Superellipse Fitting for the Recovery and Classification of MineLike Shapes in Sidescan Sonar Images
ABSTRACT Minelike 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 minelike objects in sidescan sonar images is presented. Superellipses provide a compact and efficient way of representing different minelike 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 closedform solution is not available. Hence, the parameters of the superellipse are estimated by the NelderMead 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 minelike objects) and a classification rate of better than 80% (39 of the 48 minelike objects).

Article: The ovuscule.
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ABSTRACT: We propose an active contour (a.k.a. snake) that takes the shape of an ellipse. Its evolution is driven by surface terms made of two contributions: the integral of the data over an inner ellipse, counterbalanced by the integral of the data over an outer elliptical shell. We iteratively adapt the active contour to maximize the contrast between the two domains, which results in a snake that seeks elliptical bright blobs. We provide analytic expressions for the gradient of the snake with respect to its defining parameters, which allows for the use of efficient optimizers. An important contribution here is the parameterization of the ellipse which we define in such a way that all parameters have equal importance; this creates a favorable landscape for the proceedings of the optimizer. We validate our construct with synthetic data and illustrate its use on real data as well.IEEE Transactions on Software Engineering 02/2011; 33(2):38293. · 2.59 Impact Factor  SourceAvailable from: InTech09/2011; , ISBN: 9789533073453

Conference Paper: Coupled curve evolution equations for ternary images in sidescansonar images guided by Lamé curves for object recognition
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ABSTRACT: This paper proposes a new level set segmentation method which is guided by a parametric prior force based on Lamé curves. The use of prior knowledge is advantageous in order to improve the segmentation results in terms of matching expected object types because one can in general state that for different applications some shapes are more likely than others. By avoiding complex shape training processes the level set idea is extended with a parametric prior shape which forces the level set evolution to propagate towards the desired objects by not overpowering the image properties. Also a cross talk evolution is discussed for ternary images to handle correlations between adjacent or correlated objects.Image Processing (ICIP), 2012 19th IEEE International Conference on; 01/2012
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434IEEE JOURNAL OF OCEANIC ENGINEERING, VOL. 33, NO. 4, OCTOBER 2008
Superellipse Fitting for the Recovery and
Classification of MineLike Shapes in
Sidescan Sonar Images
Esther Dura, Judith Bell, and Dave Lane
Abstract—Minelike 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 minelike objects in sidescan sonar images
is presented. Superellipses provide a compact and efficient way
of representing different minelike 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
closedform 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 minelike objects) and a classification rate of
better than 80% (39 of the 48 minelike objects).
Index
sidescan, sonar, superellipse fitting.
Terms—Classification,minelikeobjects,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 HeriotWatt University, Edinburgh, U.K.
Associate Editor: D. A. Abraham.
E. Dura is with the Institute of Robotics, Universidad de Valencia, Paterna,
Valencia 46071, Spain (email: esther.dura@uv.es).
J. Bell and D. Lane are with the Ocean Systems Laboratory, School of En
gineering and Physical Science, HeriotWatt University, Riccarton, Edinburgh
EH144AS, 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 shallowwater 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 computeraided detection (CAD)
and computeraided 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 minelike objects in sonar imagery. Superellipses provide
a compact and efficient way of representing the shadows cast
by different minelike 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 featurebased and imagebased 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
minelike object recovery and classification.
Inthiswork,superellipsedetectionisperformedwiththedual
aims of recovering and classifying minelike 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 3D re
construction of minelike objects [5].
03649059/$25.00 © 2008 IEEE
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DURA et al.: SUPERELLIPSE FITTING FOR THE RECOVERY AND CLASSIFICATION OF MINELIKE 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 nonmanmade 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.
Althoughfeaturebasedmethodsareappealing,theperformance
oftheclassifiersdepends,toasignificantextent,upontheability
of the chosen features to accurately represent all of the charac
teristics of the shadows.
Alternative modelbased approaches have been proposed for
the classification of minelike objects. Based on the observation
that minelike 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 featurebased approaches if
a priori information can be introduced.
A modelbased 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 minelike 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 modelfitting approach is also advocated for
the recovery and classification of the shadow information of
minelike objects. The scope of the work presented by Bala
subramanian and Stevenson [8] is extended by modeling the
minelike shadow with a superellipse.
In sonar imagery, minelike 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 minelike
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
describedinSectionIIIB),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 minelike 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 3D 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 2D and 3D 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 finiteelement 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 MINELIKE 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 highcurvature 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 6D 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 1D optimization. Also, nine
error of fit measures were compared. Testing on synthetic data
andrealdatacontaminatedwithnoiserevealedthatthe1Dopti
mizationwas faster,howeverwhensubstantialamounts ofnoise
and occlusion were added, the 6D optimization technique [4]
performed much better than 1D 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,aclosedform
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 welltried 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 Mestimators was consid
ered. The Mestimators 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 realtime 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 MINELIKE 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 SousMarines 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 rhomboidlike shadow shapes cast by a cylin
drical object and 21 images with sphericallike 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 lefthand side column presents the
original image, the MRF segmentation is shown in the center
column, and the resulting fitted superellipse is in the righthand
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 minelike 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 rectanglelike 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 welldefined 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 minelike objects) of the images con
taining sphericallike shapes and 81.4% (22 of the 27 minelike
convergence value
,
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DURA et al.: SUPERELLIPSE FITTING FOR THE RECOVERY AND CLASSIFICATION OF MINELIKE 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 rhomboidlike
shapes were classified correctly. This resulted in a total of
81.25% (39 of the 48 minelike 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 minelike 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 rectangularlike shapes.
Of the 33.3% rhomboidlike images misclassified, 62% of these
converged to a rectangularlike shape and 37% to sphericallike
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 rhomboidlike 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 nonminelike 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 minelike. In the second case, the object
would be classified as spherical
further analysis to classify correctly as not minelike because
visually it appears to display minelike 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 manmade 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 minelike objects) and a classi
fication rateof 81% (39 of the 48 minelike objects). The results
indicate that this may be a feasible approach for object classifi
cation purposes for use in combination with a manmade object
detection system. The technique is applicable to highresolu
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 MINELIKE 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 featurebased or imagebased approaches that
require a suitable training set.
Although the work presented in this paper has concentrated
on specific minelikes 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 SousMarines 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
HeriotWatt 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
HeriotWattUniversity,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,HeriotWattUni
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
HeriotWatt University, Edinburgh, U.K., in 1980
and 1986, respectively.
Currently, he is Professor in the School of
Engineering and Physical Sciences, HeriotWatt
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
CoFounder/Director of SeeByte 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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