Ship Detection and Segmentation using Image Correlation

Transcription

1 Ship Deecion and Segmenaion using Image Correlaion Alexander Kadyrov, Hui Yu and Honghai Liu School of Creaive Technologies, Universiy of Porsmouh, Porsmouh, UK arxiv: v1 [cs.cv] 21 Oc 213 Absrac There have been inensive research ineress in ship deecion and segmenaion due o high demands on a wide range of civil applicaions in he las wo decades. However, exising approaches, which are mainly based on saisical properies of images, fail o deec smaller ships and boas. Specifically, known echniques are no robus enough in view of ineviable small geomeric and phoomeric changes in images consising of ships. In his paper a novel approach for ship deecion is proposed based on correlaion of mariime images. The idea comes from he observaion ha a fine paern of he sea surface changes considerably from ime o ime whereas he ship appearance basically keeps unchanged. We wan o examine wheher he images have a common unalered par, a ship in his case. To his end, we developed a mehod - Focused Correlaion (FC) o achieve robusness o geomeric disorions of he image conen. Various experimens have been conduced o evaluae he effeciveness of he proposed approach. Index Terms Vessel deecion, ship deecion, objec deecion, phase correlaion, orienaion correlaion, maching, regisraion. I. INTRODUCTION Robusly deecing ships plays a crucial role in civil applicaions such as drug-smuggling ships deecion. Ship deecion problems have been researched inensively. A review [1] on his opic includes up o 5 lieraure enries. Generally speaking, wo ypes of echniques have been used for ship deecion [2]. The mos popular one is he synheic aperure radar (SAR) echnique, which is fairly robus o various weaher condiions. I is based on an invasive echnology - he scene is illuminaed wih radio rays. The deecion is achieved hrough a series of processing of refleced signals. A side-effec of his echnique is ha he airborne surveillance sysem reveals iself. As a resul, people on he deeced ship may be aware ha hey are under surveillance. For smaller ships and boas SAR echnique is less efficien [3], and hus remains an open problem which is commonly inerpreed as he need for accurae empirical modelling of sea o separae he boa from he sea. An alernaive, eiher opical, or visual based deecion is lesser developed [2], [4], hough i is considered o be imporan. For example, in [5] i is saed ha UK will have a range of mariime surveillance resources available in 22, operaing in he audio, visual and elecronic specra. I should be non-invasive and does no require special equipmens. Then i is preferable for he purpose of non-invasive deecion of small vessels by unmanned aerial vehicle (UAV), and herefore i is appropriae for improving mariime border surveillance of /13/$31. c 213 IEEE small ships and boas in order o deec illegal aciviies such as drug and human rafficking and illegal fishing aciviies ec. To he bes of our knowledge, mos ship deecion mehods currenly operae wih one image, and apply hresholding ha follows a preprocessing procedure [6]. The raionaliy behind his is sraighforward: an experienced human operaor is able o disinguish a ship in he surrounding sea based on he fac ha a ship has a specific color and shape, and he sea surface has a paricular exure. Compuers can rely upon he same assumpions. Hence hose sandard approaches are mainly based on a variey of segmenaion echniques and shape analysis mehods for suspeced inclusions [7] [11], where mos advanced echniques model sea paerns by specially designed random fields, and hey also model a ship as an elongaed inclusion. Here in his paper we propose a compleely differen paradigm. Insead of analysing a single picure, a pair of picures is considered. The mehod is based on he observaion as follows. During a shor ime sea he wave paern changes and hence he waer area canno mach wih is previous sae. On he conrary, a ship s shape does no change much wihin his ime inerval, and she can be merely displaced and/or undergo a small roaion in he image, due o movemen of he ship and he aerial based camera. Hence, he wo images of he sea do no correlae, whereas he wo images of he same boa do correlae. This observaion forms he principle of he presened research in his paper. We correlae he wo images, and if he correlaion value is significan, i is concluded ha a boa is presen in he image. However, in pracice a problem arises due o such changes in he ship appearance ha he correlaion algorihm overlooks he ship presence. To overcome his difficuly, we re-inerpre he visual informaion by creaing a conrolled uncerainy o comba possible changed in he ship appearance in he video sequence. The reminder of his paper is organised as follows: Secion II presens an explanaion of he ask and scenarios of ship deecion; Secion III gives an overview of available correlaion mehods, shows a need of heir improvemen, and suggess such an improvemen; Secion IV explains how a ship and sea can be separaed, and he presence of he ship can be deeced. However, he obained here informaion is no equivalen o segmenaion of he ship. In he Secion V we compare differen mehods for ship deecion. Secion VI evenually provides segmenaion of he deeced ship. Finally, we conclude his

2 paper wih discussion in Secion VII. II. TASK AND PROBLEM FORMULATION Imagine an unmanned aeriall vehicle (UAV) hovering over he sea as a par of a mariime surveillance sysem. An onboard camera akes images and sends hem o he base for human operaors. In his scenario wo problems arise. Firsly, mos of images conain inadequae informaion, majoriy showing an empy sea, or repeaedly sending he same informaion back o he base already observed previously. Secondly, he human operaor is overloaded wih a bulk of redundan informaion and hus can make misakes when human aenion is evenually required o analyse a non-sandard siuaion. An ideal soluion o hese problems would be o enable on-board compuer o auomaically analyse images, and send ou only hose images ha do require human aenion. Moreover, an on-board compuer can ake a par in conrolling he fligh of he UAV [12], aking more picures of a discovered boa from differen perspecive, and send hem o he base. One of he mos imporan seps of his procedure is an abiliy o deec and delineae ships and boas, because only images conaining boas and ships can raise furher ineres. We presen our work in his direcion. To narrow he ask and o specify he visual informaion of ineres, we poin o he following advanages ha an UAV can provide. The firs advanage is a high definiion camera and a powerful compuer. This means ha we can rely upon high resoluion images. Anoher advanage is a highly accurae posiioning sysem employed by UAV. Wih his informaion we can esimae posiion of he ship/boa in he image. If a boa is presen in one image, hen i is assumed o presen in anoher image aken wihin few seconds. On he oher hand, we also know ha if he fis image does no conain he boa, hen he second image also does no conain i (excep he fringe of he image). Assumed high resoluion allows o proceed images by pars, where boas will have a beer represenaion in heir sizes. Thus we formulae our ask as deecing wheher a boa is presen on he boh images aken wih a ime inerval up o a hreshold of a few seconds. The wo images of boas in he described scenarios are shifed and geomerically disored comparaively o one anoher, a mehod is sough ha is robus in case of small geomeric disorions. In spie of heir variey, exising correlaion mehods in Secion III share he same characerisics concerning geomeric disorion of images. A new modificaion is required o mee he needs of our ask. A. Sandard mehods III. CORRELATION METHODS To examine wheher wo images f and g have a common area, ha is a boa in our case, a few sandard opions are available. The general procedure is described as follows. The common area may be shifed from he is original posiion, so hen one has o ry all possible shif vecors, displacing he firs image, and compare such displaced image wih he second image. The comparison includes compuaion of a similariy or dissimilariy measure. Noe ha his is no excessively ime consuming since he compuaion uses FFT algorihm. To specify he process, we denoe he shif vecor by s and denoe by x a variable pixel in he picure. The measure depend on s only, so we obain a funcion S(s) which is called a maching surface [13]. The usage of he maching surface is as follows. The posiion of maximum (or minimum in case of dissimilariy) of he maching surface S gives he sough shif vecor beween he images. If he maximum is no high enough, hen i indicaes ha here is no common area in he wo images. We consider sandard ways of defining he maching surface. The firs formula is a regular cross-correlaion, S (s) = x f(x s)g(x), (1) and his can be used as a similariy measure. I can be argued ha i is no he bes way o compare images, so hen we consider is sandard alernaives. Insead of he iniial images, one can firsly correlae modified images, hen a more general approach would be o define an operaion O ha ransforms images o new funcions f 1 = O(f) and g 1 = O(g) and correlae hem insead of he iniial images. Thus, he generalisaion of (1) is he formula S general (s) = x f 1 (x s)g 1 (x). (2) There are hree well known ways o define he operaion O in his conex. They are Orienaion correlaion [14]. The operaion O is aking gradien of he image a each pixel and hen normalize i, ha is O(f) = (f)/ (f), hen (2), where muliplicaion means scalar produc of vecors, represens orienaion correlaion. We will refer o his paricular O as o an orienaion operaor. Phase correlaion [15]. The operaion O is reaining only phase informaion in he image, and ignoring he ampliude informaion in he frequency domain, ha is O(f) = F(f)/ F(f), (where F(f) is Fourier ransform of f) and hen (2) represens phase correlaion. For beer resuls one will need o ake care of he image borders, his is discussed in [16]. Normalized correlaion [17]. To define i, a size n of a small sliding window should be chosen. The operaion O is defined as O(f) = (f m(f,x,n))/σ(f,x,n), where m(f,x,l) is he mean value of he funcion f in he sliding square window wih side n and wih is cener a x, and σ(f,x,l) is he sandard deviaion of all he values of his funcion in he square. The image O(f) looks more random han he iniial f (and his can be proved by saisical ess), so he operaion O randomises he underlying image, for deails see [18] [21]. Oher sandard alernaives o formula (1) follow: a dissimilariy measures S 1 (s) = x (f(x s) g(x)) 2,

3 S 2 (s) = x f(x s) g(x), A B C and even a general measure S 3 (s) = x H(f(x s) g(x)), where H is a loss funcion associaed wih robus saisics. For he sake of generalizaion, he images f and g here also can be subsiued by f 1 and g 1. Le us analyse hese surveyed mehods of correlaing images. Firsly, S 1 (s) can be reduced o S (s) in (1). For his one can open he parenheses, and ge S 1 (s) = Cons 2S (s), where Cons = x f(x s)2 + x g(x)2 is independen of s. Secondly, reduce formulas S 2 and S 3 o (1), hey are expressed hrough cross-correlaion in [13]. Therefore S 2 and S 3 can be approximaed wih any desired precision by a sum of a few cross-correlaions of funcions which are obained from f and g by simple procedures in form f p = cos(c p f) or f p = sin(c p f) (where c p R). I is concluded ha known sandard mehods for invesigaing similariy of images can be presened in he form of correlaion (2) or in a sum of a few (P N) such correlaions, ha is in he form P S sandard (s) = f p (x s)g p (x), (3) p=1 where f p and g p are modified images obained from he iniial f and g by applying an operaion O p, and each operaion O p is shif-invarian, ha is i commues wih an arbirary image displacemen. B. Drawback of sandard mehods and an idea of focusing: a heurisic consideraion The observaion (3) allows criically judge all he considered mehod in a unified scheme. We are going o demonsrae a drawback of (1), and he res of he described mehods inheri his drawback from formulas (2) and (3). The drawback is ha i has over-sensiive reacion o geomeric disorion of he ship in he wo images, and his does no sui well our purposes. Raher small roaions of he ship will make he sough correspondence undeecable. This effec also is shown in his paper in experimens. The drawback is presened in a heurisic form. I sars from a general observaion ha an acual image changes is values gradually from pixel o pixel, a leas in mos of is pars, and a some disance beween wo pixels hese values become independen. We accep a simplificaion assuming ha he image consiss of small squares of consan values and hese values are values of independen random variables. This is an approximaion o a real image illusraed in Fig. 1. Suppose we have such an image f and is roaed version g. Consider a square grid of he inroduced small squares covering he image f, hey are shown in Fig. 1(A) in whie color. Afer roaion, hese squares are changed o hose in Fig. 1(B). x Fig. 1. Correlaion of roaed images. (A) squares; (B) squares afer roaion; (C) each square maches wih is roaed version. We will examine how each square in Fig. 1(A) maches wih is roaed version in Fig. 1(B). The mached areas are depiced in Fig. 1(C). I can be seen from he Fig. 1(C) ha he number of he mached squares does depend on he angle of roaion only, and i is independen of size of he squares. The correlaion (more precisely, is mahemaical expecaion) of f and g is proporional o he whie area in Fig. 1(C) divided by an area of one square. From his heurisic consrucion, we draw he following conclusions: (I) Described maching mehods are expeced o be raher sensiive o roaion of a ship. I can be seen from Fig. 1(C), where roaion significanly diminishes number of whie pars. (II) Improving resoluion of images will no improve deecion of of he ship. This is illusraed by he fac ha number of whie pars in Fig. 1(C) is fixed. (III) The maching can be improved if square areas change is size, smaller in he cener, and gradually becoming bigger o he fringe. This can be inerpreed as making he image arificially smooher when farher from he cener, and hen using such an unevenly smoohed image for furher correlaion. While applying his idea o he whole image, we call i focusing, because a chosen par is well focused, and he oher pars are ou of focus, as shown in Fig. 2. The propery (I) is widely presumed. For example, in [22] i is said ha correlaion mehods are oo sensiive in applicaions due o disorion of he objec surface under es. In applicaions usually a small window is used, like in [23], o make disorions less noiceable. In our opinion, propery (I) is he reason why he general problem of image regisraion is no ye solved saisfacory, and, insead of relying on machine vision (which necessiaes perfec regisraion), oher echniques are developed, [24]. The effec (II) was empirically discovered in oher circumsances such as [25], where i was soundly proved in experimens ha phase correlaion mehod paradoxically benefis from down-sampling of he images when i concerns robusness o affine disorions. The idea (III) is widely used for small neighbourhoods of feaure poins as an empirical echnique for ariculaing a feaure poin. The purpose is o make is neighbourhood more resilien o small roaions [26], and herefore i formally belongs o feaure-based approach of regisraion echniques [27]. In he nex secion we modify his idea for area-based echniques.

4 = =1.5 Fig. 2. Lef: Iniial crisp image; Cener: Resul of focusing wih parameers: ε =.6; focus p is chosen in he cener of an eye. Inuiively, i is obvious ha such an image, being roaed for small angle, would coincide wih he iself beer han a crisp image would do, and herefore he image informaion is presen here in a way ha suis beer for image regisraion in case of small roaion or, more generally, linear disorion wih he fixed poin a he focus; Righ: Resul of focusing of he whiened image. =2.3 =3.7 =4.7 =12 C. Focused correlaion: a way of inerpreaion of spaial informaion We define focusing procedure F wih parameer ε > and focus p, which is a posiion of a pixel. The parameer ε deermines srengh of he focusing. For each poin in he plane x se a value σ = ε x p, hen he definiion is (F(f))(x) R 2 1 2πσ 2e y x 2 2σ 2 f(y)dy. (4) The illusraion follows on an example of he sandard image Lena in Fig. 2. However, noe ha in he presened mehod we do no apply he focusing direcly o he image, bu for is whiened (randomised) version, because hen we have conrolled blurring, ha is we know in which degree he image is blurred in is differen pars. If we would apply he focusing o he iniial image, he resuling variable smoohness would no be known since he iniial image already has differen unknown smoohness degree in differen is pars. Moreover, our research demonsraes ha applicaion of focusing o he iniial image produces raher negligible benefi, and, as we can suppose, his is he reason why he idea of [26] was used locally only. In shor, we inroduce an arificial conrolled sensor measuremen uncerainy for purpose o cope wih really happening uncerainy of unknown geomeric disorion. We define a focused correlaion as a cross-correlaion of images Ff 1 and g 1, where f 1 = O(f) and g 1 = O(g). Two cases are considered in he paper: O is he orienaion operaor defined above, hen we have Focused orienaion correlaion ; O is phase reaining operaion defined above, hen we have Focused phase correlaion. The operaion F is no shif-invarian, herefore focused correlaion differs from (3), and hus we genuinely presen a new mehod. Inuiively i is apprehensible ha he bigger he parameer ε, he bigger disorion he mehod can olerae, however i is a expense of losing overall reliabiliy since for bigger parameer varepsilon informaion is los due o smoohing. Therefore, a rade-off necessiaes, and we use in our experimens varepsilon =.6 which is defined empirically. Fig. 3. A video scene aken during 12 seconds. The boa rocks, and a imes = 2.3 and = 4.7 i is less roaed han a imes = 1.5 and = 3.7. By couresy of SAGEM. According o our ask, we use wo images and find a displacemen which reains he mos unchanged muual informaion in hem, and his should be a displacemen of he ship since nohing else is expeced in he open sea. The mehod in some sense is opposie o deecion of vehicles in he land and canno use an advanage of an unchanged background [28], [29]. Focused correlaion mehod correlaes minuscule feaures in he image, and hose change in he wave paern and do no change in he ship paern. On he conrary, coarser paerns, like a wake (i.e. long waves or a rack lef by a vessel) may remain sable. This is why we focus on fine srucures, and i follows ha we would prefer higher resoluion in images, less compression in image informaion, and beer randomised images, all hese underline minuscule paerns. Anoher propery of he focused correlaion is ha i is raher more robus, in comparison wih ordinary correlaion, o small roaion and alike geomeric disorion which he ship can undergo. All hese properies are demonsraed in he presened experimens as follows. IV. SEA AND SHIP SEPARATION IN MATCHING SURFACE To solve he ask posed in Secion II, we have o deermine how o le he waer under he UAV be gahered ino one place, so ha a dry ship may appear. Firsly we do his no in he iniial real images, bu in he maching surface; for he iniial images he separaion is inroduced laer in Secion VI. Each poin s in he maching surface S expresses he shif s beween he wo iniial images f and g. However, he shif s is meaningful, ha is an area in he image wih such shif exiss, only if he value S(s) is a few imes above he sandard deviaion of all he values of S. To demonsrae his idea, consider images of a boa in Fig. 3. The firs image is an iniial image aken a ime = sec, and he res of images were aken a imes =1.5, 2.3, and 12 seconds. We scruinize he iniial period from = o = 2.3 sec. in Fig. 4. We show he process of sea and ship separaion.

5 = sec Ship and sea =.5 sec Sea =1. sec Sea =2.3 sec Sea is no deeced Ship Ship Ship Fig. 4. Maching surface a differen imes corresponding video a Fig. 3. The shif vecor of he boa and he shif vecor of he sea gradually separae, hen he shif vecor of he sea disappears, while he shif vecor of he ship becomes presened by a blob due o roaion of he ship. A he saring momen = he sea and he ship boh have zero displacemen ye. This is refleced in he firs image in Fig. 4. Afer.5 sec. hey have differen moions: he sea paern moves down quicker ha he ship. In his, he second image of Fig. 4, one can see ha shif vecor of he sea sars o loose is cerainy, because differen pars of he sea move differenly. In he nex image, = 1., his effec is even more prominen. Evenually, in he las image of he maching surface he sea shif vecor disappeared. The shif vecor of he ship also suffered: i is no concenraed as before, because he ship changed i geomeric appearance. From his experimen we conclude, ha in abou a second, he sea vanished from he maching surface, bu he ship is sill presen. This experimen is also illusraed in Fig. 5, where wo graphs are presened. The boh graphs presen signal-o-noise raio () which is defined as a raio of a maximum value of he maching surface o he sandard deviaion of he values of he surface, ha is (S) = max(s) sdev(s). (5) The upper graph is of he maching surface beween he iniial frame a = and a frame a > from he video sequence parly shown in Fig. 3. I is seen ha when he ship s appearance in he images differ less, hen is higher. Since he ship rocks, he graph has a periodic appearance. The lowes occurred a he momen = 12 sec. The laer demonsraes he limi of he mehod, and hen for his paricular image a = 12 sec. we esimae a geomeric ransform beween he images as follows. Ship s roaion (comparaively wih he ime = ) is.21 radian, and he scale along is lengh is.88. More precise descripion of he happened disorion of he ship from ime = o = 12 is given by an affine ransform, which we esimaed as ( ).92.2 C =.8.87 The srengh of he disorion in erms of norm is C I =.24, (I is an idenical marix). (6) The second, lower, graph in he Fig. 5, presens of he he same images bu wihou he boa. To eliminae he boa form he images, we jus reained he lef one hird of he images, see Fig. 3, and cu ou he res wo hird of i. This graph allows us o exrac wo bounding characerisics sea and sea of he sea defined by heir properies: Afer passing a ime inerval of sea sec presence of he sea vanishes in he maching surface. The of he sea (wihou boa) is bounded by sea. Now we can formulae resuls of his experimen. From comparison of he wo graphs in Fig. 5 we can conclude ha sea = 1 sec and sea = 7. We also observed ha he maximum deecable deviaion of he ship is described by (6). Therefore, presence of he boa in he image is indicaed by condiions: > sea a a momen > sea. The value of sea is empirical, while he value of sea has some heoreical backing. Assuming ha he maching surface is a Gaussian random field, we can esimae an expeced value of sea as 2logN, see [3], where N is he number of pixels in he maching surface. Taking sea slighly bigger han ha, we again come o he value sea = 7. V. COMPARISON OF THE METHODS In he previous secion we demonsraed how focused orienaion correlaion can benefi deecing a ship. In his secion we compare differen mehods and come o a conclusion ha a combinaion of wo mehods is necessary. A. Example of prevalence of Focused Phase correlaion Using he same video in Fig. 3, we consider four mehods: orienaion correlaion, phase correlaion, and heir focused versions. The resuls are presen in Fig. 6. Each of he mehods produces wo graphs, as shown in Fig. 5, and he graphs from ha figure are also presened in he Fig. 6. The lowes four graphs are no labelled, hey presen of he boaless lef one hird par of he scene. The greaes difficuly for

6 25 2 =3.7 = =12 1 =2.3 = = sec =1.1 sec =2.7 sec Fig. 8. A scene wih lower frequency informaion in he ship area, and his leads o failure o deec presence/absence of a boa while using phase informaion for correlaion; however, he gradien orienaion informaion (in he form of focused orienaion correlaion) suffices for deecing. By couresy of SAGEM. Fig. 5. of he maching surface corresponding o he video in Fig. 3. The used mehod is focused orienaion correlaion. Compare wih capion of Fig. 3 for explanaion of momens = 1.5, 2.3, 3.7, Focused Orienaion Corr. =1.1 =2.7 2 Focused Phase Corr Focused Phase Correlaion Focused Orienaaion Correlaion Orienaion Corr Phase Corr. 15 Orienaaion Correalion Phase Correalion Fig. 9. Four mehods applied o he scene in Fig. 8. The upper graphs (hick lines) presen of he maching surfaces of he whole picure. For comparison, he lower graphs (hin lines) presen for he lef par of he picure which does no conain he boa. Fig. 6. Example of prevalence of focused correlaion mehod. The graphs from Fig. 5 are presen here for comparison of all he ried mehods. ship deecion is momen = 12 sec, and i is demonsraed separaely by four maching surfaces in Fig. 7. From hese daa i is concluded ha for his paricular mariime scene he focused phase correlaion mehod ouperforms he res. Focused Orienaion Correlaion Orienaion Correlaion True shif was found True shif was no found Focused Phase Correlaion Phase Correlaion True shif was found True shif was no found Fig. 7. Maching surfaces for he four mehods for he las frame (a = 12) in Fig. 3. Focused versions of he mehods could deec he presence of he ship, while he original mehods couldn. B. Example of prevalence of Focused Orienaion correlaion Consider an example of images wih less high frequency informaion, hey are presen in Fig. 8. For he four considered mehods we have following graphs in Fig. 9 arranged as before. These graphs show ha in his case focused orienaion correlaion is he mos reliable, while focused phase correlaion is unable o provide a proper soluion for ship deecion. C. Conclusion: Reliable mehod These wo experimens illusraed our following findings: Focused correlaion can solve he ask, while correlaion iself only does no sui he ask due o sensiiviy o geomeric disorion of he boa. We also ried oher, simpler mehods such as S, S 1, S 2, and found ha hey canno provide a decen resul for he scenes. For differen kinds of scenes here is always one of he wo varians of he focused correlaion ha works beer, so we applied he boh of hem. The boa was deeced if one of he focused correlaions robusly exceed value of sea = 7 a he ime in beween one and hree seconds. The maximum deecable deviaion of he ship is described by (6), however he reliable condiion was found as C I <.1, (his corresponds o roaion less han 6 ). The bound 3 sec is an empirical value o guaranee ha he ship normally roaes no more ha

7 Fig. 1. Upper row: wo picures of a boa by couresy of SAGEM. Lower row: machabiliy map and he segmened common area. Fig. 11. Upper row: wo picures of a boa by couresy of SAGEM. Lower row: machabiliy map and he segmened common area. o 6. These findings were confirmed in our experimens wih more han 2 available mariime scenes. VI. SEA AND SHIP SEPARATION IN IMAGES To build an inelligen vision sysem we evenually will need he locaion of an objec [31], ha is o segmen i in he image. Suppose a ship is deeced, ha is > sea a ime > sea. The displacemen beween he ship images is found as a 2D vecor s max a which he maching surface reaches is maximal value (5). If we align he second image, ha is, obain he shifed image g(x+s max ), hen i should coincide wih he firs image f(x) while x belongs o he (unknown ye) ship area. Wih his observaion we can deermine he ship area. Our soluion is o use he orienaion operaor O, and compare images Of and Og(x+s max ). The ship area is hen found as a se of poins where he angle beween Of(x) and Og(x + s max ) is less han a paricular number, which was empirically chosen o be arccos.4. The resul is visible on he machabiliy map which is defined as a cosine beween uni vecors Of(x) and Og(x + s max ) a each pixel x. The machabiliy map shows which pars of he image can mach is counerpar in he second image by displaying a degree of maching qualiy as a correlaion coefficien ranging from 1 o 1. The resuls of his auomaic segmenaion are presen in Figs. 1, 11 and 12. These scenes presen differen degrees of difficuly for a human operaor: obviously, for a human i would be he easies o delineae he ship in Fig. 12. VII. CONCLUDING REMARKS Due o long hisory of maching and correlaing images, i seems raher difficul o propose a beer and feasible approach for applicaions. Papers on his opic appear a a rae of a leas 1 papers each year, [27]. The same siuaion is wih he ship deecion opic, where many aemps were made, which seems o leave only a possibiliy for incremenal furher developmen. Fig. 12. Upper row: wo picures of a boa by couresy of SAGEM. Lower row: machabiliy map and he segmened common area. We, however, proposed a novel way of subsanial improvemen of he mos known mehod of correlaion phase correlaion. This enables us o arrive a a new approach for boa deecion and hen resolve difficul cases when no prior informaion abou saisical properies of he sea is available. The novely presened in he paper can be herefore lised 1) A new correlaion mehod was proposed, and i shows reinforced robusness o geomeric disorions of he involved images; 2) A new boa deecion mehod was proposed, which is based enirely on comparison of images; 3) A usage of he observaion ha a fine paern of he sea changes compleely was proposed. The broader implicaion is ha he proposed more robus modified phase correlaion can be used everywhere where oher similar correlaion echniques are used. The proposed focused correlaion benefi from higher resoluion, herefore i can

8 subsiue he sandard mehods especially when larger images come abou, for example medical images which usually have very high resoluion. The main advanage is ha he mehod needs no uning and can even cope wih scenes ha are difficul o analyse for a human operaor. We presened a novel correlaion echniques ha is able o align geomerically muually ranslaed and disored pairs of 2D images. The mehod recovers he ranslaional componen of misalignmen and i is more robus o small geomeric disorion han known similar echniques. The mehod is based on a new way of inerpreing spaial sensor informaion in he presence of geomeric disorions. We examined he performance of he mehod in several mariime scenes compared o a few oher mehods as reference. The proposed mehod showed a low sensiiviy o geomeric disorion of he common areas and low sensiiviy o surrounding changing background. In he considered mariime scene he common area is a ship (or boa) area, and he changing background is he image of he surrounding waer in he sea. This enabled us o deec wheher a ship is presen in boh images, since is presence manifess iself as an unchanged area ha can be aligned. We also considered a direc exension of he mehod for furher segmening of he deeced ship. This sep proceeds by comparing aligned images. The mehod s behaviour was sable, which is promising for is usage for large variey of daa. The deecion of he ship was conduced by compuaion of movemen beween he wo images only, and wihou aking ino consideraion he image conen as opposed o oher mehods. Therefore, he proposed mehod for ship deecion can serve as a complemen o he previously published work and hen can be added as a new elemen o already working surveillance sysems. ACKNOWLEDGMENT The auhors would like o hank SAGEM (SAFRAN) for providing he mariime videos. 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