Despite significant technical advances, only a limitednumber of pattern-recognition problems are solved atpresent by conventional optical correlators. In thiscase, for pattern-recognition procedures for which apattern is not recognized by itself ~e.g., by correlationwith a reference basis! but rather by identification ofits attitude andyor behavior, the pattern-recognitionproblem becomes a situation- or signature-recognition problem. Various techniques can beused to generate a signature, depending on the ap-plication and the available data ~multisensor ~MS!,ime–frequency domain representations, etc.!. Inuch a framework Fourier analysis is one of the pos-ible candidates for data space representation. Theain argument justifying this choice lies in the rel-
tive simplicity and efficiency of its implementationith either optical or digital hardware. This choice
s particularly justified when applications requireeal-time processing.
On the basis of a previous study,1 we propose toinvestigate this principle in the case of optical corre-lators, by introducing technical constraints that are
The authors are with the Departement d’Optique, Unite Mixtede Recherche, Centre Nationale de la Recherche Scientifique 6616,Ecole Nationale Superieur de Telecommunications de Bretagne,
P 832, 29285 Brest Cedex, France. J. L. de Bougrenet de laocnaye’s e-mail address is [email protected] 23 October 1998; revised manuscript received 11 June
due to optical filter implementations. The idea is tomake minor changes in commonly used optical cor-relator architectures benefit from a better exploita-tion of the results. An illustration is given fordifferent signature synthesis approaches, on the ba-sis of simulations including constraints in optical fil-ter design and implementation.
2. Principle of Signature Synthesis and Analysis
Our basic idea is to use a time sequence that de-scribes the pattern behavior to create a characteristicsignature of the object attitude and then to comparethis signature with a bank of learned signatures,with use, for instance, of a correlator. The sugges-tion here is to involve, as much as possible, the sameoptical architecture both for generating the signatureand for analyzing it, thereby considerably simplifyingthe implementation. The process is, of course, de-pendent on the available information extracted fromthe observed phenomenon. We illustrate this prin-ciple with two cases: pattern recognition by atti-tudes and by behaviors.
Figure 1 gives a description of the generic architec-ture that is characterized by two blocks and threedistinctive layers. The upper layer corresponds tothe observation and measurement level, involvingthe input data, the signatures, and the decision ma-trix. The lower layer corresponds to the knowledgeand data-bank layer, involving the filter and the sig-nature basis. When preprocessing is required, anadditional transform set can be included. Here, asdiscussed in Appendix A, a wavelet set was consid-ered, but the approach can be generalized to anyother relevant transforms. The intermediate level
10 January 2000 y Vol. 39, No. 2 y APPLIED OPTICS 199
e
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corresponds to the physical and hardware layer. Itis made up of two double optical Fourier transform~FT! processors. In the first block ~called signaturextractor!, filter ~Fm! and wavelet set ~Gl! are loaded,
in the case of an optical implementation, onto one ortwo spatial light modulators. In the second block~called signature correlator! Bp are the only requireddata. The use of a nonlinearity in the first block isoptional and justified by reasons of detection ~this
oint is detailed below!. The critical point here con-erns the signature extraction, which can be obtainedith different procedures, depending on the system
nput.The input plane can be formatted in different man-
ers. For instance, it can be made up of a combina-ion of pictures obtained from different sensors, fromifferent scenes, or from the same scene taken atifferent times. Similarly, elaboration of the signa-ure is made in different manners. In a multisensorpproach the signature is obtained either from theutocorrelation or the cross correlation of simulta-eous sequences for both sensors. This result isalled the autosignature of the observed object. Inhe case of a combination of observations and refer-nces, it can be obtained from the cross correlation ofhe observed sequence with itself ~or a part of itself !r with any other associated sequences or situations.n this case, the result is called, respectively, theutosignature or the cross signature ~this point isllustrated by an example in Section 4!.
According to the above definitions, data that form aignature are tested with two fundamentally differ-nt algorithms. The basic information, correspond-ng to each elementary autocorrelation or crossorrelation and weighted by the filter Fm, can be rep-esented by a scalar, a vector, or a matrix, resultingn a particular organization and complexity of theignature representation space S. The dimension l
Fig. 1. Generic architecture, characterized by two blocks and thbasis layer, and processing layer. The first block creates the sign
00 APPLIED OPTICS y Vol. 39, No. 2 y 10 January 2000
s intrinsic and corresponds, for instance, to theavelet set whose dimension is limited and which issed only in the final decision stage to make theecision either more selective or more robust.The first block of the proposed architecture ~signa-
ure extractor! is the most elaborate part of the rec-gnition system. This part can give rise to variousptical implementations, among them conventionalorrelators such as the VanderLugt correlator andhe joint transform correlator ~JTC!. Its main role iso produce a signature that corresponds, in most ofhe considered applications, to a bar code, thereforeimplifying considerably the optical processing in theecond architectural stage ~signature correlator!.To describe obtaining signatures and to scale the
imension of the signature space, we present twoomplementary approaches that illustrate the gen-ral architecture presented above.
3. Signature Synthesis
Many solutions, based on Fourier analysis, can besuggested for creating temporal signatures, such as asynthetic aperture signature.2 Here we considertwo cases that are fundamentally different in termsof both signature representation and computing timeand burden.
A. Algorithm Based on Peak-to-Correlation-Energy
This case is based on a conventional Fourier filteringapproach. The input $xi, yi% is correlated to each
lter of a reference filter bank. In general, Fm areobtained as a result of a complex learning process.Here, for sake of simplicity, Fm are the filters associ-ated to each picture of the learning basis itself. Var-ious filters can be considered at this stage.3 Asmentioned in Appendix A, Gl operate like filters andcan be merged with Fm. Here we considered a wave-
ayers: observation and measurement layer, filter and signaturees, and the second one recognizes this signature.
ree latur
f
c
icp
wtt
let set ~this choice is justified below!. Therefore Fmare given by
Fm 5X*m
uXmu2k , (1)
where Xm is the spectrum of picture. Taking rela-tion ~10! into account, Eq. ~1! can be rewritten asollows:
F9ml 5F*muGluuFmu
. (2)
In the case of a digital implementation the filterhoice is theoretically free. In the case of an optical
Fig. 2. Simplified architectures: MS and PCE ~MS–PCE
mplementation, energetic criteria become signifi-ant. This is why we chose, as an illustration, thehase-only filter ~POF! for Fm. According to Javidi,4
the POF corresponds to k 5 0.5. This filter is highlyselective and optimizes the peak-to-correlation en-ergy ~PCE!. Therefore a PCE scalar value3 is com-puted from the result of the following operation:
FT21~cml! 5 @$Xi, Yi%F9ml# (3)
obtained as a FT of the filter plane. For each l ~theavelet order!, each PCE value constitutes a pixel of
he signature array Sim. Figure 2 ~MS–PCE! giveshe reduced architecture corresponding to such sim-
and SF curve ~MS–SF!, and MR and SF curve ~MR–SF!.
!, MS
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2
plifications. Both approaches have been assessedexperimentally.1
B. Curve-Based Algorithm ~Multisensor–Space Filling!
Another algorithm may be preferred, for instance, toreduce the computing time. In the above case a sca-lar value has been extracted ~i.e., the PCE! for eachF9ml. Similarly a vector can be obtained from a two-dimensional image with techniques such as spacefilling ~SF! based on growing fractals.5 Other tech-niques can be proposed; however, SF approaches areoften used when it is necessary to scan an imagealong an optimal path. Among possible representa-tions, the most commonly used are the Hilbert curve~Hc!, with selection of paths that cross each pixel onlynce, or the Peano curve, with two crossings. Theseaths have interesting properties such as self-imilarities. In addition, they can be obtained byecursive algorithms where an elementary pattern isractionized to reach the required resolution. Heree chose the Hc to describe the cross-correlationlane. Its main advantage is that it maintains apatial neighborhood between pixels during theransformation applied to a global operator such ashe cross correlation. Figure 3 shows the example of16 3 16 Hc path length.This algorithm contributes to the establishment of
structural neighborhood links between the picturescombined in the input plane ~according to the pathlength! when applied to a cross-correlation domain~which can be seen as a global link!. For this pur-pose we introduce an additional operation by taking apower 2k of the modulus of the filter plane, resultingin the following signature extraction output:
Ciml 5 FT@u$Xi, Yi%F9mlu2k#. (4)
Fig. 3. Hc used for scanning the cross-correlation plane: a Hil-bert path of 256 pixels fills a 16 3 16 pixel image.
02 APPLIED OPTICS y Vol. 39, No. 2 y 10 January 2000
This extension allows us first to easily locate thecross-correlation domain of interest and second tointroduce additional criteria for optimizing the filterselectivity and robustness.4,6
Filters Fm can be used, for instance, to assign aparticular part of the correlation plane to the SFanalysis, with respect to m. Different parts of thecorrelation plane can be activated by the filters withrespect to m.
An illustration of this principle can be given byconsideration of the following simplification, in whichno filters Fm are used and k 5 1:
Sil~r! 5 SF$FT@u$Xi, Yi%u2uGlu2#%. (5)
From the above relation we notice that the SFcurve SF~r! has to be applied to a significant part ofthe correlation plane, i.e., here the cross-correlationpart, obtained by consideration of the case k 5 1.This results in obtaining a signature Sil~r!, for eachwavelet order l. In this case the signature extrac-tion stage can be a standard JTC. Figure 2 ~MS–SF!shows the architecture corresponding to such simpli-fications.
4. Experimental Illustrations
To illustrate the above architectures we consideredtwo applications. The first ~face recognition! is aypical MS pattern attitude recognition, whereas theecond one ~moving target! is a typical pattern be-avior recognition. In the first case pictures are ob-ained from optronic sensors and in the second caserom range gate Doppler ~RGD! radar imaging. Thehoice of a wavelet transform is justified in bothases. In the face-recognition case its use enables uso take the face’s structural details into account ~e.g.,yes, mouth7!, which is complementary to the use of
a global comparison operator such as correlation. Inthe case of radar imaging this transform is known tobe well suited to the extraction of structured objectsfrom a noisy background ~e.g., fluctuating sea condi-tions8!.
A. Multisensor Attitude Recognition
The strategy, in this case, is to improve the decisionreliability by introduction of information redun-dancy. This case leads us to intrinsic simplificationsof the main architecture. For instance, we assumethat the sensors are synchronized and that the sameangles of view are considered. Therefore this meansthat no relevant information is extracted from pic-tures obtained from both sensors at different times.This results in a simplification of the input plane.Pictures are simultaneously displayed; therefore in-dex j ~the slipping index! can be removed, and thenput plane is made up of a combination of xi and yi,
denoted $xi, yi%.The learning and the test bases were built up fromcombination of data coming from two different
ptronic sensors, operating in two different spectralands: visible and infrared ~3–5 mm of linear sensi-ivity!. Both sensors give a picture of a face with the
aivTm
wbt
asI
same view angle, and acquisitions are synchronizedat the same rate. Data are recorded and digitized bymeans of a specific interface ~Diamond Crunch It2000! on a personal computer. The different facettitudes were reduced to sequences of 21 character-stic images. We considered, for two different faces,arious behaviors or attitudes divided into two bases.he learning basis included the following head move-ents: yawn, nod, and left rotations ~Fig. 4, left-
hand side!. In contrast, the test basis included yawnith frown, nod with yawn, and rotation with eyelink, which can be considered to be structural dis-ortions of the original pattern set ~Fig. 4, left-hand
side!.In the PCE approach, signatures are obtained by
correlation of all the images of the learning basis with
Fig. 4. Examples of attitude for Emmanuel and bearded bases,attitude.
all the images forming the input sequence. Figure 5shows the corresponding Fm for the POF and thebinary POF ~BPOF!. This means that signaturesre obtained from face autocorrelations. The deci-ion is made with a PCE criterion between 0 and 1.n this case the filters Fm are made from the spectra
of the learning basis @Eq. ~1!#. Therefore each ele-ment of the input sequence forms a signature line Sm,each pixel of this line being a PCE obtained from thecorrelation of one element of the input sequence withimages of the learning basis.
We assume that signatures are sufficiently dis-criminant to make a decision in this case. The de-cision is then made by analysis of the differentsignatures for each resolution ~depending on thewavelet order!. The learning basis is split into faces
ding nod as the learning attitude and nod and yawn as the test
inclu
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Fig. 5. Examples of images and their corresponding filters for two different faces ~Emmanuel and bearded!. BPOF, binary POF.
Fig. 6. Signatures obtained by the MS–PCE approach. Left-hand column, signatures obtained for a nod attitude, and right-handcolumn, signatures obtained for a nod and yawn attitude, for two different faces ~E, Emmanuel; B, Bearded!.
04 APPLIED OPTICS y Vol. 39, No. 2 y 10 January 2000
sWu
sre
Table 1. Nod and Yawn Signatures Obtained by MS–PCE Approach for Two Faces ~Emmanuel and Bearded! and Compared by Correlation with the
n
and attitudes. Figure 6 gives the signatures ob-tained by a PCE approach for the learning basis madeup of nod and the test basis made up of nod and yawn.The different wavelet orders show that the signa-
Fig. 7. On the top appears the cross correlations between visibleand infrared images for each sequence element. We extracted acurve from each cross-correlation plane by following a SF curve~Hc! that forms a signature line.
Bp Signature Basis, f
Wavelet Level Face
Em
Yawn N
Without wavelet Emmanuel 14Bearded 5
a 5 2 Emmanuel 13Bearded 10
a 5 1 Emmanuel 17Bearded 15
a 5 1⁄2 Emmanuel 18Bearded 10
a 5 1⁄4 Emmanuel 20Bearded 5
All levels Emmanuel 68 1Bearded 40
aPCElp extracted from the correlation plane are printed on eachonlinear combination of PCElp with uniform weights.
tures between different faces are not discriminated atlow resolutions ~from 1 to 2!: We were able to usethese orders to select only some attitudes ~the mostignificant! at higher orders in a hierarchical way.e also noticed that robustness can be achieved by
se of medium-order wavelets ~from l 5 1⁄2 to l 5 1⁄4!.To recognize the faces we correlate the signaturesobtained for each wavelet order to the correspondinglearning basis. A PCE measured in the decisionplane of the signature correlator enables the consti-tution of the decision matrix ~Table 1!. The attitudeto be extracted here is the nod and yawn for bothfaces. We note that, order 1⁄4 excepted, the face isrecognized for each wavelet. This is mainly becausethe corresponding wavelet kernel size ~i.e., here 5 35 pixels! is no longer relevant with respect to char-acteristic details of the considered faces. In addi-tion, the nod attitude is recognized for both facesexcept for the bearded face of wavelet order 1.
Therefore a more robust decision ~reducing thefalse alarms! but less selective can be made from acombination of the PCE’s with respect to the waveletorder; for example, if PCEpl is the PCE obtained forthe signature Bp and the wavelet order l, the criterioncan be
PCEp 5 (l
sl~PCEpl!gl. (6)
For the sake of simplicity, sl and gl are taken to beequal to 1 ~uniformly weighted!. In the examplespresented in Table 1 PCEp were calculated by addi-tion of all PCEpl that appear in the bottom row. Theface is recognized by selection of the face and attitudecorresponding to the PCEpl maximum.
In the SF approach, for the sake of simplicity, weconsidered the case in which no filter is used and k 51 @Eq. ~5!#. This assumption is relevant when theensor redundancy is fully exploited here. The cor-elation is no longer the only decision criterion. Asxplained above, this allows for the introduction of an
ch Wavelet Order la
uel Bearded
Rotation Yawn Nod Rotation
8 8 6 54 9 14 10
11 8 9 88 14 17 11
12 17 13 611 24 20 1213 15 9 36 17 17 9
11 2 1 35 7 15 15
47 42 32 2030 62 69 47
, where underlined values indicate the maximum. Bottom row,
or Ea
man
od
235
141134246510506
6351
row
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o Fa
2
artificial link between two images of different physi-cal origins but representing the same object. Thefirst link between the pictures is obtained after com-bination with a wavelet filter by the introduction of anonlinearity that generates, as in the JTC approach,autocorrelation and cross-correlation terms. Thesecond link is obtained thanks to the SF algorithmapplied to the cross-correlation domain. This meansthat a signature line is assigned to each image of theinput sequence S~r! for a given i. This allows us torepresent each cross correlation by a one-dimensional
Fig. 8. Signatures obtained by a MS–SF approach. Left-hand coobtained for a nod and yawn, for two different faces ~E, Emmanuecross correlation between infrared and visible images of input seq
Table 2. Nod and Yawn Signatures Obtained by MS–SF Approach for TwSignature Basis, fo
Wavelet Level Face
Em
Yawn N
Without wavelet Emmanuel 16Bearded 16
a 5 2 Emmanuel 51Bearded 52
a 5 1 Emmanuel 72Bearded 26
a 5 1⁄2 Emmanuel 22Bearded 6
a 5 1⁄4 Emmanuel 32Bearded 11
All levels Emmanuel 177 2Bearded 95 1
aPCElp extracted as for Table 1; underlined values indicate the
06 APPLIED OPTICS y Vol. 39, No. 2 y 10 January 2000
line, thereby reducing the signature space dimensionsignificantly. This process is described in Fig. 7.
Similar to the PCE approach we consider the samesequences ~nod and nod and yawn! for both facespresented in Fig. 5. The signatures extracted ~Fig.8! are compared with the learning basis of signatures.A comparison between Figs. 6 and 8 confirms thatdifferent signature representations can be obtainedfrom the same phenomenon. These representationsexhibit different characteristics ~such as particulartextures!, which are not exploited here but which can
, signatures obtained for a nod, and right-hand column, signaturesd B, bearded!. For a signature, each line holds the result of thee elements.
ces ~Emmanuel and Bearded! and Compared by Correlation with the Bp
be observed. The PCE’s measured in the signaturecorrelator output plane are presented in Table 2.We note that face discrimination is difficult to obtainwithout wavelet filtering. Because each attitude issymmetric in time, the signature exhibits a verticalaxis symmetry. The formatting of the learning basiscreates a diagonal line ~from bottom left to top right!
hen autocorrelations between the input image andhe learning image are activated. Because of theime symmetry of attitudes, this diagonal is doubledy a second diagonal ~from top left to bottom right!.n the other cases the discrimination is obtained;owever, we observe the presence of some falselarms for the bearded attitudes: This is due to facerientations, which are not strictly the same forearded. These errors can be partially removed, asas done above with the PCE combination given by
elation ~6! ~see bottom row of Table 2! or a compositelter,9 with introduction of some rotation robustness.
B. Behavior Recognition
In this case the strategy is different. We obtain theincrease in reliability by constraining combinationsof the observed sequence with representative learnedsituations. This means that no physical link is im-posed between the observed scene and a referencesequence. Similarly, in theory, no synchronizationand time correspondence are required between thecombined pictures in the input plane. This meansthat the observed sequences have to be comparedeither with themselves or with others that have beenlearned, resulting in different processing strategiesand applications.
The types of signature that are produced depend onthe time evolution of signals during the picture grab-
Fig. 9. Examples of RGD radar images obtained for three diffsuccessive images of the learning and the test bases are presentedboat.
bing. Three kinds of time evolution can also be con-sidered, which form different signatures types:
• High-frequency time evolution created by sto-chastic processes: The signature smooths thesetemporal effects; the signature is like a bar code.
• Medium-frequency time evolution created bytarget behavior: The sensor detects a moving target~swell sensitive boat, for example!, and the signaturellustrates these target characteristics.
• Low-frequency time evolution created by sen-sor: The sensor moves relative to the target. Thistime evolution depends on the situation chosen by thesensor for picture grabbing. The signature repre-sents the target motion observed from differentpoints of view, distances, or heights.
In these cases specific signatures are generated.In the first case, the signals ~Figs. 9 and 10! illus-trates the random temporal fluctuations we wouldlike to avoid.
In addition, the input plane can be made up ofvarious combinations. Let xi be the unknown obser-vation and $x9, x0, . . . , x~p!% be a basis of learnedsituations or attitudes. A first strategy consists ofconsidering the following input with the combination$xi, xi1j%. The observation at time i of the sequencexi is associated to a part of the sequence, xi1j itselfwith respect to a temporal slipping window of lengthn with j 5 0, . . . , ~n 2 1! ~this case is illustrated inSection 4!. The decision is made by comparison ofthe result with a basis of learned signatures Bp, eachof them corresponding to autosignatures of learned psituations or attitudes noted @$x9i, x9i1j%, $x0i, x0i1j%, . . . ,$xi
~p!, xi1j~p! %#. The philosophy is to assume that au-
boats: tugboat ~TB!, trawler ~TR!, and oil tanker ~OT!. Twoe deviation between two successive images can be noted for each
erent. Th
10 January 2000 y Vol. 39, No. 2 y APPLIED OPTICS 207
t
tsmo
2
tosignatures are discriminant features that can thenbe substituted efficiently to cross correlations ~this isan extension from pattern correlation to signaturecorrelation!. This assumption is relevant in most ofhe common situations.
If this is not the case, a more sophisticated strategycan be applied when we generalize the previous case.The input is made up of the following combinations:@$xi, x9i1j%, $xi, x0i1j%, . . . , $xi, xi1j
~p! %#. Therefore theresulting signature has to be compared with thoseforming the signature bank and which are obtainedfrom the input combinations @$x9i, x9i1j%, $x9i, x0i1j%, . . . ,$x0i, x0i1j%, $x0i, x-i1j%, . . . , $xi
~p!, xi1j~p! %#. This corre-
sponds to a decision based on a cross-signature anal-ysis instead of an autosignature one, as in the previ-ous case. Considering this principle, the filter planeis then given in the general case by
ci1j,ml 5 u@$Xi, Xi1j% 3 F9ml#u2k. (7)
Fig. 10. Stochastic attitude for TB, TR, and OT bases.
08 APPLIED OPTICS y Vol. 39, No. 2 y 10 January 2000
As above, signatures are obtained with various al-gorithms based, for instance, on a PCE criterion, aSF, analysis or both. When a filter bank is avail-able, a generalization can be obtained resulting in asignature set Si1j,m or Si1j,m~r!, for each wavelet l.However, to reduce the dimension of the signaturespace, it is preferable for the result of each filtering,for a given i 1 j and m, to be a scalar. In addition,because of the difficulty in building a significant filterbank, with the considered illustrations, the investi-gation of such a general case became irrelevant.Therefore, as above, we considered the same simpli-fications resulting in the following expression:
ci1j,l 5 @u$Xi, Xi1j%u 3 uGlu#2k. (8)
A PCE or a SF approach can be applied to the firstdiffraction order of the filter plane, i.e., in the cross-correlation domain. In this case the signature foreach l is either Si, j ~PCE! or Si1j,~r! ~SF!. Equation~8! presents a strong analogy in its principle with theJTC architecture. Figure 2 ~MR–SF; MR is mul-tireference! gives the simplified architecture in theSF case. Figure 11 illustrates the successive stepsof a signature elaboration in the MR–SF configura-tion. The final decision, in both options, is thenmade by comparison of the obtained signature with abank of signatures Bp. In the general case, Bp areobtained with respect to Fm in a sophisticated learn-ing procedure involving, for instance, a priori exter-nal information. This comparison is implementedby means of a single correlation stage, resulting in adecision matrix Dlp. This matrix can be reduced to avector Dp by use of a cost function based on a combi-nation of wavelets ~more generally of the transformkernels!.
The selected application is a single-sensor ap-proach, and the refresh time of RGD radar images isvery slow ~a few hertz! compared with the referencerefresh time ~a few kilohertz!; this means that n canbe large. To illustrate this case, we considered theproblem of the recognition of ship radar signatures~Fig. 9!, by identification of their behaviors on a shortime scale ~a few seconds, corresponding to 36 con-ecutive 64 3 64 pixel pictures!. The data basis isade up of three different ship radar signatures: an
il tanker ~OT!, a tugboat ~TB!, and a trawler ~TR!.The learning basis is made up of the final 18 picturesof a sequence and the test basis of the first 18 ~Fig.10!.
The slipping window was chosen to be equal to thesequence size, i.e., n 5 18. In this configuration, theautosignatures are made up of the cross correlationsbetween each element of a sequence and the wholesequence itself. Results are presented Fig. 12 andTable 3. With regard to the face-recognition prob-lem, we note the importance of wavelet processing.A discrimination is impossible where no wavelets areused. Each wavelet order enables a good ship dis-crimination. As mentioned above, a signature canbe assimilated in this case to a bar code. In addition,we note that each wavelet representation contains
bnedsWsT
complementary information, which is not capitalizedon here. In this short time scale the signaturesmooths the stochastic aspect strongly. Over alonger time range, the objects will be recognized bytheir attitude. Compared with a direct approach,based, for instance, on direct correlation, this methodsignificantly reduced the false alarms that are due tothe important fluctuations of the target profile in asequence. The PCE results obtained from a waveletcombination are quite discriminating. However,there is some ambiguity between the TB and TRbecause of similar sizes. This demonstrates that apart of a sequence is sufficient to identify anotherpart of a sequence of the same object. This empha-sizes that the object is recognized by its attitudes~e.g., here with respect to the sea conditions!.
5. Discussion
We have presented the principle of an architecturethat provides the synthesis and the analysis of tem-poral signatures representative of pattern behaviorsandyor attitudes. This architecture is characterizedy its versatility and its simplicity in terms of tech-ical implementation, taking advantage of the prop-rties of Fourier optics. Within such a frameworkifferent algorithms can be chosen to generate theignatures, depending, in part, on the applications.e investigated two complementary algorithms re-
ulting in two different signature characteristics.hese signatures were compared with learned signa-
Fig. 11. Steps in MR–SF architecture: FT’s are used to changeto a power elevation. After these operations, in direct space, thfollowing Hc.
tures in a conventional correlator, exhibiting goodrecognition performance. However, we did not fullyexploit signature characteristics, such as specific tex-tures or templates that could be recognized directly~with the same correlation principle! instead of awhole signature comparison. Similarly, we can con-sider that the selected examples ~in particular, facerecognition! are insufficient to assess the potentialityof the proposed approach in terms of recognition per-formance. Concerning the technical implementa-tion, both digital and optical options can beconsidered.
We have focused here on the optical one. The firstobvious consequence is a limitation in the filterchoice, owing to technical and real-time constraints.Despite this constraint we have shown that an exten-sion toward complex pattern-recognition problemsdoes not necessarily imply the implementation of so-phisticated optical hardware. The architecture isbuilt of two cascaded correlators with a common in-terface, whose the function is defined by the algo-rithm selected to represent the signatures. The firstcorrelator, generating the signatures, enables stan-dard optical architectures to be considered ~e.g.,VanderLugt or JTC!. The intermediate nonlinear-ity can be achieved, for instance, either electronicallyor optically.10 The practical consequence is a shiftfrom a need for high-speed spatial light modulatorstoward a need for high-volume and high-speed access
. In spectral space the result is multiplied by a filter and raisedoss-correlation part is extracted with a SF curve. Curve, path
spacee cr
10 January 2000 y Vol. 39, No. 2 y APPLIED OPTICS 209
a
Table 3. Signatures Obtained by a MR–SF Approach for Three Boats
m
210 APPLIED OPTICS y Vol. 39, No. 2 y 10 January 2000
memories. This point remains true in the case of adigital processing implementation.
Appendix A
Preliminary processings have been shown to improvesignificantly the correlation performance. If thepreprocessing is linear, it can be included easily inthe filter design itself. If x is the pattern, X is itsFourier transform, fm is the reference, and Fm is thessociated matched filter, for instance, gl, the prepro-
cessing kernel of order l and Gl, its Fourier trans-form, then the correlations cml and Cml ~the spectrumdensity!, respectively, can be looked at in two differ-ent manners:
Whereas relation ~A1! separates the preprocessingfrom the filtering, relation ~A2! operating in the Fou-rier plane shows that both operations can be mergedin the filter F9m. As an illustration the wavelet set isa possible kernel set ~gl is a wavelet daughter!. This
n, signatures obtained for the first 18 RGD images, and right-handats: TB, TR, and OT. For a signature, each line holds the resultf the input sequence.
Fig. 12. Signatures obtained by a MR–SF approach. Left-hand columcolumn, signatures obtained for the final 18 images, for three different bofrom the cross correlation between the first image with each element o
~TB, TR, and OT! and Compared by Correlation with the Bp SignatureBasis, for Each Wavelet Order la
Wavelet Level Boat Tugboat Trawler Oil Tanker
TB 12 12 12Without wavelet TR 16 16 16
OT 18 18 18TB 45 19 34
a 5 2 TR 32 44 31OT 44 37 66TB 74 30 31
a 5 1 TR 67 65 42OT 32 21 93TB 54 20 20
a 5 1⁄2 TR 46 40 19OT 26 26 92TB 60 29 31
a 5 1⁄4 TR 42 43 20OT 55 36 44TB 233 98 116
All levels TR 187 194 112OT 157 139 295
aPCElp extracted as for Table 1; underlined values indicate theaximum.
wTf
Mf
3. B. V. K. Vijaya Kumar and I. Hassebrook, “Performance mea-
choice is well known for improving the correlationperformance in the case of textured targets, wheremultiresolution analysis is appropriate.11
Extension to nonlinear processing is obtainedstraightforwardly by wavelet combinations.12 The
avelet sets used are based on the Mexican hat.he general form of this wavelet image is given by the
ollowing expression @the a factor reflects the scale ofthe c~x, y! function#:
ca~x, y! 51uau
4
3ÎpS1 2
x2
a2DS1 2y2
a2DexpS2x2 1 y2
2a2 D .
(A4)
We thank D. Bardon from Sfim for supplying theS data basis and G. Coppin from Thomson Dexteris
or supplying the ship sequence basis.
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10 January 2000 y Vol. 39, No. 2 y APPLIED OPTICS 211
