apid developments in autonomous underwater ve-icle technology have altered the direction of mine-ounter measures research toward more automatedechniques.1–3 These techniques generally requireraining, and their success can be dependent on theimilarity between the training and test data sets.he approach detailed here uses a three-phase pro-ess. The first phase employs model based on aarkov Random Field �MRF� model to directly seg-ent the raw image into regions of object highlight,
hadow, and background. Unlike many previous de-ection models,4,5 this one requires no training. TheRF structure of the model also allows known infor-ation to be modelled and included through the use
f priors.6The second phase uses a cooperating statistical
The authors are with the Ocean Systems Laboratory, School ofngineering and Physical Sciences, Heriot-Watt University, Ric-arton Campus, Edinburgh, EH14-4AS, United Kingdom. S.eed’s e-mail address is [email protected] 11 April 2003; revised manuscript received 29 July
nake �CSS� model7 to consider each of the detectedinelike objects �MLOs�. This model was originally
eveloped to ensure the accurate segmentation of ob-ect shadow regions onto complex seabeds, such asand ripples, when other models failed.8 The modelegments both the highlight and shadow regions ofhe object by assuming the regions to be statisticallyeparate, thereby enforcing a dependency betweenhe two snakes and constraining their movement.he CSS model is also effective in identifying falselarms.The third and final phase of the procedure entails
lassification of the MLO by use of a sonar simulatorodel. By using the known range and height of theLO, one can iteratively produce synthetic presen-
ations of possible objects �restricted to cylinders,pheres, and truncated cones here�. A Dempster–hafer �DS� approach9–11 is used to assign a belief toach of the possible classes, taking into account theegree of match �using the Hausdorff distance12� andhe plausibility of the synthetic object’s parameters.his novel approach extends the traditional mine orot-mine classification to provide useful shape andize information. The DS framework also permitsultiview analysis. This is important for sidescan
roach, often covering the same area of seabed mul-iple times.
In Sections 2 and 3 we review the detection andSS models previously presented by Reed et al.7 Inection 4 we present the results for these first twohases. The classification theory and results fromoth the monoview and multiview analyses are dis-ussed in Section 5. In Section 6 we present ouronclusions.
. Detection Model
. MRF Theory
eneral MRF models are composed of two fields:he observed image Y and the underlying true labeleld X. A pixel s is assigned a label xs based on tworobability measurements. The first of these con-iders the probability that label xs will produce ob-ervation ys. The second considers the labels of theeighboring pixels. This interspatial dependencymong pixels has ensured the successful use of MRFodels in a variety of difficult segmentation
roblems.13–15
We consider a set of three random fields Z � �X, Y,�. Field Y � �Ys, s � S� is the field of gray-level
bservations and thus takes its values from the gray-evel range �0 . . . 255�. Label field X � �Xs, s � S� ishe underlying label field that we wish to recoverith the segmentation. Label Xs can take values
e0 � shadow, e1 � seabottom reverberation, e2 �bject highlight�. Field O � �Os, s � S� is defined ashe object field; Os is drawn from �o0 � object, o1 �onobject� and is determined directly by consider-tion of label field X. Label field O, therefore, showshe clustering of object pixels. The probability of thenobservable true data given the observed field Y cane expressed by use of Bayes theorem as follows:
y expressing the posterior distribution as PX,O�Y�x,�y� � exp��U�x, y, o��,16 the desired underlying labeleld can be obtained by minimizing posterior energy:
U� x, y, o� � �s�S
s� xs, ys� � �s,t�
�st 1 � �� xs, xt��
� �s�S
�� xs, e2�ln�X�s� � �s�S
�s� xs, os�.
(2)
he first and second terms on the right-hand sideorrespond to the likelihood and Markovian termssed in general MRF models. The third and the
ourth terms incorporate some of the knowledgebout the appearance of objects in sidescan imagery.he third term acts only on pixels with label xs �
2�object highlight�. A directional potential fieldenerated by pixels labeled xs � e0�shadow� discour-ges pixels far from a shadow region from being la-eled xs � e2�object highlight�. This uses an adaptedotential term6 and models the a priori informationhat a mine highlight region usually has a corre-
ponding shadow region �see Fig. 1�. The fourtherm considers field O and favours clustering of xs �
2�object highlight� in compact, separated clusters ofinelike dimension. �See Reed et al.7 for a complete
xplanation of the detection model.�
. Postprocessing Phase
he detection-orientated segmentation detailed inubsection 2.A highlights possible MLOs. Some ofhese will be obvious false alarms and can be re-oved. First, object highlight regions that are ob-
iously too large or small can be removed �see areanclosed within ABDE in Fig. 1�. The height of theLO can also be computed and used by consideration
f the length of the accompanying shadow region t,long with navigational data such as the sonar fisheight h. This method is useful in the removal ofalse alarms produced by complex sea floors.
. Cooperating Statistical Snake Model
. CSS Model Theory
he CSS model7 was developed in response to theailure of conventional techniques8,17 to extract the
LOs shadow region on complex seafloors. TheSS model extracts both the object highlight andhadow regions. We consider the detected MLO’sugshot image y � y�i, j� with its corresponding
emplate image w � w�i, j�, the latter of which de-nes the shape of the two snakes at any given time.ndices i and j represent pixel positions in the image.t is assumed that the image is composed of object-ighlight, object-shadow, and background regions,escribed by �h � ��i, j����i, j� � 2�, �p � ��i, j����i, j�
1� and �b � ��i, j����i, j� � 0�, respectively. Allhree regions are described by probability densityunctions �pdf ’s� p�h, p�p, and p�b, where � , � , and
ig. 1. As in radar, the wave �here it is sound� is blocked bybjects and a shadow is generated. Given the relative position ofhe sonar fish, an estimate of the object’s height and size canherefore be obtained. This information can then be used to re-ove obvious false alarms.
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b are the parameters of the three pdf ’s. If the prob-bility densities are assumed to be Gaussian,18 thenhe segmentation w can be obtained by maximizing
nd Nu�w� is the number of pixels in region u and u �h, p, b�. The log-likelihood term in Eq. �3� is simplyfunction of gray-level sums and thus can be rewrit-
en as a summation around the perimeter of the twonakes.7,18 This ensures that the iterative processequired for finding the most likely solution is com-utationally fast.
. Incorporating A Priori Information
he a priori knowledge that the object-highlight re-ion is generally much brighter than the object-hadow region can be modeled using prior term
log Pmean�w�� � � tanh�12
��m� � ��� � c, (5)
here m� is the difference in mean gray level amonghe pixels within each of the two snakes. The otherarameters are constants that control the dynamicange and crossover rate of the function. The flat-opped form of the tanh function prevents the snakesrom simply collapsing, thereby ensuring a high m�
alue. As seen in Fig. 1, the object-highlight regionnd corresponding object-shadow region must alsoave roughly the same along-track size �enclosed byand E�. We define �max � max�ih� � max�ip� and
min � min�ih� � min�ip�, where ih and ip are the yoordinates on the perimeter of the object-highlightnd object-shadow snakes, respectively. The heightrior term can then be defined as
log Pposition�w�� � C � t1 U���max� � ����max�2
� t2 U���min� � ����min�2, (6)
here t1 and t2 are constants that penalize largeifferences in �max and �min. The constant C en-ures that the prior operates in the correct dynamicange. U is the Heaviside function, which allows thenakes some flexibility of movement, where constantis set arbitrarily to a small, nonzero number.The final posterior energy to be maximized during
he segmentation process is
J�y, w� � �0 log Preg�w�� � �1 � �0�
� ��1 log Pposition�w�� � �2 l�y, w� � �1.0
� �1 � �2� log Pmean�w���, (7)
here log Preg�w�� is a smoothing prior18 and �k k �0, 1, 2� are weights used to control the importance of
ach term. Here �1 and �2 are set at 0.2 and 0.6,espectively, and �0 is incremented graduallyhroughout the process.7
. Initializing the CSS Model
he detection result from Section 2 ensures a goodnitialization for the CSS model. Both snakes arenitialized as rectangles with only four points. The
aximum and minimum rows and columns for eachbject were used to define the object-highlight rect-ngle. The object-shadow snake was initialized byonsidering the homogeneity of the e0�shadow� pixelsithin it, whereas the height of the object-shadow
ectangle was set to that of the object-highlight rect-ngle.
. Removing False Alarms with the CSS Model
omplex backgrounds can provide situations inhich the MRF-based detection model falsely identi-es a MLO that the postprocessing phase does notemove. In these situations the CSS model can of-en identify the false alarm. The CSS model oper-tes on the assumption that there are three distincttatistical regions �object highlight, object shadow,nd background�. When an object is present, therior log Pmean�w�� prevents the object-highlightnakes from expanding. False alarms that do notave these three distinct distributions often result inn uncontrolled expansion of the snakes. If thenakes expand beyond minelike dimensions, theLO can be identified as a false alarm and can be
emoved.
. Detection and Shadow Extraction Results
he combination of the detection and CSS modelsas tested on more than 200 sidescan images.hese images were obtained from the BP’02 �battlereparation� trials conducted at the NATO Saclantnderwater Research Centre in Italy. This largeatabase of images ensured that the model wasested on a large variety of terrains under dramati-ally different conditions. Of the 200 images, 70 ob-ects were marked by human operators as possible
LOs, many of which were the same object seen fromifferent views. The model succeeded in detecting6 of these isolated objects, resulting in an 80% de-ection rate. Many of the objects that were not de-ected were removed because of the presence of aatermark in many of the images, a phenomenon
hat is due to the sea-surface return when the sonarsh lies close to the surface. When this watermarkorrupts the MLO’s shadow, the object-height calcu-ation is affected, which results in the object’s re-
oval. Manual removal of the watermark resultedn a detection rate of 91%. Future research will ex-lore ways to automate this process. The detection-SS model detected 55 false alarms, usually due to
he presence of complex seabed types. This resultedn an average of 0.275 false alarms or images. Theetection-CSS model is demonstrated in Fig. 2, whichllustrates a complex example in which some of thebjects are lying on sand ripples. The process is
xplained by use of three images; arrows indicate themage order. The first image contains the raw sonarmage. The second image contains the initial MRFetection result. The third image contains the com-leted detection result after the postprocessing andSS processes have been completed. All imagesonsidered were 1024 � 1000 pixels in size. Figure
shows that the correct detection results are ob-ained and that the object shadows are accuratelyxtracted even when they are corrupted by shadowsrom the ripples. This was possible because of theonstraining behavior of the CSS model. All thealse alarms are removed during the postprocessingnd CSS stages. It should be noted that only a fewf the false alarms detected by the CSS model haveeen shown. The computation time for this resultas 163 s on a Pentium 4 1.3-GHz personal com-uter. A simpler sonar image would require sub-tantially less analysis time.
ig. 2. Detection CSS model result for an image containing objecidescan image. The second image contains the MRF detection rehe detection result obtained. Accurate shadow segmentation resuf the CSS model.
an-made objects generally produce more regularlyhaped shadows than do natural objects. This char-cteristic can be used to classify an unknown MLO.revious research has focused on template-matchingodels,17,19 which attempt to fit shadow templates of
ossible man-made objects to the MLO’s shadow.lthough these approaches have yielded good results,
hey generally do not take into account the underly-ng sonar shadow formation process, that is, the plau-ibility of the tested templates is generally notonsidered during the testing process. The methodetailed here, however, uses a sonar simulator modelo produce synthetic shadow representations fromonsidered classes �limited here to cylinders, spheres,nd truncated cones�. Sonar simulator models haveeen used in the past to train feature-based super-ised classification models.20 Here the simulator
dden within the sand ripple seafloor. The first image is the rawefore the post-processing or CSS stages. The third image shows
or all objects have been obtained due to the constrained movement
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odel is used within the classification process. Theest match from each class is considered by a DSodel. Although most models produce a hard, clas-
ification result, the DS approach allocates to eachlass a belief that can be updated as more informatione.g., another view� is made available.
The classification decision uses predominantlyhadow information. The highlight region can beery dependent on the MLO’s composition, whereomplex elastic scattering effects can significantly al-er the highlight’s appearance. These effects areery difficult to incorporate accurately into a simpleimulator model. As a result, only the elongation ofhe highlight region is considered during the classi-cation phase. This increases the separability be-ween the classes, as discussed later in Subsection.C. The shadow region is related predominantly tohe shape of the object so that information regardinghe object’s composition is not required. In addition,ecause the classification process is iterative, simu-ation of the shadow alone significantly decreases theomputational effort.
. Generating Synthetic Shadows
he shadow-forming process in sidescan imagery isummarized in Fig. 3, which shows the cross sectionf a spherical object at slant range s and depth h fromhe sonar fish. As shown, the sonar cannot reach theegion of seafloor behind the object. As the sonarsh moves along, successive pings are placed to-ether until a complete sonar image is formed. Fig-re 3 also shows examples of synthetically generatedhadow regions from the cylinder, sphere, and trun-ated cone classes. Object shadows from each of thelasses can be generated by consideration of a simpleay-tracing model. This model is an approximationrom an existing sonar simulator,21 which assumes
ig. 3. Description of the shadow formation process. Individueft-hand side�. Synthetic shadow representations from the thretop�, sphere �middle�, and truncated cone �bottom�. These can b
sovelocity conditions and a simple point source re-eiver, where the source and receiver are colocated.ompensated for effects, such as the beam pattern, isssumed by the model. This reduction in modelomplexity is appropriate when only the generatedhadow is of interest rather the full backscatteredignal, which would require a more complicated sim-lator. The cylinder, truncated cone, and spherelasses are assumed to be completely described byarameters �cyl � �rcyl, lcyl, dcyl, �cyl�, �sph � �rsph,sph� and �cone � �rcone, dcone�, respectively, where l ishe length, r is the radius and d is the depth of eachbject. The angle of the cylinder with respect to thelong-track direction is represented by �cyl. Withhese parameters synthetic shadow representationsrom these object classes can be generated under theame sonar conditions �sonar fish height, range, res-lution� that the MLO was detected.
. Comparing Shadow Regions
he Hausdorff distance12 is a technique that mea-ures the resemblance between two shapes. If A �a1, , ap� and B � �b1, , bq� are defined as the pointsn the perimeter of the real and the synthetic shadowegions, respectively, then the Hausdorff distance isefined as
H� A, B� � max h� A, B�, h�B, A�� (8)
here
h�a, b� � maxa�A
minb�B
�a � b� (9)
nd � � � is some underlying norm on the points of And B.Function h�A, B� is a directed Hausdorff distance
nd is computed by first calculating the distance be-ween each point in A to its nearest neighbour in B.
gs are added together to form an overall sonar image �bottomsidered classes are also shown on the right-hand side: cylinderpared with the real sonar shadow to find a match.
he maximum of this set of values is h�A, B�.herefore if h�A, B� � d, each point in A must beithin distance d from some point in B. A similarrocess is carried out to compute the second directedausdorff distance h�B, A�. The Hausdorff distance�A, B� is designated the maximum value of the twoirected distances h�A, B� and h�B, A�. H�A, B� isherefore a measure of mismatch between A and B.
Parameters �cyl, �sph, and �cone were iterativelyhanged so that the best match—and the smallestausdorff distance H�A, B�—could be found for each
lass. Initial parameter estimates for the iterativeearch were provided by applying moment analysisn the MLO’s extracted highlight region obtained byhe CSS model. It should be noted that this initial-zation step was possible only because the CSS modelxtracted both the MLO’s highlight and shadow re-ions. Large margins were set on each of the initialarameter estimates to define a discretized parame-er space for each class that must be searched to findhe best fit to the MLO’s shadow. The parameterpace for both �sph and �cone was two dimensional,llowing an exhaustive search to be used. The pa-ameter space for �cyl was four dimensional and re-uired Monte Carlo Markov chain techniques8 tonsure a good maximum estimate. Estimates forhe best Hausdorff distance for each class took ap-roximately 60 s to compute on a Pentium 4 1.3-GHzersonal computer.
. Obtaining Class Membership Functions
ssuming that the best Hausdorff solution Hj forach class j � �cyl, sph, cone� was obtained with objectarameters �j
b and that the highlight region ex-racted from the MLO had elongation �, an overalllass membership function can be defined by
�jfinal�Hj, �j
b, �� � �jhaus�Hj��j
par��jb��j
elong���. (10)
unction �jhaus�Hj� considers the best Hausdorff
istance value for each class. The shape of thisunction was determined for each class by training.he data used for training and testing were taken
rom two different data sets, each under very dif-erent sonar conditions. The training and testingata sets were completely disjointed, with no over-ap. On the objects of known class j, a perfect so-ar simulator would be expected to produceynthetic shadow representations with Hj � 0.owever, the ray-tracing model used here produced
oughly Gaussian distributions around nonzeroausdorff values, leading to the function
�jhaus�Hj� � 1 if Hj � m� j
� exp���Hj � m� j�
2
2�j2 if Hj � m� j,
here m� j and �j2 are the mean and variance values
f the class Gaussian distributions, respectively.priori information on the shape and expected di-ensions of minelike objects was introduced
imple trapezium fuzzy functions to allocate highalues ��1� to parameters believed to be minelikend low values ��0� to the others. The trapeziumunctions were made suitably broad to ensure thatbjects with parameters relatively close to minelikeimensions could still achieve a high membershipunction.
Function �jelong��� considered the elongation of the
ighlight region. MLO’s with high elongation areore likely to belong to the cylinder class, whereasLOs with low elongation probably belong to either
he sphere or truncated-cone class. These functionsere again simple trapezium functions determined
rom the training data, where �sphelong��� �
coneelong���.
The overall membership function �jfinal�Hj, �j
b, ��ay in the 0, 1� range. These membership functionsere used within a DS model to provide a classifica-
ion decision. The use of fuzzy functions within a DSramework was chosen over other classification mod-ls for a variety of reasons. First, the limitedmount of data available for training made methodsuch as the K-NN �nearest neighbor� classifier or aeural-network-based approach difficult. Second,ecause the number of parameters varied with class,fuzzy classifier model seemed simpler to implement
han a clustering model. The simplicity of the sonarimulator model also required that functionsjpar��j
b� be robust enough to cope with inaccuraciesnherent to the simple ray-tracing assumptions usedn the simulator. An improved sonar simulator
odel would perhaps permit a more rigorous cluster-ng approach to the classification but at the expensef slowing the iterative process.
. Dempster–Shafer Model
empster–Shafer theory,10 frequently used as anlternative to Bayesian theory22 and fuzzy logic23
or data fusion, allows the representation of impre-ision and uncertainty through the definition of twounctions: plausibility �Pls� and belief �Bel�.hese are derived from a mass function m, which isnalogous to the well-known probability densityunction. Mass functions are defined on the poweret of the space of discernment D. For classifica-ion purposes, D may be the set of possible classes.pecific to DS theory, D may also contain union oflasses.11 Denoting 2D as the power set of D, wean define mass function m�A� for every element Af 2D such that
m��� � 0, �A�2D
m� A� � 1. (11)
or the mine classification model presented here, thellowed classes were A � �clutter, cyl, sph, cone, sph
cone�. Class A � sph � cone was used to modelonfusion between the sphere and cone classes. Theass functions were generated from the class mem-
ership functions �jfinal�Hj, �j
b, �� j � �cyl, sph, cone�.iven the set of mass functions, the belief �Bel� and
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lausibility �Pls� of each possible outcome can be de-ermined by
Bel��� � 0,
Bel� A� � �B�A
m�B�, � A � D, A � �, (12)
Pls��� � 0,
Pls� A� � �B�A��
m�B�, � A � D, A � �. (13)
decision can be made by considering either thelausibility or belief function. In this paper, theLO was allocated the singleton class �i.e., the MLO
annot be classified as sph � cone� with the maxi-um belief.
. Multiview Classification
hen the same object has been viewed from multiplespects, DS theory allows the monoview mass func-ions to be combined. Considering mass function mkrom source k �k � 1, . . . , n�, this rule is expressed by
m1 � m2 � . . . � mn�� A�
�
�B1�...�Bn�A
m1�B1�m2�B2� . . . mn�Bn�
1 � �B1�...�Bn��
m1�B1�m2�B2� . . . mn�Bn�(14)
or all nonempty subsets A of D. The summation onhe bottom line of Eq. �14� is often referred to as theonflict and is �1. A value of 1 means that thevidence from the sources are completely conflictingnd thus cannot be fused. Once the fused massunctions have been determined, the belief �Bel� func-ions can be determined as in Eq. �12�, and a multi-iew classification result can be obtained.
. Results
he classification model was first tested on monoim-ge cases. This assumes that each MLO was de-ected only once. The test data were provided byRDC–Atlantic in Canada and Groupe de Etudes
Fig. 4. Examples of �a� cylinder, �b� sphere, �c� truncated c
ous-Marine l’Atlantique �GESMA� in France. TheRDC-Atlantic data were collected with a Klein 5500ultibeam 550-kHz high-resolution sidescan sonar.he images considered were 90 � 60 pixels in sizend had been processed to ensure that both the acrossnd along-track resolution were 0.10 m. The datarovided from GESMA were obtained with a DF1000ual-frequency sidescan sonar and provided imagesith a resolution of 0.03 m � 0.03 m. Examples
rom the four considered classes �cylinders, spheres,runcated cones, and clutter� can be seen in Fig. 4.s shown, the clutter objects are often visually veryimilar to the man-made objects.The classification model was tested on 50 objects:
0 each from the cylinder, truncated cone, and cylin-er classes and 20 clutter objects. The testing dataere completely disjointed from the training data.he results are shown in Fig. 5. The solid curveepresents a standard mine–not-mine classificationrocess. The model correctly identified more than0% of the mines and correctly classified approxi-ately 50% of the clutter objects. The dashed curve
enotes a more specific classification in which thelassification is deemed correct only if the mine’slass was also successfully identified. Under theseonstraints, more than 80% of the mines were stillorrectly classified when the same clutter classifica-ion rate was maintained. Obtaining the correcthape classification �as well as the parameter infor-ation� makes it possible to identify the mine type
nd thus affects how the specific threat is handled.he difference in the two classification performances
s due to cases in which the sonar conditions are suchhat the shadow regions from all classes are verymall and similar, leading to confusion between thelasses. Better separability between classes shoulde achieved with a more complex sonar simulator.The multiview classification model is demon-
trated on two different objects. The first is a cylin-rical object seen from four different views. Theecond object is a truncated cone, which has also beenetected in four different passes. The differentiews can be seen in Fig. 6. The observed difference
and �d� clutter objects used to test the classification model.
n appearance of each object under different sonaronditions highlights the difficulties that a feature-ased classification model would have in classifyingach of the objects as the same shape. However, theonar simulator model described here uses this infor-ation to model the underlying shadow forming pro-
ess, allowing a correct classification to be obtained.ables 1 and 2 show the monoimage and multiimagelassification results for the cylinder and truncatedone images, respectively. Tables 1 and 2 show howoth the objects are correctly classified with a strongelief. The cylindrical example is straightforward,
Fig. 5. Percentage of correctly classified mine objects plot
ig. 6. �a� Four different views of the same cylinder. �b� Four diifferent directions, fish heights, and slant ranges.
Table 1. Belief Functions for Different Classes for the Individ
ith three of the four images providing the correctonoview classification result. Object 4 in Fig. 6
as a weak belief in the cylinder class owing to largestimates for �cyl
b. However, the fused result pro-uces a very high belief for the cylinder class. Theruncated cone example is more difficult, with threeut of the four images providing incorrect monoviewlassification results. However, when images areused, the consistently high truncated cone belief issed to correctly classify the object. Although onlywo examples are shown here, they are representa-ive of other results obtained. The results demon-
gainst the percentage incorrectly classified clutter objects.
t views of the same truncated cone. These views are taken from
ages and the Overall Fused Result for a Cylindrical Objecta
trate the advantages of considering multiviewnalysis for classification.
. Conclusion
his paper has presented a model-based mine detec-ion and classification system for use in sidescan im-gery. The detection model used a MRF model toetect possible MLOs. This model allowed the in-lusion of a priori information through the use ofriors. Unlike many detection models currently inse, the process is completely automated and re-uires no training. The highlight and shadow re-ions of the MLOs are then extracted with a CSSodel for classification. The model obtained accu-
ate segmentation results—even on complexeabeds—by restraining the movements of the snakey use of a priori knowledge on the relationship be-ween the highlight and shadow regions. The CSSodel also allowed many false alarms to be removed
rom the initial detection result. A novel model-ased classification system was then presented.his model classified the object by modeling the un-erlying physical shadow-forming process. Thisystem extended the normal mine–not-mine classifi-ation to provide shape and size information on thebject. The classification decision was provided by aS framework, which allowed monoimage and mul-
iimage analyses. This feature is especially desir-ble in sidescan surveys, where the same object isften viewed multiple times. Results were pre-ented for real sidescan data. This work would alsoe directly applicable to detection and classificationodels in other media such as SAR imagery.
The authors thank the Mine and Torpedo Defenceroup at DRDC-Atlantic �Canada�, the NATOaclant Undersea Research Centre �Italy� andESMA �France� for providing the sidescan datased to present our results.
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2. C. M. Ciany and J. Huang, “Computer aided detection�com-puter aided classification and data fusion algorithms for auto-mated detection and classification of underwater mines,” inProceedings of the MTS�IEEE Oceans Conference and Exhibi-tion, �Institute of Electrical and Electronics Engineers, NewYork, 2000�, Vol. 1, pp. 277–284.
Table 2. Belief Functions for Different Classes for the Individua
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