# Superellipse Fitting for the Recovery and Classification of Mine-Like Shapes in Sidescan Sonar Images

**ABSTRACT** Mine-like object classification from sidescan sonar images is of great interest for mine counter measure (MCM) operations. Because the shadow cast by an object is often the most distinct feature of a sidescan image, a standard procedure is to perform classification based on features extracted from the shadow. The classification can then be performed by extracting features from the shadow and comparing this to training data to determine the object. In this paper, a superellipse fitting approach to classifying mine-like objects in sidescan sonar images is presented. Superellipses provide a compact and efficient way of representing different mine-like shapes. Through variation of a simple parameter of the superellipse function different shapes such as ellipses, rhomboids, and rectangles can be easily generated. This paper proposes a classification of the shape based directly on a parameter of the superellipse known as the squareness parameter. The first step in this procedure extracts the contour of the shadow given by an unsupervised Markovian segmentation algorithm. Afterwards, a superellipse is fitted by minimizing the Euclidean distance between points on the shadow contour and the superellipse. As the term being minimized is nonlinear, a closed-form solution is not available. Hence, the parameters of the superellipse are estimated by the Nelder-Mead simplex technique. The method was then applied to sidescan data to assess its ability to recover and classify objects. This resulted in a recovery rate of 70% (34 of the 48 mine-like objects) and a classification rate of better than 80% (39 of the 48 mine-like objects).

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**ABSTRACT:**Target recognition in sonar imagery has long been an active research area in the maritime domain, especially in the mine-counter measure context. Recently it has received even more attention as new sensors with increased resolution have been developed; new threats to critical maritime assets and a new paradigm for target recognition based on autonomous platforms have emerged. With the recent introduction of Synthetic Aperture Sonar systems and high-frequency sonars, sonar resolution has dramatically increased and noise levels decreased. Sonar images are distance images but at high resolution they tend to appear visually as optical images. Traditionally algorithms have been developed specifically for imaging sonars because of their limited resolution and high noise levels. With high-resolution sonars, algorithms developed in the image processing field for natural images become applicable. However, the lack of large datasets has hampered the development of such algorithms. Here we present a fast and realistic sonar simulator enabling development and evaluation of such algorithms. We develop a classifier and then analyse its performances using our simulated synthetic sonar images. Finally, we discuss sensor resolution requirements to achieve effective classification of various targets and demonstrate that with high resolution sonars target highlight analysis is the key for target recognition.Journal on Advances in Signal Processing 01/2010; · 0.81 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**In this paper the problem of contour extraction in sonar images is addressed. We talk in this context about naval mines placed on the seafloor which are still a vast restraint in civil and military shipping. This potential risk is typically encountered by advanced sonar signal processing techniques and a huge amount of human interactions. To reduce at least the human interactions an automatic procedure is desired. Therefore we introduce a novel automatic target extraction algorithm based on active contours employing a specific shadow locating energy motivated by our experiments. Additionally we use a K-means based thresholding process and a Kolmogorov Smirnov (KS) test for improving the initial guess and therefore optimizing the overall performance.01/2011;

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434IEEE JOURNAL OF OCEANIC ENGINEERING, VOL. 33, NO. 4, OCTOBER 2008

Superellipse Fitting for the Recovery and

Classification of Mine-Like Shapes in

Sidescan Sonar Images

Esther Dura, Judith Bell, and Dave Lane

Abstract—Mine-like object classification from sidescan sonar

images is of great interest for mine counter measure (MCM)

operations. Because the shadow cast by an object is often the

most distinct feature of a sidescan image, a standard procedure

is to perform classification based on features extracted from the

shadow. The classification can then be performed by extracting

features from the shadow and comparing this to training data

to determine the object. In this paper, a superellipse fitting ap-

proach to classifying mine-like objects in sidescan sonar images

is presented. Superellipses provide a compact and efficient way

of representing different mine-like shapes. Through variation of

a simple parameter of the superellipse function different shapes

suchasellipses,rhomboids,andrectanglescanbeeasilygenerated.

This paper proposes a classification of the shape based directly

on a parameter of the superellipse known as the squareness

parameter. The first step in this procedure extracts the contour

of the shadow given by an unsupervised Markovian segmentation

algorithm. Afterwards, a superellipse is fitted by minimizing the

Euclidean distance between points on the shadow contour and

the superellipse. As the term being minimized is nonlinear, a

closed-form solution is not available. Hence, the parameters of the

superellipse are estimated by the Nelder–Mead simplex technique.

The method was then applied to sidescan data to assess its ability

to recover and classify objects. This resulted in a recovery rate of

70% (34 of the 48 mine-like objects) and a classification rate of

better than 80% (39 of the 48 mine-like objects).

Index

sidescan, sonar, superellipse fitting.

Terms—Classification,mine-likeobjects,recovery,

I. INTRODUCTION

W

for use in scientific, industrial, and military applications.

The spectrum of applications in which AUVs are involved is

considerable. These include surveying the pipes and cables

of telecommunications and oil companies, seafloor mapping,

mine counter measure (MCM) operations and sea recovery

operations. Given the potential applications, a self contained,

ITHIN the last decade autonomous underwater vehi-

cles (AUVs) have become a very attractive technology

ManuscriptreceivedFebruary02,2007;revisedApril18,2008;acceptedJuly

11, 2008. Current version published February 06, 2009. This work was sup-

ported by Heriot-Watt University, Edinburgh, U.K.

Associate Editor: D. A. Abraham.

E. Dura is with the Institute of Robotics, Universidad de Valencia, Paterna,

Valencia 46071, Spain (e-mail: esther.dura@uv.es).

J. Bell and D. Lane are with the Ocean Systems Laboratory, School of En-

gineering and Physical Science, Heriot-Watt University, Riccarton, Edinburgh

EH14-4AS, U.K.

Digital Object Identifier 10.1109/JOE.2008.2002962

intelligent, decision making AUV is the current goal in under-

waterrobotics.Inparticular,correctvisualizationandautomatic

interpretation of sonar images can provide AUVs with a wealth

of information, facilitating planning, and decision making, and

therefore, enhancing vehicle autonomy.

In recent years, countermine warfare has become an increas-

ingly important issue and the inherently covert nature of AUVs

make them an appealing platform for shallow-water MCM op-

erations. Images produced from sidescan sonars mounted on

the vehicles are generally used for these purposes. As a re-

sult of the low levels of contrast apparent in the images, the

shadow cast by objects within these images frequently appears

more prominent and gives better clues about the shape and the

size of the object than the highlight. For this reason, much of

the research applying image processing and pattern recognition

techniques to MCM concentrates on analyzing the shadow in-

formation as it is crucial for computer-aided detection (CAD)

and computer-aided classification (CAC) operations. Although

muchresearchhasbeencarriedoutonCAC[1]–[3],theproblem

of classifying mine type and orientation (CAC operations) has

not been widely addressed.

Themaincontributionofthisworkliesintheuseofasuperel-

lipse fitting procedure for CAC operations to recover and clas-

sify mine-like objects in sonar imagery. Superellipses provide

a compact and efficient way of representing the shadows cast

by different mine-like shapes. By simply varying the square-

ness of the superellipse function, different shapes such as el-

lipses, rhomboids, and rectangles can be easily generated. It is

an appealing alternative to feature-based and image-based ap-

proaches because it provides a smart and efficient solution. Al-

though up to date superellipse models have been previously ap-

plied for the detection of primitives in mechanical objects in

video images and segmenting curves into several superellipses

[4], they have not been previously employed in the context of

mine-like object recovery and classification.

Inthiswork,superellipsedetectionisperformedwiththedual

aims of recovering and classifying mine-like shadow shapes.

• Shape recovery: The shadow produced in sonar images

may be not well defined due to speckle noise and the en-

vironment (spurious shadows, sidelobe effects, and multi-

path returns). This may result in missing and noisy bound-

aries, which makes identification difficult. When fitting a

superellipse to the data, the final configuration aids in re-

vealing the closest shape and location of the object. The

recovery process is particularly important to aid 3-D re-

construction of mine-like objects [5].

0364-9059/$25.00 © 2008 IEEE

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DURA et al.: SUPERELLIPSE FITTING FOR THE RECOVERY AND CLASSIFICATION OF MINE-LIKE SHAPES435

• Shape classification: This determines which of the class

representativesismostsimilar. Inthiswork,aparameterof

thesuperellipse,knownasthesquarenessparameter,deter-

mines a variety of shapes including rhomboid, rectangular,

and spherical shapes, and is exploited here to discriminate

between them. In addition, other superellipse parameters,

for example, the axis lengths and the degree of rotation,

may be used to characterize the dimensions and orienta-

tion of the mine.

It is assumed that this classification procedure is part of a

broader detection and classification system and that the region

ofinteresthasbeenobtainedonthebasisofsomepriordetection

method (such as that proposed by Reed et al. [6]) and that man-

made objects have been separated from nonman-made objects.

II. RELATED WORK

In general, classical models consisting of feature extraction

andsubsequentclassificationhavebeenwidelyusedinCACop-

erations. First, using a presegmented shadow, a set of features is

extracted fromthe shadow.This allowstherepresentation of the

imagebyafewdescriptorsprovidingrelevantinformationabout

the extracted shadow rather than the whole set of pixels. Then,

the set of features is normally presented as input to a classifier.

Commonly used feature vectors include Fourier descriptors [7],

[8], shape descriptors [9]–[14], and intensity descriptors [15],

[11],[8],[13].Recently,Zerretal.[16]and Myers[17]usedthe

object height profile of shadow information as a feature vector.

Althoughfeature-basedmethodsareappealing,theperformance

oftheclassifiersdepends,toasignificantextent,upontheability

of the chosen features to accurately represent all of the charac-

teristics of the shadows.

Alternative model-based approaches have been proposed for

the classification of mine-like objects. Based on the observation

that mine-like objects cast a regular and easily identifiable geo-

metrical shape, a priori knowledge can be taken into account to

detect instances of shapes of a determined object. In particular,

thecastshadowofasphereisan ellipseand thecastshadowofa

cylinder is a parallelogram in most of the cases. Therefore, dif-

ferent templates can be defined to detect ellipses and parallelo-

grams.Thisapproachcanbeusedforclassifyingandrecovering

cast shadows more efficiently than feature-based approaches if

a priori information can be introduced.

A model-based approach that combines available properties

of the shape (as a prior model) and an observation model (as a

likelihood model) was proposed by Mignotte et al. [18], to de-

tect and classify mines in sonar imagery. In such terms, they de-

fined a prototype template, along with a set of admissible linear

transformations, to take into account the shape variability for

every type of mine. They also defined a joint probability den-

sity function (pdf), which expresses the dependence between

the observed image and the deformed template. The detection

of an object class was based on an objective function measuring

how well a given instance of deformable template fits the con-

tent of the segmented image. The function was minimal when

the deformed template exactly coincides with the edges of the

shadow contour and contains only pixels labeled as shadows. A

threshold determined whether the desired object was present.

Along similar lines, Balasubramanian and Stevenson [8]

assumed that the shadows from targets such as cones, cylinders,

and rocks were close to an ellipse and hence modeled the

shadow shapes as ellipses. To this end, the edges of the shadow

regions were extracted and then elliptical parameter fitting was

performed using the Karhunen–Loève method. Then, the pa-

rameters were used as features to describe the ellipse. Although

this approach is relevant for spherical mine-like shapes, it was

not the best approach to provide good class separation.

Another classical partial shape recognition technique based

on the extraction of landmarks is that presented by Daniel et al.

[19]. This implementation extracted landmarks from the scene,

followed by a match between these landmarks and model land-

marks, quantified by the difference between the model and the

scene’s Fourier coefficients. In particular, this implementation

performed very well when objects were occluded in the scene.

Alternative approaches have been proposed. Fawcett [20]

worked directly with the image itself as a feature. The basic

approach consisted of applying a principal component analysis

to the image and then a discriminative analysis was used to

determine the vectors that best discriminate the object class.

Afterwards these vectors were used to cluster the images.

Quidu et al. [21] also used a similar technique relying on the

junction of the segmentation and classification steps by using

Fourierdescriptors and genetic algorithms.Although the results

presented in these works are promising, only synthetic data

were used.

In this work, a model-fitting approach is also advocated for

the recovery and classification of the shadow information of

mine-like objects. The scope of the work presented by Bala-

subramanian and Stevenson [8] is extended by modeling the

mine-like shadow with a superellipse.

In sonar imagery, mine-like objects, due to their regular

shape, tend to produce a shadow that also represents a regular

geometrical shape such as those illustrated in Fig. 1. In partic-

ular, the shadow cast by a spherical mine almost always is an

ellipse. For cylindrical mines, the associated shadow may be a

rhomboid, an ellipse, or a rectangle. Therefore, two different

types of templates, as stated by Mignotte et al. [18], could be

defined to characterize these shapes. The main drawback of this

approach [18] is that it may be computationally expensive be-

cause different templates must be defined to describe different

shapes. Consequently, to determine the presence of a mine-like

object, all of the defined templates have to be searched.

Thesuperellipse providesa more compact and interestingap-

proach for representing this variety of shapes. With a simple an-

alytical function composed of small number of parameters (as

describedinSectionIII-B),awiderangeofobjectsincludingel-

lipses, rectangles, rhomboids, ovals, and pinched diamonds can

be represented. In addition, the range of shapes described by a

superelliptical model can be extended by adding parameters to

describe model deformation [5].

III. SUPERELLIPSE MODEL FITTING

A. Superellipses

Superellipses are a special case of curves that are known in

analytical geometry as Lamé curves [22], named after the math-

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436IEEE JOURNAL OF OCEANIC ENGINEERING, VOL. 33, NO. 4, OCTOBER 2008

Fig. 1. Ideal synthetic images of the cast shadow (in black) and echo (white) associated with a spherical and cylindrical mine-like object.

Fig. 2. Various superellipses generated for constant values of ? and ? and dif-

ferent values of ? (denoted as ? in the figure).

ematician GabrielLamé who described these curves in the early

19th century. Piet Hein popularized these curves for design pur-

posesinthe1960sandnamedthemsuperellipses.Barr[23]gen-

eralized the superellipses to a family of 3-D shapes named su-

perquadrics, which became very popular in computer graphics,

and in particular, in computer vision, with the work of Pent-

land [24]. They can represent many closed 2-D and 3-D shapes

in a straightforward and natural way using only a few parame-

ters, and moreover, simple deformations can be applied to ex-

tend their modeling capabilities.

B. Definition of Superellipses

A superellipse centered on the origin, with its axes aligned

with the coordinate system, can be represented by the following

implicit equation:

(1)

wherethelengthsoftheaxesaregivenby and andthesquare-

ness is determined by . Equation (1) involves a complex root

for negative values of

and . Due to the symmetry of the su-

perellipse,thiscanbeavoidedusingtheabsolutevaluesof

as

and

(2)

This would produce the curve in the positive

The curve can then be reflected into the other quadrants.

Fig. 2 shows a superellipse with

, and . A value of

tangle with round corners (very low values of

fect rectangle),

produces an ellipse,

andquadrant.

and

produces a rec-

result in a per-

produces a

equal to

rhomboid, and for values larger than 2, it produces pinched di-

amonds (very large values result in a cross).

The function

(3)

is called the “inside–outside” function because its value de-

termines whether a given point

boundary, or outside the superellipse contour

lies inside, right on the

outside

on the contour

inside

(4)

This can also be defined in parametric form by

(5)

(6)

where

To have real values that can be plotted for every meaningful

value of , (5) and (6) are implemented as

.

(7)

(8)

where

represents the sign.

C. Related Work on Superellipse Fitting

Superellipsecurvesextendthescopeofconicsectionssuchas

ellipses, circles, and lines. Two different approaches have been

explored for fitting superellipses to data points: point distribu-

tionmodels(PDMs)andnonlinearleastsquareminimizationon

an appropriate error of fit function.

Fitting superellipses by PDM was investigated by Pilu [25].

PDM is a term coined by Cootes et al. [26] to indicate statis-

tical finite-element models built from a training set of labeled

contour landmarks of a large number of shape examples. The

key idea of the work proposed in [25] is to use a mathemat-

ical model, which itself represents a class of shapes, to train a

PDM. The training set is built from randomly deformable su-

perellipses and then a method is used for fitting these models to

data points. This approach represents a good balance between

ease of fittingand representational power. However,the compu-

tational requirements are high as a large training data set needs

to be generated.

Few authors have used the superellipse for curve represen-

tation, however segmentation of range images into patches by

usingvariousnonlinearleastsquareminimizationtechniqueson

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DURA et al.: SUPERELLIPSE FITTING FOR THE RECOVERY AND CLASSIFICATION OF MINE-LIKE SHAPES437

an error of fit function [27]–[29] has been wellstudied. Most re-

searchers used the inside–outside algebraic function and some

variations of it as an error of fit.However, as pointed out in[27],

this error function introduces a high-curvature bias that often

leads to counterintuitive results. Based on these results, an error

of fit function relying on the Euclidean distance was suggested

by Gross [27], providing better results [30]. These results in-

spired the work presented by Rosin and West [4].

Rosin and West [4] started working on the problem of su-

perellipse fitting by using a Powell’s optimization technique to

minimize an appropriate error metric based on the Euclidean

distance. However, the technique presented in this earliest work

was computationally expensive as it was a 6-D optimization

problem. Later, Rosin [31] revised this problem setting all the

parameters using either an ellipse or a rectangle except for the

squareness, which was found by 1-D optimization. Also, nine

error of fit measures were compared. Testing on synthetic data

andrealdatacontaminatedwithnoiserevealedthatthe1-Dopti-

mizationwas faster,howeverwhensubstantialamounts ofnoise

and occlusion were added, the 6-D optimization technique [4]

performed much better than 1-D optimization techniques. Hu

[32] used a similar technique to the one proposed by Rosin and

West [4]. The main difference lay in the initialization of the pa-

rameters. Whereas [4] estimated the orientation and the trans-

lation by principal moments and the main axis by fitting an el-

lipse,Hu[32]estimatedthembycomputingthezerothharmonic

of Fourier descriptors. The similarity of the results showed that

any of the techniques can be applied. Thus, both techniques are

good methods for superellipse detection.

D. Technique Implemented for Fitting Superellipses

In this work, superellipses are fitted by finding the set of pa-

rameters that minimize the error measure proposed in [4] and

[27]. In essence, the method is equivalent to the one proposed

in [4], however both the aim and the optimization technique are

different.

Metrics similar to those used for the ellipse fitting [33] and

polynomial fitting [34] have been investigated for fitting a su-

perellipse to a contour of points. The simplest measure is the

algebraic distance given by

(9)

However, experimental results showed that a high curvature

bias is involved, in which the algebraic distance from a point

to the superellipse is underestimated. Other methods such as

weighting the algebraic distance [35] by its gradient have been

proposed to cope with this problem, but they also proved to be

unstable.

Instead, as proposed in [4] and [27], it was chosen to mini-

mize the Euclidean distance

from a data point

shadow contour to the point

the line that passes through

perellipse

(see Fig. 3), where

on the

on the superellipse along

and the center of the su-

(10)

Fig. 3. Illustration of Euclidean distance calculation.

(11)

(12)

Equations (10)–(12) involve evaluating complex roots for

negative values of

and . Nevertheless, this can again be

avoided by using absolute values of

a solution that is evaluated in the positive

The solution can then be reflected into the other quadrants by

determining the quadrant in which the point lies.

The previous equation has been evaluated with the contour

centered on the origin. Nevertheless, to allow for rotation

and translation of the center of the superellipse to the point

, (9) should be modified to

and . This produces

and quadrant.

(13)

whichwouldresultinthemodificationof(2)and(12),andthere-

fore, in more complex calculations. Instead it was decided to

keep the superellipse centered at the origin and aligned with the

coordinates axes. Hence, when fitting data, rather than trans-

forming the superellipse, the data is inversely transformed to fit

the model.

Becausethetermbeingminimizedisnonlinear,aclosed-form

solution is not available. The Nelder–Mead simplex technique

[36], which requires simply the term being minimized, is there-

fore used. The advantage of using this is that it only requires

function evaluations, not derivatives. Also compared to other

optimizationtechniques, thisalgorithm is a simple(numerically

less complicated), robust, and well-tried method for undercon-

strained nonlinear optimization.

With such iterative techniques, it is important to provide

a good initial estimate of the superellipse parameters. In this

work, the initial values of the axis lengths ( and ), the rotation

, and the translation parameters (

fitting an ellipse to the data using the method proposed in [37].

and ) are found by

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438IEEE JOURNAL OF OCEANIC ENGINEERING, VOL. 33, NO. 4, OCTOBER 2008

Fig. 4. Evolution of the superellipse contour during the Nelder–Mead simplex optimization procedure. (a) Original sidescan image. (b) Initial position of the

superellipse contour. (c)–(i) Successive iterations during optimization procedure. (i) Final segmentation with ? ? ?????? leads to classifying the shape as a

rectangular one. (a) and (b) ? ? ???, (c) ? ? ????, (d) ? ? ????, (e) ? ? ????, (f) ? ? ????, (g) ? ? ????, (h) ? ? ??????, and (i) ? ? ??????.

This provided a reasonable initial estimate of all the parameters

except for the squareness. The squareness was initialized to

1.9, which corresponds to a parallelogram shape. Preliminary

experiments showed that initializing the squareness to this

value avoided converging in a local minimum. These initial

values were then used as input to the Nelder–Mead technique

described above, where each parameter

reestimated iteratively until the cost function was minimized

providing a superellipse with the best fit to the data.

The algorithm relies on the fact that the data set does not con-

tainoutliers.Thisisparticularlyimportanttoconsiderastheout-

lying data gives an effect so strong in the minimization that the

estimated parameters may be distorted. As the resulting contour

points are corrupted in most of the cases by some artifacts such

as spurious shadows and the speckle noise effect, consequently

resulting in outliers, a class of robust M-estimators was consid-

ered. The M-estimators attempt to reduce the effect of outliers

by replacing the cost function by another version of the original

cost function.

For this particular case, the cost function

another cost function

was

is replaced by

(14)

where

minimum at zero and

butions have been proposed, because selecting a distribution is

difficultand ingeneral ratherarbitrary.Reasonably goodresults

were obtained by adopting the Geman–McClure distribution

isasymmetric,positive–definitefunctionwithaunique

is the number of points. Several distri-

(15)

Fig.4illustratesthestagesoftheevolutionofthesuperellipse

contour during the Nelder–Mead simplex procedure on a real

sidescan image of a rectangular shape on the seabed. The value

of

at each of these stages is also shown.

E. Extraction of the Contour

Before the superellipse detection procedure, several steps are

required to extract the data points, as illustrated in Fig. 5. First,

the image is segmented by an unsupervised Markov random

field (MRF) algorithm [38]. Second, the image is labeled to

search for the largest region, which corresponds to the mine

shadow. Afterwards an opening morphological operator with

a

structural element is applied to the region to remove

spurious shadows that perturbed the object shape. Finally, the

contour, which contains the data points to be fed into the su-

perellipse detection algorithm, is extracted by using a simple

boundary following algorithm [39]. At this point, it is assumed

that a set of image points plausibly belonging to a superellipse

has been found.

Acontourextractionapproachwasemployedasthisprovided

a robust and fast solution for real-time applications. To extract

the contour points, an accurate and reliable segmentation or

edgemapisrequired.Theextractionofedgesusingedgesopera-

torsfromsonar imagesisdifficultdue tothepresenceofspeckle

noise. However, it has been shown that MRF algorithms are ro-

bust and well suited for the segmentation of sonar images into

shadow and reverberation [38], [40], [41]. Hence, an MRF seg-

mentation algorithm was used to extract the shadow and from it

the contour points [38].

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DURA et al.: SUPERELLIPSE FITTING FOR THE RECOVERY AND CLASSIFICATION OF MINE-LIKE SHAPES439

Fig. 5. Preprocessing of an image to extract the contour.

IV. EXPERIMENTAL RESULTS

A. Data Set

In the following, the performance of the method is qualita-

tively demonstrated with real data. The data was collected in

May 2001 by Groupe d’Etudes Sous-Marines de L’Atlantique

(GESMA) near Brest, France, with the Klein 5400B multibeam

sidescan sonar. The sidescan sonar operated at a frequency of

455 kHz. The system was towed at an average speed of 5 kn by

the GESMA research vessel Aventuriere II.

Fortyeight regionof interest images of targets were extracted

from the data. These images corresponded to 27 images with

rectangular- and rhomboid-like shadow shapes cast by a cylin-

drical object and 21 images with spherical-like shadow shapes

cast by a sphere lying on a pebble seabed. The cylindrical ob-

ject was 2 m long with a radius of 0.5 m and the spherical object

had a radius of 1 m. The images of the targets were acquired at

different azimuth angles and ranges. The dimensions of the ex-

tracted images were 256

128 pixels and had a resolution of

3.3 cm in both

(across range) and (along range).

B. Recovery

The superellipse fitting procedure described in Section III

wasappliedtoall48images.Figs. 6and7displaysomeofthese

results. For each case, the left-hand side column presents the

original image, the MRF segmentation is shown in the center

column, and the resulting fitted superellipse is in the right-hand

side column with the corresponding squareness value. It can

be seen that in the majority of the examples the outline of the

shadow is accurately recovered.

However, in some of the cases, in spite of not accurately rep-

resentingthedimensionsoftherecoveredshape,theyconverged

to the right shape. This is particularly important for classifi-

cation purposes as will be discussed in the next section. It is

also worth notinghowwellthis techniquerecoveredincomplete

shapeswithaveryirregularcontour,asillustratedinFigs.6(c.1)

and 7(c.2).

The recovery rate, which is the percentage of images where

the superellipse fits well to the boundaries of the shadows, re-

sulted in 70.8% (34 of 48 images were well recovered). The

degree of fit was made qualitatively through visual inspection

by looking how well the superellipse was fitting to the bound-

aries oftheshadow. The recoveryratemaybe different from the

classification rate, because the correct shape may be identified

even when the superellipse does not have the correct physical

dimensions (i.e., it is not recovered well).

C. Classification

One of the primary aims of fitting a superellipse to data con-

tour points is to aid the classification task. In this section, the

squareness parameter, which determines the shape of the su-

perellipse, is exploited, sidestepping the use of feature extrac-

tion and classification procedures commonly used in the MCM

operations,forclassificationpurposes.Basedontheobservation

that by varying the squareness at certain ranges specific shapes

are generated (see Fig. 8), the classification procedure relies on

the following decision rule.

• If

or

ogram.

• If

, the cast shadow is spherical.

In particular, for the case of parallelogram shapes, may also

aid in identifying the direction of travel of the sonar with re-

spect to the mine-like object by looking at the skewness of the

shape. If

varies between 0 and 0.6, this signifies that there is

no skewness of the shape (square- or rectangle-like shapes), and

therefore, thedirection ofensonification isorthogonal totheob-

ject’s main axis. On the other hand, when

and 2.5, there is skewness (rhomboid shapes), and therefore, the

direction of ensonification is not orthogonal to the main axis of

the object.

To test the performance of the classification rule, it was ap-

plied to the previously described data set. All images were pre-

processed using the algorithm presented in the previous section.

The initial value of

was set to 1.9.

Table I shows the theoretical and estimated

drical and spherical objects. According to the classification rule

seen above (see Fig. 8), the convergence to a determined value

relates the shadow to classifying the shadow as rectangular,

rhomboid, or spherical. It can be observed that in particular for

, the cast shadow is a parallel-

varies between 1.2

for the cylin-

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440IEEE JOURNAL OF OCEANIC ENGINEERING, VOL. 33, NO. 4, OCTOBER 2008

Fig. 6. (a) Images containing cylindrical mines. (b) Segmentation results using the MRF model. (c) Shadow extraction results using the superellipse model. (a.1),

(b.1), (c.1) ? ? ????; (a.2), (b.2), (c.2) ? ? ????; (a.3), (b.3), (c.3) ? ? ????; (a.4), (b.4), (c.4) ? ? ????; (a.5), (b.5), (c.5) ? ? ????; (a.6), (b.6), (c.6) ? ? ????.

the case of the cylinder for 0 , 178 , and 185 angles of view,

the convergence value is less than 0.6 and hence classifies the

shapes as rectangular. Although the correct shape should be a

perfect rectangular shape, the estimated values represent a rect-

angular shape with curved corners. For the 89 angle of view,

the superellipse did not converge to the right value; it converged

to a square shape

, whereas the right shape should

be an ellipse with

shapepresentedsomeskewness,andtherefore, variedbetween

1.2 and 2.1. For the case of the sphere, it can be observed that

the majority of the

values were well estimated lying within

the range 0.6–1.2. It is worth highlighting that depending on the

. For the rest of the cases, the

slant range to the sphere, the shadow length and therefore the

shape generated varied. This affected the

as can be seen in Fig. 7(c.2) for an angle of 67 , where the el-

liptical shadow shape is not so well defined resulting in a value

of

of 0.85. However, in the criteria used for the classification,

this shape is still considered an elliptical shape. On the other

hand, for well-defined elliptical shadow shapes, such as the one

depicted in Fig. 7(c.4), the algorithm converged with

which is very close to a perfect elliptical shape.

Fig. 9 illustrates the classification results. In summary,

80.95% (17 of the 21 mine-like objects) of the images con-

taining spherical-like shapes and 81.4% (22 of the 27 mine-like

convergence value

,

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DURA et al.: SUPERELLIPSE FITTING FOR THE RECOVERY AND CLASSIFICATION OF MINE-LIKE SHAPES441

Fig. 7. (a) Images containing spherical mines. (b) Segmentation results using the MRF model. (c) Shadow extraction results using the superellipse model. (a.1),

(b.1), (c.1) ? ? ????; (a.2), (b.2), (c.2) ? ? ????; (a.3), (b.3), (c.3) ? ? ????; (a.4), (b.4), (c.4) ? ? ????; (a.5), (b.5), (c.5) ? ? ????; (a.6), (b.6), (c.6) ? ? ????.

objects) of those containing rectangular- and rhomboid-like

shapes were classified correctly. This resulted in a total of

81.25% (39 of the 48 mine-like objects) over all the images.

When discriminating between rhomboid and rectangular

shapes, the total percentage of correct classification dropped to

75% (36 of the 48 mine-like objects). All 3 of the square shapes

(100%) and 16 of the 24 rhomboid shapes (66.6%) were classi-

fied correctly, resulting in total classification rate of 70.37% for

the images containing rhomboid- and rectangular-like shapes.

Of the 33.3% rhomboid-like images misclassified, 62% of these

converged to a rectangular-like shape and 37% to spherical-like

shapes. In this case, it is a preferable for the algorithm to

misclassify the shapes as rectangular because this is closer than

the sphere shape to the correct classification of rhomboid.

Theclassificationcouldthenbeimprovedusingtheadditional

superellipse parameters. These would provide an indication of

the size of the object from the axis lengths, and its orientation

on the seabed. This would require a calibration of the technique

usingtheresolutionofthesonar,andtherangeofthetargetfrom

the sensor. This could assist in the elimination of some false

alarms, if their other superellipse parameters were found to be

unrealistic of typical mine dimensions. Further work could also

lookatsubsequentlyfittingasuperellipsetothehighlightaswell

as the shadow to extract further information about the target.

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442IEEE JOURNAL OF OCEANIC ENGINEERING, VOL. 33, NO. 4, OCTOBER 2008

Fig. 8. Various superellipses generated for constant values of ? and ? and different values of ? (denoted as ? in the figure) showing the influence of ? for classifi-

cation purposes: (a) and (b) square- and rhomboid-like shapes (parallelogram shapes), respectively, and (c) elliptical shapes. All figures show upper right quadrant

only. The minimum and maximum values of ? are placed near the correct line, with an increment of 0.1 for the lines in between.

Fig. 9. Classification results with and without making a distinction between

rhomboid and rectangular shapes.

The classification procedure may not be able use the square-

ness parameter,

in isolation, without considering the degree

of fit obtained from the fitting procedure or a prior detection

stage to eliminate nonmine-like targets. The examples shown in

Fig. 10 show two objects that are not mines. In the first case, the

superellipse converged to a parallelogram

everthedegreeoffitobtainedfromthecostmeasurewouldhave

rejected the object as mine-like. In the second case, the object

would be classified as spherical

further analysis to classify correctly as not mine-like because

visually it appears to display mine-like characteristics.

, how-

, and would require

Fig. 10. (a) Images containing nonmine objects (clutter) (b) with shadow ex-

traction using superellipse model.

V. CONCLUSION AND FURTHER RESEARCH

This work presented a simple approach for the classification

and recovery of man-made object shapes in sidescan sonar im-

ages using a superellipse template matching scheme. The ap-

proach used a priori knowledge of the geometry of the cast

shadow in sidescan sonar images. The method was tested on a

large number of noisy sidescan images providing an overall re-

covery rate of 70% (34 of the 48 mine-like objects) and a classi-

fication rateof 81% (39 of the 48 mine-like objects). The results

indicate that this may be a feasible approach for object classifi-

cation purposes for use in combination with a man-made object

detection system. The technique is applicable to high-resolu-

tion sidescan images, where the shadow region is represented

by several pixels in either direction. The resolution of the sonar

will determine the smoothness of the shadow contour, which

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DURA et al.: SUPERELLIPSE FITTING FOR THE RECOVERY AND CLASSIFICATION OF MINE-LIKE SHAPES443

TABLE I

THEORETICAL AND EXPERIMENTAL VALUES FOR ? FOR THE CYLINDER AND THE SPHERE SEEN UNDER DIFFERENT ANGLES OF VIEWS. FOR THE CYLINDER,

THE RESULTS ARE CLASSIFIED IN THREE CATEGORIES: 1) WITHIN THE EXPECTED RANGE, 2) CYLINDER BUT IN ANOTHER RANGE WINDOW, AND

3) OUTSIDE THE EXPECTED SHAPE RANGE. THOSE IN CATEGORY 2) ARE ANNOTATED BY AN ASTERISK. THE ONES IN CATEGORY 3)

ARE INDICATED IN BOLD. FOR THE SPHERE, THE RESULTS ARE CLASSIFIED IN TWO CATEGORIES: 1) WITHIN THE EXPECTED

RANGE AND 2) OUTSIDE THE EXPECTED SHAPE RANGE (ANNOTATED BY AN ASTERISK)

can be extracted and will have implications on the degree of fit

to the superellipse. However, the technique provides an alterna-

tive to traditional feature-based or image-based approaches that

require a suitable training set.

Although the work presented in this paper has concentrated

on specific mine-likes shapes, with further extensions, the po-

tential of the superellipse could be expanded. In particular, the

superellipse could also represent the shadows cast by truncated

cone and pipeline shapes with the inclusion of bending and ta-

pering transformations [5].

ACKNOWLEDGMENT

The authors would like to thank B. Zerr from Groupe

d’Etudes Sous-Marines de L’Atlantique (GESMA) for pro-

viding images for the elaboration of this work.

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Esther Dura received the M.Eng. degree in com-

puting science from Universidad de Valencia,

Valencia, Spain, in 1998, the M.Sc. degree in

artificial intelligence from The University of Ed-

inburgh, Edinburgh, U.K., in 1999, and the Ph.D.

degree in computing and electrical engineering from

Heriot-Watt University, Edinburgh, U.K., in 2003.

Her thesis investigated the use of computer vision

and image processing techniques for the classifi-

cation and reconstruction of objects and textured

seafloors from sidescan sonar images.

From 2003 to 2006, she was a Postdoctoral Researcher working on remote

sensing and biomedical applications at the Departments of Electrical and Com-

puting Engineering and the Department of Biomedical Engineering, Duke Uni-

versity, Durham, NC. Her research interest include artificial intelligence, pat-

ternrecognition,computerandimageprocessingtechniquesforremotesensing,

imageretrieval,andmedicalapplications.SheiscurrentlyworkingasaLecturer

at the Department of Computer Engineering, Universidad de Valencia.

Judith Bell received the M.Eng. degree (with merit)

in electrical and electronic engineering and the Ph.D.

degree in electrical and electronic engineering from

Heriot-WattUniversity,Edinburgh,U.K.,in1992and

1995, respectively. Her thesis examined the simula-

tion of sidescan sonar images.

Currently, she is a Senior Lecturer in the School of

EngineeringandPhysicalSciences,Heriot-WattUni-

versity and is extending the modeling and simulation

work to include a range of sonar systems and to ex-

amine the use of such models for the verification and

development of algorithms for processing sonar images.

David Lane received the B.Sc. degree in electrical

and electronic engineering and the Ph.D. degree in

electrical and electronic engineering for robotics

work with unmanned underwater vehicles from

Heriot-Watt University, Edinburgh, U.K., in 1980

and 1986, respectively.

Currently, he is Professor in the School of

Engineering and Physical Sciences, Heriot-Watt

University, Edinburgh, U.K., and Director of the

University’s Ocean Systems Laboratory. He has

previously held a Visiting Professor appointment

in the Department of Ocean Engineering, Florida Atlantic University and is

Co-Founder/Director of See-Byte Ltd. He leads a multidisciplinary team who

partners with U.K., European, and U.S. industrial and research groups on

multiple projects supporting offshore, Navy, and marine science applications.

He has published over 150 journal and conference papers on tethered and

autonomous underwater vehicles, subsea robotics, image processing, and

advanced control.

Dr. Lane has been an Associate Editor of the IEEE JOURNAL OF OCEANIC

ENGINEERING, and regularly acts on program committees for the IEEE Oceans

and Robotics and Automation annual conferences.

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