Canonical Coordinates for Detection and

Cassification Underwater Objects Fro onar

Imager

James D. Tucker a, Mahmood R. Azimi-Sadjadi a, and Gerry J. Dobeck ba Department of Electrical and Computer Engineering, Colorado State University,

Fort Collins, Colorado 80523, Email: dtucker@engr.colostate.edub Naval Surface Warfare Center Panama City Panama City, FL, USA 32407-7001

Abstract-Detection and classification of underwater objectsin sonar imagery are challenging problems. In this paper, a newcoherent-based method for detecting and classifying potential tar-gets in high-resolution sonar imagery is developed using canonicalcorrelation analysis (CCA). Canonical coordinate decompositionallows us to quantify the changes between the returns from thebottom and any target activity in sonar images and at the sametime extract useful features for subsequent classification withoutthe need to perform separate detection and feature extraction.Moreover, in situations where any visual analysis or verificationby human operators is required, the detected/classified objectscan be reconstructed from the coherent features. In this paper,underwater target detection and classification using the canonicalcorrelations extracted from regions of interest within the sonarimage is considered. Test results of the proposed method onunderwater side-scan sonar images provided by the Naval SurfaceWarfare Center (NSWC) in Panama City, FL is presented. Thisdatabase contains synthesized targets in real background varyingin degree of difficulty and bottom clutter. Results illustratingthe effectiveness of the CCA-based detection and classificationmethod are presented for various densities of background clutterand bottom difficulty.

I. INTRODUCTION

Detection and classification of underwater objects in sonarimagery is a complicated problem due to various factors suchas variations in operating and environmental conditions, pres-ence of spatially varying clutter, variations in target shapes,compositions and orientation. Moreover, bottom features suchas coral reefs, sand formations, and the vegetation may totallyobscure a target object.

Various methods have been explored for target detectionand classification in sonar imagery. In [1], [2] Dobeck utilizesa nonlinear matched filter to identify mine-size regions inthe sonar image that match the target signature. For eachdetected region several features are extracted based on thesize, shape, and strength of the target signature. A stepwisefeature selection process is then used to determine the subsetof features that optimizes the probability of detection andclassification. A k-nearest neighbor and an optimal discrim-ination filter classifier are used to classify each feature vectorand the decisions of the two classifiers are fused for thefinal decision In [3] Ciany segments the sonar images into"sub-frames" on which each frame is adaptively thresholded

to identify the target structure. Geometric features are thenextracted from contiguous target structure regions of interestwithin the sub-frame. Classification of each region as targetor non target is done through a multi-level weighted scoring-based classification system. In [4] Adridges presented anadaptive clutter filter detector which exploits the differencein correlation characteristics between clutter and targets. Afterdetection, features are extracted and then orthogonalized andthen the classification is performed on the orthogonal featureset through an optimal Bayesian classifier. Chandran in [5]presented the use of a matched filter designed to capture thetarget structure. Higher order spectra are then extracted asthe feature set to classify objects using a k-nearest neighborclassifier, a minimum distance classifier, and a thresholdclassifier based on the minimum and maximum values of afeature obtained over all classes, and the final decision arefused.One detection and feature extraction method that has not

been explored for sonar imagery is Canonical CoordinateAnalysis or (CCA). This method has shown great promise inunderwater target classification problems using sonar backscat-ter [6]. The canonical coordinate decomposition method de-termines linear dependence [7] or coherence between two datachannels. This method not only determines the amount ofdependence or independence between two data channels (e.g.two sonar pings with certain separation) but also extracts,via the canonical coordinates, a subset of the most coher-ent features for classification purposes. Canonical coordinatedecomposition allows us to quantify the changes betweenthe returns from the bottom and when target activities arepresent and at the same time extract useful features for targetclassification without the need to perform separate detectionand anomaly feature extraction.

In this paper a new coherent-based detection and classifi-cation method for high resolution sonar imagery is developedusing CCA as an optimal Neyman-Pearson detection schemeand a feature extraction process In both cases the canonicalcorrelations are formed from region of interests (ROI) withinthe sonar image. From tbese canonical correlations, coherence(or incoherence) can be measured and used to determine if a

target is present in the processed ROI and then the extracted

1-4244-0635-8/07/$20.00 ©2007 IEEE

features can then be used to classify the detected ROI's. Thedata set used in this study was provided by the NSWC inPanama City, FL. The data-set consists of high-resolution side-looking sonar imagery that contains either no targets, onetarget, or multiple targets.

This paper is organized as follows: Section II reviewsthe CCA method and its application as a feature extraction(estimation framework) or as a detection tool for imple-menting the Neyman-Pearson detector. Section III describesthe preprocessing and feature extraction process done on theNSWC Scrub data set to extract the canonical correlations. InSection IV, the detection and classification results of usingCCA to detect and classify of underwater targets in sonarimagery are presented. Finally, conclusions and observationsare made in Section V.

II. REVIEW OF CANONICAL COORDINATEDECOMPOSITION

CCA is a method that determines linear dependence (orcoherence) between two data channels by mapping the data totheir canonical coordinates where linear dependence is easilymeasured by the corresponding canonical correlations. Thelanguage and terminology used in this section is taken mostlyfrom [7], [8].

Consider two data channels x c IR and y c RnJxRwhere m < n, when it is assumed that x and y are zero meanrandom vectors that yield a composite covariance matrix

E (x ) Hff H R0. z Rxy (1

where, RXX, RA and Rxy = RH are the covariance matricesof data channels x, y, and between x and y respectively. Thesingular value decomposition (SVD) of the coherence matrixC may then be written as [7]

C~ A 20xR -072 FKGH and FHCG = K

FHF= I, GHG = I, K = diag[kl, k2 -.. .,k];(2)

where A-1/2R R-f I, and R1/2RH2 = R, Notethat for this SVD, only the nonzero singular values of C andtheir corresponding nonzero vectors are considered.The canonical coordinates of x and y can now be defined

as [7]

x - , r,> Classification

R K~~~~R 1/2 GH r

Ryy G

y J Detection

Fig. 1. Canonical Coordinate Decomposition Process.

via the canonical decomposition matrices WH = FHR 1 /2and DH = GHR0112 (see Figure 1). The canonical coordi-nates u and v share the composite covariance matrix

E u UH vH) Ru Ru0

WHRXXW WHR,YDDHRyxW DHR00D

where the diagonal cross-covariance matrix

K = R,, = FHCG = WHR,YD

_FI K (K I 2'

-(5)

(6)is the canonical correlation matrix of canonical correlationskj; i = 1, 2, . .. 7 m, with I > ki > k2 > ..> km > 0 [7].Note that we have E[uiv ] = ki (i-J), where 8( ) representsthe Kronecker delta function.One of the most important properties of canonical corre-

lations is that they are invariant under uncoupled nonsingulartransformations of x and y [7]. Canonical correlations can alsobe used to determine useful properties regarding x and y, suchas linear dependence (coherence) and mutual information [7].A. CCA As An Detection Tool [8]

The detection problem is stated as a hypothesis testing prob-lem of distinguishing hypothesis of Ho: y CN [0 ARn]i.e. noise alone, versus hypothesis H1: y CN [0, Ryy =

Rxx+Rrn] i.e. signal plus noise, where CNn[0, Rxx] denotesthe n-variate proper complex normal distribution with meanvector zero and covariance matrix RXX. In [8] the Neyman-Pearson detector for testing Ho and HI as defined aboveis written as the log-likelihood ratio in terms of canonicalcoordinates and correlations as,

I (y) = (RA00'2y))H(j _CH) (R- 1/2wy))

,-1/2 xA 1120 1 x (3)0 AR> [Yj

where elements of the u and v vectors are the canonicalcoordinates of x and y, respectively.Hence x and y are mapped to their respective canonical

coordinates using

U=WHx and v DHy (4)

(GHRI 2 )H([ K2_ ]JJy 1-[ )(GH -'/2 )I GRyy y(7)

This is the standard Gauss-Gauss log-likelihood ratio, but inthe canonical coordinates v GGHAR y and I(y) is theweighted sum of the magnitude-squared of the canonical coor-dinates weighted by canonical correlation-dependent weights.If we define G& Y Yrg then (y) can be written asfollows,

0

i yy0*-1

k2\ik27 )I (8)

u]1 7H oH]v = L GH

The J-divergence [8] between H1 and Ho is

J =EHI(Y) -EHol(Y) = tr(CCH + (CCH)-1- 21)tr(KKH + (KKH)-1 -21)

(9)where EHO and EH1 are the expected values of I(y) under Hoand H1, respectively. We then can rewrite the J-divergence interms of the canonical correlations as,

m2

J r(ki- 1)2 (10)i=1

The function (ki - _1_)2 is non-increasing in the interval(0, 1]. Consequently the rank-r detector that maximizes thedivergence is the detector that uses the dominant coordinatescorresponding to the dominant canonical correlations ki. Thedivergence between the two hypothesis considering the rdominant canonical correlations is,

Ir2

Jr = E(ki - ) (11)kbji=l

Thus, tor building low-rank detectors, the dominant canonicalcoordinates need to be retained in order to find the coherencebetween the two data channels x and y. Using the coherenceone can find the information necessary to detect presence ofa target in the environment.

B. CCA As An Estimation or Feature Extraction Tool [8]

The estimation problem is stated as estimating channel x

(signal) from channel y (observation). The minimum mean

square error estimator of x from y can be written as [8],

x R1/2FGH - /2y (12)

with minimum error covariance

Qxx = R-j /2F(I K2)FHRH/2 (13)

The volume of the error concentration ellipse divided by thevolume of the prior concentration ellipse is

det (QxV = = det(I -K2). (14)

det (RXX)The processing gain (PG) and the information rate (R) given[8] in terms of V as PG = v` and R = -(1/2)logV,respectively. It is clear that the dominant canonical coordinatesare the ones that minimize V, maximize PG, and maximizeR. Thus the optimal rank-r < n estimator of x, of x, from

y, is the estimator that retainls only the dominanlt canonicalcoordinates and maximizes the coherence between x and y.

In canonical coordinate domain this rank-r estimator can bedefined as

X-k=R-1/2F GH- 1/2 5xx FKrG yyR Y (15)

and it can be shownu = Krv, (16)

where Kr holds the top r dominant canonical correlations.In this framework, classification can then be made by using

Classification

Detection

Channelizeby Columns

x(m,n)

SonarImage

Normalization Image-* & > Partitioning _

Preprocessing into ROI'sEach ROI

EstimationFramework

DetectionFramework

Fig. 2. Block Diagram of the Side Scan Sonar CCA-based Detection Method.

either the dominant canonical correlations as a feature vectoror using u- KrV which shows how well x can be estimatedfrom y where the target is more coherent than the environmentin which it is found.

III. CCA ANALYSIS OF HIGH RESOLUTION SONARIMAGERY

In order to prepare the data for CCA, the high resolu-tion images are first normalized using a serpentine forward-backward filter [9]. The purpose of this normalization is tohelp distinguish the target's highlight and shadow signaturefrom the bottom and artifacts present in the image. Thepurpose of the normalization is to reduce the variability ofthe local mean throughout the image in order to use it asa reference level so that the highlight and shadow of thetarget can be more easily identified. The serpentine forward-backward filter (SFBF) normalizer first uses a forward secondorder digital filter and attempts to select a path in which thefilter output best follows the original image. Basically the pathis generated by taking the next point on the path to a pointwhere its neighbors intensity are near the filtered output value.The purpose of the forward and backward filters is to estimatethe local mean on one side of a pixel and the backward filteris used to estimate the local mean on the opposite side of thepixel. The local mean estimate that is nearest to the originalimage value is selected to normalize that pixel. Processing theimage in the forward-backward direction helps preserve targetedges, highlights, and shadows. Any background non-ideals,.e. target size artifacts are normalized out to the underlyingmean of the image. or a more detailed explanation of thenormalization algorithm the reader is referred to [9].

After the normalization process, the first 120 pixels areignored which corresponds to the sonar altitude as it traveledthrough the water column, which is I 10h of the maxiumrange. Next, the image is partitioned into overlapping ROI'sof size Al x N. For this data set the ROI size of 12 x 34was experimentally determined to be optimal considering theaverage size and shape of the targets in the data set. Theoverlap along the horizontal and vertical directions was 500

&i

in order to ensure that a target would be covered by more thanone ROI in case of splitting. Each ROI is then channelized in acolumn-wise fashion for CCA. The x and y channels consistof the first 8 pixels in one column x and the first 8 pixelsin the adjacent column y. This process is continued movingin the horizontal direction across the ROI. On the next passthrough the ROI, the channels are given a 50% overlap in thevertical direction to ensure complete coverage of the target inthe ROI (see Figure 2). The idea behind this channelizationis to look for common coherent attributes that can be usedto relate one channel to the other according to the frameworkdiscussed in Section It-A. Clearly, for background ROI s highlevel of coherence among consecutive columns (channels) doesnot exist. Note that in this paper we use the dominant canonicalcorrelations which hold the coherent information between thetwo channels. One may also use the subdominant canonicalcorrelations in the detection framework to detect incoherence(or change) between the two channels. From the dominantcanonical correlations namely k, and k2 a scalar detectionmeasure of k1 x k2 was formed for each processed ROI. Basedon this measure (instead of J-divergence in (I 1)) a threshold isdetermined experimentally to separate the ROI's that containtargets from those that do not. Following the detection, all thecanonical correlations extracted from each ROI are used toclassify target and non-target ROI's using a back propagationneural network (BPNN) classifier.

IV. TEST RESULTS ON SONAR IMAGERY

CCA was applied to a data set of high-resolution side-looking sonar images provided by the NSWC, Panama City.More information on high-resolution side-looking sonars canbe found in [10], [11]. The database contains 512 imageswith 293 images containing 310 targets with some of theimages containing more than one target. The data set wasbroken up into easy, medium, and hard cases depending onthe difficultly of the background clutter and bottom types, e.g.vegetation and coral reefs. Easy cases are considered to havelow background variation and an overall smooth bottom withtargets that are easily identifiable by a skilled operator. Themedium cases contain background clutter and more difficultbottom conditions. However, the targets are still somewhatdiscernible to a skilled operator with some effort. Lastly, thehard cases are those where it is difficult to detect and classifythe targets from a visual inspection due to a high variability ofbackground clutter and very difficult bottom conditions. Thedata set was separated into these three classes based on a visualinspection of where the target was located and whether or notvariation in the background and high density of clutter waspresent.

To show the separability of the dominant canonical cor-relations for ROI's that contain targets and background andthose that contain only background, a test was conducted onthe entire set of target ROI's and a random set of ROI'scontaining mainly background (for all three cases) of thesame number of target ROI s. The plots of the 8 canonicalcorrelations of ROI's containing targets and those containing

Target vs. Background

0.4

0.3

k.'s

Fig. 3. Plot of Canonical Correlations for Target and Background.

0.91

0.8

TargetBackground

0.7 t

0.6 t

,g,0.5 _x

0.4 x

0.3

0.2 O 0 - u

0i50 100 150 200 260 300 360Cases

Fig. 4. Separation of Target versus Background for k, x k2i

background only are shown in Figure 3. As can be seen,there is good separation, especially for dominant canonicalcorrelations, between targets and background, which can beattributed to the greater coherence in the channels acrossthe targets versus the background where there is more pixelvariation. This is attributed to the greater coherence betweenx and y over an ROI where a target is present.

Using the dominant canonical correlations, k, and k2 ascalar decision measure of k x k2 can be formed for theentire target set This scalar value was formed and plottedfor the entire target set and random set of backgrounds andis presented in Figure 4. A detection threshold was chosenbased upon this measure to detect potential targets from thebackground From this set of targets and limited number ofbackgrounds the optimal threshold value was chosen to be0.3.

Each image in the entire NSWC database is then blocked

ROC curve on Testing Set

0.9 -

P =92%

0.8 - Pfa=8%

0.7

0.1 0.2 0.3 0.4 0.5pFA

0.1 0.2 0.3 0.4 0.5pFA

Fig. 5. Performance Curve for Two Layer BPNN Classifier on Testing Set.

into 12 x 34 ROI's with a 50% overlap for each block inboth the range and cross-range directions. For each ROI thecanonical correlations were formed as well as k, x k2 scalardetection measure and then compared against the optimalthreshold. For the easy cases, there are 186 images containing201 targets. The canonical correlation detector detected all butI of the targets in the set with an average of 127 detections per

image. For the medium cases, there are 86 images containing89 targets and the canonical correlation detector again detectedall but I of the targets in the set with an average of 213detections per image. Lastly, for the hard cases, there are 21imiages, containinlg 21 targets, and the canLonLical correlationdetector detected all but 2 of the targets and averaged 228detections per image. It is important to note that with 50%overlap in the ROI's there will be at least 4 ROI's overlappingthe object depending on the object length. Taking this intoaccount into the number of detections, it was determined whichof the detected ROI's were actually over the target whichthen gives an average of 116 detections on the easy set, 200detections on the medium set, and 213 detections on the hardset.

The detected ROI's were then broken up into training anda testing set to train and test BPNN classifier. A networkstructure was determined experimentally and the structure thatperformed the best was a two-layer network with 8 inputs,20 neurons in the first hidden layer, and 2 output neurons.

The receiver operator characteristic (ROC' curve for the entiretesting set is presented in Figure 5. The BPNN performsextremely well on the testing set with the knee point on

the ROC gives 92% correct classification rate and 8% false

alarm rate This shows the power of the CCA based featureextraction method.The trained classifier was then applied to all the detected

ROI's in the easy, medium, and hard data sets that were

mentioned earlier The classifier ROC curves are presented inFigure 6 for the three cases. The classifier performs extremely

Fig. 6. Performance Curve for Two Layer BPNN Classifier on Target Sets.

well on the easy and medium sets with the knee points at90% correct classification rate and 110% false alarm rate forboth cases. The classifier did not perform as well on thehard data set with only 84% correct classification and 16%false alarm rate. Nonetheless, considering the difficulty of thebottom conditions and background clutter the classificationrate is acceptable. Overall, the classifier performs well on allthe data sets by keeping the correct classification rate high andthe false alarm rate low using just the canonical correlationsas the feature vector.

V. CONCLUSIONS AND OBSERVATIONS

In this paper, CCA was used as an optimum Neyman-Pearson detector to detect underwater targets and as a featureextraction tool for classification of underwater targets in high-resolution side-looking sonar imagery. The basic idea is thatwhen an object (target or non-target) is present in an ROI inthe sonar image there will be a change in the coherence levelcompared to the case when there is no object. Further it hasbeen shown that using the dominant canonical correlations a

scalar decision measure can be formed in order to separate theROI's that contain a target from those that contain backgroundonly and can also be used to classify the ROI's that contain a

target from those do not. The extracted features, or canonicalcorrelations, can then also be used as a classification toolto classify the ROI's which contain a target and those thatdo not without the need to perform a separate anomalyfeature extraction for classification. Our experiments on thedata set provided by the NSWC demonstrated that there isgood separability of the canonical correlations, especially thedominant ones, extracted over ROI's containing targets fromthose extracted from ROI's that do not contain targets Overall.CCA did well in detecting all of the targets in all of the imagesmissing only 4 of the possible 310 targets in the set, whilekeeping the probability of detection high and false alarm ratelow. Classification using CCA features gave good results given

C)

0.9

0.8

0.7

Easy Set

Medium Set

Hard Set

0.6

0 .

DC. 0.5

0.4

0.3

0.1

O _0 0.6 0.7 0.8 0.9 10.6 0.7 0.8 0.9

the limited size of the training set. The results showed anaverage of 88% correct classification rate with an average of12% false alarm rate. Thus, CCA shows great promise as aprimary detection and classification tool for underwater targetsin sonar imagery.

ACKNOWLEDGMENT

This work was supported by the Office of Naval Research,Code 3210E under contract #N61331-06-C0027

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