relaively low false posiive rae and robus rejecion of noise processes, even o he exen of ignoring anchor scars on he seabed (gure 6). This is aribued o he divide-and-conquer sraegy involved in he piecewise specicaion of muliple co- Figure 7: Two exures, one false posiive.

5 sysem has been oulined which describes an approach o objec deecion in sidescan sonar. This approach srucures he search hrough he daa using observed feaures of he objecs required, inegraed ino a formal ayesian framework. The advanage of his echnique is ha priors on he daa being esimaed are easily implemened, and can considerably improve he segmenaion and objec deecion reliabiliy. The echnique also has he advanage of direcly speciying he geomery of he objecs required, and direcly relaing he parameers o feaures readily calculable from an example of he daa se. These make he model easier o iniialise. Figure 8: Two exures, wo false posiives. operaing models o implemen he whole sysem. In addiion, he use of sampling echniques o simulae he ayesian poserior improves noise reducion as well as providing a formal framework which allows he analysis o be implemened eecively. The srucure implici in he sampler implemenaion also allows for inegraion of oher informaion sources, so i would be possible in he fuure o include furher knowledge o improve he classicaion and objec deecion. Thus, for insance, if he area had been surveyed before, informaion from he las survey on ypical objec locaions could be used o apply spaial priors on likely locaions in he curren work. noher improvemen would be o include exper opinion abou he ineracion of objecs and sedimen ypes or more accurae models of sedimen behaviour. Developmen and uning of he model is a relaive weakness of his approach, alhough he majoriy of he parameers involved can be esimaed from simple observaion of he daa. In addiion, i is almos cerainly easier o ge a feel for he daa being analysed if pilo runs of he sampler are aemped before running over all of he daa se. s wih all sampler based reconsrucion echniques, here are a number of issues of convergence rae, mixing speed and sabiliy which need o be considered as each model is se up (5, 8). Esimaing balancing parameers while doing his does no signicanly increase modelling complexiy. 5 ONLUSIONS The resuls show ha he sysem developed can reliably nd objecs agains variably exured backgrounds. The false posiive rae is very low, once he priors are calibraed correcly. alibraion of he model is, however, only required on a per daa se basis, raher han on a per image basis. The srucure of he model presened also provides a mehod for inclusion of generalised prior knowledge on he reconsrucion ask o be aemped. In his example only very general descripion of objec locaion is added, bu any relevan informaion which can be quanied could be added hrough he same scheme. Possible exenions are o include emporal and spaial prior models from previous surveys, or exper opinion on objec morphology wih respec o dieren sedimen ypes. References 1. J. M. ell. Model for he Simulaion of Sidescan Sonar. PhD hesis, Dep. omp. & Elec. Eng., Herio-Wa Universiy, Scoland, R. alder, L. M. Linne, and S. J. larke. Spaial ineracion models for sonar image daa. In Sonar Signal Processing, volume 17 of Proc. Ins. cousics, December D. R. armichael, L. M. Linne, S. J. larke, and. R. alder. Seabed classicaion hrough mulifracal analysis of sidescan sonar imagery. Proc. IEE, 143(3), H. Derin and H. Ellio. Modelling and segmenaion of noisy and exured images using Gibbs Random Fields. IEEE Trans. PMI, 9(1), Gelman and D.. Rubin. Inference from ieraive simulaion using muliple sequences. Sa. Sci., 7(4), S. Geman and D. Geman. Sochasic relaxaion, Gibbs disribuions and he aysian resoraion of images. IEEE Trans. PMI, 6(6), W. R. Gilks, S. Richardson, and D. J. Spiegelhaler, ediors. Markov hain Mone arlo in Pracice. hapman and Hall, G. O. Robers and. F. M. Smih. Simple condiions for he convergence of he Gibbs sampler and Meropolis-Hasings algorihms. Sochasic Processes and heir pplicaions, 49, 1994.