Experimental verifications of a joint transform correlator using compressed reference images

Experimental verifications of a joint transform correlatorusing compressed reference images

Joewono Widjaja and Ubon Suripon

Single-target and multiple-target detections by using a joint transform correlator (JTC) with compressedreference images are experimentally verified. Two high-contrast images with different spatial-frequencycontent are used as test scenes. Although an effect of the additive noise on detection performance of theproposed correlator is more severe than that of the compression, the experimental results confirm thefeasibility of implementing the JTC with compressed reference images. © 2006 Optical Society ofAmerica

OCIS codes: 070.4550, 070.5010.

1. Introduction

With the development of spatial light modulators(SLMs), a joint transform correlator (JTC) has beenfound advantageous for target detection systems1–5

because the synthesis of complex matched filters inadvance is eliminated and reference images can beupdated in real time. In a real-time JTC, the corre-lation between an input target detected by an imagesensor and a reference image stored in a computersystem is accomplished by displaying the two imagesside-by-side onto a SLM. By capturing its opticalFourier spectrum with a CCD sensor, a joint powerspectrum (JPS) of the images is recorded. The cap-tured JPS is then redisplayed on the same SLM inorder to be optically Fourier transformed. This yieldsa correlation output. For additional discussions ofvarious aspects of the JTC, the reader may wish toconsult Ref. 6.

However, the use of an electrically addressed SLM(EASLM) in the JTC has several drawbacks. For oneexample, the process of displaying the target and thereference images onto the EASLM causes a bottle-neck because of the serial nature of the signal com-munication between the computer and the SLM. Thistime delay is dependent on the file size of the images.Owing to the inherent rotation and scale variances

of the JTC, the stored reference images must con-tain all possible variations of the rotation and scalechanges of the target. Thus the application of a JTCto automatic target recognitions requires consider-able storage.

To obviate this problem, JPEG compression7 of thereference images has been proposed and theoreticallystudied by Widjaja and Suripon.8,9 In their researchthe effects of the JPEG compression of reference im-ages on single- and multiple-target detection by usinga JTC are quantitatively studied by using computersimulation. The studies are conducted using twotypes of image with different spatial-frequency con-tent in a situation in which overlapping noise ispresent in the input and there is a contrast differ-ence between the target and the reference images.In contrast with the use of the compressed referencewith high spatial-frequency content, the results ofour studies show that the JTC using a compressedreference image with low spatial-frequency contentoffers a better recognition performance in that it isrobust to noise and contrast difference for a widerange of compression levels.

In this work the optical implementation of single-and multiple-target detection using a JTC with JPEGcompressed reference images is experimentally veri-fied. For the experiments, the same set of imagesused in our previous works is employed as testscenes. The performance of the single-target detec-tion is quantified by using a ratio of the correlationpeak intensity to the standard deviation of the corre-lation output or peak-to-correlation deviation (PCD),while that of the multiple-target detection is a ratio ofthe primary to the secondary peaks or peak-to-

The authors are with the Institute of Science, Suranaree Uni-versity of Technology, Nakhon Ratchasima 30000, Thailand. J.Widjaja’s e-mail address is [email protected].

Received 6 April 2006; revised 5 June 2006; accepted 16 June2006; posted 19 June 2006 (Doc. ID 69596).

0003-6935/06/318074-09$15.00/0© 2006 Optical Society of America

8074 APPLIED OPTICS � Vol. 45, No. 31 � 1 November 2006

secondary ratio (PSR). Section 2 introduces the the-oretical background of the optical implementation ofthe JTC using compressed reference images and re-views the JPEG compression algorithm. Experimen-tal results are discussed in Section 3. Our conclusionsare discussed in Section 4.

2. Theoretical Background

A. Joint Transform Correlator with CompressedReference Images

Figure 1 shows a schematic of an optical setup forperforming experimental verifications. For the sakeof simplicity of the discussion, single-target detectionis considered. The input target image t�x, y� capturedby the CCD image sensor and the compressed ref-erence image rc�x, y� stored in a computer system areassumed to have the same size of Nx � Ny pixels. Letus consider the EASLM placed at the front focalplane of lens L1, comprised of a matrix of rectangu-lar light-modulating elements with a resolution ofMx � My pixels, a pixel size of Lx � Ly, and a pixelpitch Px and Px in the x and y directions, respectively.The amplitude transmittance of the EASLM can bewritten as

tEASLM�x, y� � �n��My

�My

�m��Mx

�Mx

��x � mPx, y � nPy�

� rect� xLx�rect� y

Ly�, (1)

where R denotes the convolution operation. If the hor-izontal separation between the target and the com-pressed reference images displayed on the EASLM isMPx, the joint input image can be expressed as

finput�x, y� � t�x �MPx

2 , y�rect�x � MPx�2NxPx

�� rect� y

NyPy�� rc�x �

MPx

2 , y�� rect�x � MPx�2

NxPx�rect� y

NyPy�. (2)

The amplitude transmittance of the joint input imageis given by

fJTC�x, y� � tEASLM�x, y�finput�x, y�

� �n��My

�My

�m��Mx

�Mx

��x � mPx, y � nPy�

� rect� xLx�rect� y

Ly��t�x �

MPx

2 , y�� rect�x � MPx�2

NxPx�rect� y

NyPy�

� rc�x �MPx

2 , y�rect�x � MPx�2NxPx

�� rect� y

NyPy��. (3)

The joint Fourier spectrum at the back focal plane oflens L1,

FJTC�x�, y�� 1�f

LxLy

PxPy �

n��My

My

�m��Mx

Mx

� ��x�

�f �mPx

,y�

�f �nPy�sinc�Lxx�

�f �� sinc�Lyy�

�f �� Finput�x�, y��, (4)

is recorded by the CCD sensor and is then transferredto the computer. Here, � and f are the wavelength ofcoherent light and the focal length of lens L1, respec-tively. The Fourier spectrum of the joint input imageis equal to

Finput�x�, y�� T�� x�

�f ,y�

�f�exp�j2�MPxx�

2�f �� Rc��x�

�f ,y�

�f�exp��j2�MPxx�

2�f �, (5)

where

T��x�

�f ,y�

�f�� T�x�

�f ,y�

�f�� NxNyPxPy sinc�NxPxx�

�f �� sinc�NyPyy�

�f �, (6a)

Rc��x�

�f ,y�

�f�� Rc�x�

�f ,y�

�f�� NxNyPxPy sinc�NxPxx�

�f �� sinc�NyPyy�

�f �. (6b)

Fig. 1. Schematic of an optical setup for performing experimentalverifications of the JTC with compressed reference images.

1 November 2006 � Vol. 45, No. 31 � APPLIED OPTICS 8075

The recorded JPS of the images can be expressed as

�FJTC�x�, y��2 �1

�2f 2 �LxLy

PxPy�2

�n��My

�My

�m��Mx

�Mx

sinc2�mLx

Px�

� sinc2�nLy

Py��Rc��x�

�f �mPx

,y�

�f �nPy��2

� �T��x�

�f �mPx

,y�

�f �nPy��2

� Rc��x�

�f �mPx

,y�

�f �nPy�

� T��x�

�f �mPx

,y�

�f �nPy�

� exp�j2��x�

�f �mPx�

� Rc��x�

�f �mPx

,y�

�f �nPy�

� T�*�x�

�f �mPx

,y�

�f �nPy�

� expj2��x�

�f �mPx��. (7)

Equation (7) shows that the pixel structure of theEASLM produces the multiple power spectrum ofthe joint input image at intervals of �f�Px and �f�Py

in the horizontal and vertical directions, respectively.Since they are modulated by a broad 2D sinc function,only the zero order �m � 0, n � 0) of the JPS has thehighest intensity, while the higher orders are atten-uated. For this reason, the recorded zero-order spec-trum will be used for the next computation. Byexpressing the complex field distribution Rc��x�, y��and T��x�, y�� into their amplitude and phase distri-butions

Rc��x�

�f ,y�

�f�� Rc�x�

�f ,y�

�f��expjR�x�

�f ,y�

�f�,T��x�

�f ,y�

�f�� T��x�

�f ,y�

�f��expjT�x�

�f ,y�

�f�,the zeroth-order JPS can be expressed as

�FJTC0�x�, y��2 � �Rc��x�

�f ,y�

�f��2

� �T��x�

�f ,y�

�f��2

� 2�Rc��x�

�f ,y�

�f��T��x�

�f ,y�

�f�� cos2�MPxx�

�f � R�x�

�f ,y�

�f�� T�x�

�f ,y�

�f�. (8)

The third term in Eq. (8) is in particular interestbecause it provides the desired correlation output.This term contains the desired product of the Fourierspectra of the target and the compressed referenceimages that are sampled by the sinusoidal fringes.Since the CCD sensor inherently has finite resolu-tion, the sensor must record the fringes faithfully.If the CCD sensor used has a spatial resolution of2MCCDx � 2MCCDy with pitches of PCCDx and PCCDy, thedigitized zeroth-order JPS can be mathematicallywritten as

�FJTC0�x�, y��2 ��Rc��x�

�f ,y�

�f��2

� �T��x�

�f ,y�

�f��2

� 2�Rc��x�

�f ,y�

�f��T��x�

�f ,y�

�f�� cos2�MPxx�

�f � R�x�

�f ,y�

�f�� T�x�

�f ,y�

�f�� n��MCCDy

�MCCDy

�m��MCCDx

�MCCDx

� ��x� � mPCCDx , y� � nPCCDy�

� rect� x�

LCCDx�rect� y�

LCCDy�, (9)

where LCCDx � LCCDy represents the size of the light-detecting rectangular element of the CCD. Whenthe active area of the sensor is greater than the sizeof the zeroth-order spectrum, a faithful recording isachieved provided that the sampling theorem10 issatisfied. Therefore the sampling frequency of thesensor must be at least two times higher than thefrequency of sinusoidal fringes fCCD 2 fFringes or

�f2MPx

PCCDx. (10)

Inequality (10) indicates that the spatial separationof the target and the compressed reference images inthe input plane are determined by the focal length ofthe Fourier transform lens, the operating wavelengthof the coherent light, and also the spatial resolution ofthe CCD sensor.

Next, the digitized JPS is redisplayed on theEASLM in order to produce the correlation output.Since the pixel pitch of the CCD sensor is differentfrom that of the EASLM, the spatial extension ofthe redisplayed joint power spectrum is scaled bythe ratio of the pixel pitch given by

rpx �PCCDx

Px, rpy �

PCCDy

Py(11)

in the horizontal and the vertical directions, respec-tively. By taking this ratio into account, the am-


plitude transmittance of the redisplayed JPS isproportionally equal to

�FJTC0�x�, y��2 ��Rc��rpxx�

�f ,rpyy�

�f ��2

� �T��rpxx�

�f ,rpyy�

�f ��2

� 2�Rc��rpxx�

�f ,rpyy�

�f ��T��rpxx�

�f ,rpyy�

�f �� cos2�rpxMPxx�

�f � R�rpxx�

�f ,rpyy�

�f �� T�rpxx�

�f ,rpyy�

�f �� n��MCCDy

�MCCDy

�m��MCCDx

�MCCDx

� ��rpxx� � mPCCDx, rpyy� � nPCCDy�

� rect�x�

Lx�rect�y�

Ly�. (12)

The subsequent optical Fourier transform of the re-displayed JPS using lens L1 produces the correlationoutput intensity of the form

Ic�x, y� � �c�x, y� � LxLy

PxPysinc�Lxx

�f �sinc�Lxy�f �

� �n��My

My

�m��Mx

m��Mx

��x �m�fPx

, y �m�fPy

��2

, (13)

where c�x, y� is the desired correlation signal given by

c�x, y� � rc�� xrpx

,y

rpy�� rc��x

rpx,

�yrpy

�� t�� xrpx

,y

rpy�

� t��xrpx

,�yrpy

�� rc�� xrpx

,y

rpy�� t��x

rpx,

�yrpy

�� x � MPCCDx, y� � rc��x

rpx,

�yrpy

�� t�� x

rpx,

yrpy

�� x � MPCCDx, y�, (14)

with

rc�� xrpx

,y

rpy�� rc� x

rpx,

yrpy

�rect� xNxPCCDx

�� rect� y

NyPCCDy�,

t��xrpx

,�yrpy

�� t� xrpx

,y

rpy�rect� x

NxPCCDx�

� rect� yNyPCCDy

�. (15)

Expression (13) shows that, owing to the pixelstructure of the EASLM, the correlation output c�x, y�of Eq. (14) is periodically replicated with the separa-tions �f�Px and �f�Py in the horizontal and the verti-cal directions, respectively. In Eq. (14), the first twoterms correspond to the autocorrelations of the com-pressed reference and of the target images that have

appeared at the same position, while the last twoterms are the desired cross correlation signals sepa-rated from the first two terms by distance �MPCCDx.The maximum width of each correlation signal isconfined in the area 2NxPCCDx � 2NyPCCDy. The crosscorrelation and the autocorrelation signals will notoverlap provided M 2Nx. Figure 2 illustrates thecross-sectional scan of the replicated correlation out-put along y � 0, where c0�x, y� and c1�x, y� stand forthe zeroth-order and the first-order correlation sig-nals, respectively. For the sake of clarity in thefigure, the replicated correlation signals are drawnby not taking the modulating sinc functions intoaccount. Each replicated correlation signal consistsof three patterns; the center pattern is the strongestbecause it corresponds to the first two terms of Eq.(14), and the other two patterns represent the lasttwo terms.

To prevent overlapping of the adjacent replicas,the spatial separation between replicas must bechosen sufficiently wide. It can be seen from Fig. 2that the separation is determined by the followingcondition:

�fPx

2MPCCDx � 2NxPCCDx, (16)

which is dependent on the characteristic of theEASLM, the CCD sensor, the focal length of the Fou-rier transform lens, and the wavelength of the laserlight. When M � 2Nx, the focal length of lens L1 mustsatisfy

f 6NxPCCDxPx

�. (17)

B. JPEG Compression

JPEG compression is one of the digital compressionstandards designed for still images.7 To compress stillimages, the JPEG algorithm divides picture elementsof the input image into 8 � 8 pixel blocks. The spatialfrequency of each block is independently calculatedby using the 2D discrete cosine transform (DCT). TheDCT generates 8 � 8 spatial frequencies consisting of1 dc and 63 ac frequency coefficients. Since as a gen-eral rule the pixel values of the image vary slowly, thevalue of the dc coefficient is larger than that of the ac

Fig. 2. Locations of the zero-order and the first-order correlationsignals.


coefficient. Next, the resultant DCT of each block isquantized by dividing each value of the DCT coeffi-cient by a corresponding number from a quantiza-tion table. To discard high-spatial-frequency content,the quantization values for the ac coefficients are setto be larger than those of the dc coefficients. Eachquantized DCT coefficient is then rounded to thenearest integer. As a result, most ac coefficientsbecome zero, which causes irretrievable loss. To ob-tain higher compression, the dc coefficient is thenprocessed by storing the difference between the dccoefficients of consecutive blocks. As for the ac co-efficients, which consist of zero values, further com-pression is achieved by using run length encodingand Huffman coding.

3. Experimental Verifications

To perform experimental verifications, high-contrastfingerprint and human face images were prepared andduplicated as the target and reference images. Unlikein our previous work,8,9 a low-contrast image was notemployed, because the limited contrast ratio of theEASLM used prevented an efficient display of imageswith small variations of gray-level pixels. The imagesconsisted of 124 � 186 pixels with 8-bit gray scalelevels, and their size was 23 kbyte. The referenceimages were compressed into JPEG format by usingthe ACDsee software (ACD Systems, Ltd.) with adifferent quality factor (QF) whose value could bevaried from 100 to 0. A high value QF discards lessinformation than one with a small value. Thus thehigher the value of the QF, the better the imagequality and the bigger the file size of the compressedimage. Figures 3(a) and 3(b) show the compressedfingerprint and human face images with QF � 10, 50,and 100, respectively. It can be seen from Fig. 3(b)that as the QF is lowered the quantization appliedindependently on 8 � 8 pixel blocks generates more

visible gray scale discontinuities along the blockboundaries called the blocking artifacts.7 This is be-cause the human face image contains more pixelswith slowly varying values compared to the finger-print image. Thus its blocking artifacts appear on alarger area.

The quality of the compressed image was objec-tively measured by using a peak signal-to-noiseratio11 (PSNR) given by

PSNR � 10 log10�2552

1Nx � Ny

�j�1

Ny

�i�1

Nx

f�i, j� � fc�i, j��2�.

(18)

Here f�i, j� and fc�i, j� are the original and the com-pressed images with dimensions of Nx � Ny pixels,respectively. f�i, j� takes integer values between 0and 255 for an 8-bit gray scale image. The largePSNR means that the degree of similarity betweenthe original and the compressed images is high.Figure 4 shows the PSNR of each compressed ref-erence image as a function of the QF. It can be seenfrom the figure that the PSNRs become higher asthe QF increases. However, the PSNR of a com-pressed human face is higher than that of the fin-gerprint. This is because the fingerprint imagecontains more high spatial-frequency componentsthan the human face image does. Since the highspatial-frequency determines the fine details of theimage, discarding high spatial-frequency componentsof the fingerprint degrades the fine detail informationmore than that of the human face image. Thereforeowing to severe degradation the PSNR of the com-pressed high-contrast fingerprint is lower.

Fig. 3. JPEG compressions of (a) high-contrast fingerprint and(b) high-contrast human face images.

Fig. 4. PSNR of the compressed fingerprint and the human faceimages as functions of the QF.


In the experiments the single-target and themultiple-target detections were performed by combin-ing the target and the compressed reference imagesas the joint input image finput�x, y� with the horizon-tal separation of M � 248 pixels. In the case ofmultiple-target detection, the input scene containedtwo different images with one of them identical to theoriginal reference image. Since as a practical matterthe input targets captured by CCD sensors are farfrom ideal, an additive Gaussian noise generated byusing the IMNOISE command of MATLAB 6.0 wasadded to the target images. The joint input image wasthen displayed on a Jenoptik SLM-M�460 EASLMwith a resolution of 832 � 624 pixels with a pixel sizeof 27 m � 23 m and a pixel pitch of 32 m � 32�m. By perpendicularly illuminating the EASLMwith collimated coherent light generated from aHe–Ne laser source operating at a wavelength of632.8 nm, the JPS was generated at the back focalplane of lens L1. An 8-bit Pulnix TM-2016-8 CCDsensor with a pixel resolution of 1920 � 1080 and apixel size and pitch of 7.4 m � 7.4 m was used tocapture the generated JPS and the correlation outputintensity. To reduce the excessive light intensities ofthe JPS and the correlation output, a neutral density(ND) filter was installed in front of the sensor. How-ever, because the amplitude and the bandwidth of theFourier components of the human face image aresmaller than those of the fingerprint,8 the sinusoidalfringes of the JPS generated during the human facedetection is weaker. Therefore to faithfully record thefringes, the ND filter was not employed during therecording of the JPS of the human face. As for Fouriertransforming lens L1, a lens with the focal length off � 300 mm was used. This is because substitutionsof the related parameters into Eq. (15) give the focallength of f 278 mm.

A. Single-Target Detections

1. Compressed High-Contrast Fingerprint asReferenceFigures 5(a), 5(b), and 5(c) show the experimentaloutput correlations of the JTC. The autocorrelationpeak of the uncompressed fingerprint shown in Fig.5(a) is almost two times higher than the cross corre-lation generated by using the compressed fingerprintwith a QF of 10 shown in Fig. 5(b). As reported in ourprevious work,8 this is caused by the degradation ofthe reference image by compression. Figure 5(c)shows the output of the correlation of the noisy fin-gerprint target with a variance of �2 � 1 and thecompressed fingerprint reference with a QF of 10. Itcan be seen from the figure that the correlation peakdisappears. This is because, besides the additivenoise, the sinusoidal fringes are corrupted by specklenoise that is inherently generated by light scatteringand multiple internal reflections from the EASLMand the surface of the sensor. Therefore the correla-tion peak cannot be detected.

Figure 6 shows the normalized PCDs as a functionof the QF of the compressed fingerprint for different

target scenes. It is clear that, when the fingerprinttarget is free from noise or is corrupted by noise withvariance �2 � 0.01, the PCDs increase gradually asthe QF increases. However, when the fingerprint tar-get is corrupted by strong noise, the PCD reducesdrastically regardless of the compression quality. Incomparison with the simulation, the detection of thesingle-fingerprint target using the proposed JTC ismore dependent on noise level than on compression.

2. Compressed High-Contrast Human Face asReferenceThe experimental output correlations generated bythe proposed JTC are shown in Figs. 7(a)–7(c). Theoutput correlations are not as broad as those obtainedby the computer simulations,8 because the correla-

Fig. 5. Experimental results of the single-fingerprint detectionusing the proposed JTC. (a) Autocorrelation output of the uncom-pressed fingerprint and cross correlation outputs using the com-pressed fingerprint reference �QF � 10� in a situation in which thetarget is (b) noise-free and (c) noisy ��2 � 1�.

Fig. 6. PCD of single-fingerprint detection as a function of the QFof the compressed fingerprint reference.


tion peak intensities are reduced by the ND filter. Asa consequence, the peak height and width of the cor-relation signal reduce greatly. When the noise-freehuman face target is detected by the reference imagecompressed at a QF of 10, the correlation outputshown in Fig. 7(b) decreases slightly. However, itspeak is almost as sharp as the autocorrelation outputshown in Fig. 7(a). In comparison with the outputs ofthe fingerprint detections shown in Fig. 5, the corre-lation planes of Figs. 7(a) and 7(b) appear to be nois-ier. This is because the recording of the JPS withoutthe ND filter causes the low-frequency components ofthe generated JPS to become clipped; however, morefringes in the higher frequencies are recorded. As theclipped JPS is subsequently redisplayed onto theEASLM, not only is more light diffracted but alsomore speckle noise is generated to the correlation out-put. Therefore although the correlation peak height ishigh, the speckle noise increases. Moreover, as theblocking artifact increases, more low-frequency com-ponents of the JPS are clipped. This in turn furtherincreases the speckle noise. The correlation output ofthe noise-corrupted human face target with the vari-ance �2 � 1 is depicted in Fig. 7(c). For the samereason discussed previously, the correlation peakcannot be observed because it is buried in the noise.

Figure 8 shows the normalized PCDs as a functionof the QF of a compressed human face for differenttarget scenes. When the target is a noise-free humanface, the PCD decreases gradually as the QF be-comes smaller. However, when the QF is less than10, the PCD reduces rapidly. As mentioned in thediscussion of Fig. 5(c), owing to the increase of theblocking artifact the speckle noise in the correlationplane increases. In the presence of additive Gauss-ian noise with variance �2 � 0.01 in the input tar-get, the PCD drops below 0.5 because the fringestructure has been corrupted by the speckle noise.As the additive noise exists, the correlation peakdegenerates. When the additive noise becomesstronger, the correlation peak reduces rapidly. Sub-

sequently, the PCD further decreases. Thereforeowing to the presence of the speckle noise, the de-tection performance of the proposed JTC using acompressed human face depends on both the com-pression and the additive noise. Note that severalmethods for enhancing the fringes of the JPS by dcblocking, binarizing, or manipulating the fringeshave been reported.12–14

B. Multiple-Target Detections

1. Compressed High-Contrast Fingerprint asReferenceFigures 9(a)–9(c) show the experimental outputs ob-tained from the detections of the multiple fingerprintby using the proposed JTC. The correlation outputshown in Fig. 9(a) consists of two distinctive peaks

Fig. 7. Experimental results of the single-human-face detectionusing the proposed JTC. (a) Autocorrelation output of the uncom-pressed human face and cross correlation outputs using the com-pressed human face reference �QF � 10� in a situation in which thetarget is (b) noise-free and (c) noisy ��2 � 1�.

Fig. 8. PCD of a single human face detection as a function of theQF of the compressed human face reference.

Fig. 9. Experimental results of the multiple-fingerprint detectionusing the proposed JTC. (a) Correlation output using the uncom-pressed fingerprint reference and correlation outputs using thecompressed fingerprint reference �QF � 10� in a situation in whichthe target is (b) noise-free and (c) noisy ��2 � 1�.


with different heights. The peak with the greaterheight is generated by the autocorrelation of the un-compressed high-contrast fingerprint, while the lowpeak is the cross correlation output of the referenceand the nontarget fingerprint. Here the correlationpeaks obtained from the detection of the target andthe nontarget are defined as the primary and thesecondary peaks, respectively. The decrease of bothcorrelation peaks resulted from the detection of thenoise-free multiple fingerprint by the compressed ref-erence with a QF of 10 can be seen from Fig. 9(b).Figure 9(c) shows the detection of the noisy multiple-fingerprint target with a variance of �2 � 1 by theJTC using the reference compressed at a QF of 10. Itis clear that no apparent correlation peaks are de-tected. In particular, the secondary correlation peakis minimized.

Figure 10 shows the PSRs as a function of the QFof the compressed fingerprint reference for differentmultiple-target scenes. In the detection of the noise-free target, the PSR increases gradually as the QFbecomes higher. When the target is the noise cor-rupted multiple fingerprint with a variance of �2 �0.01, its resultant PSR is higher than that of thenoise-free target. As shown in Fig. 9(b) when thetarget is corrupted by noise, the decrease of the sec-ondary peak caused by compression is more signifi-cant than that of the primary peak. Since the value ofthe denominator reduces faster than that of the nu-merator, the PSR becomes higher. Furthermore, asthe variance of the noise increases to unity, the JPSis strongly corrupted by the noise. Since the primarycorrelation peak is further degraded, its PSR reducessharply to less than 1.5. Although multiple-targetdetection depends on the compression of the refer-ence images, the experimental results confirm thatthe proposed JTC can distinguish the desired targetfrom the nontarget.

2. Compressed High-Contrast Human Face asthe ReferenceFigure 11(a) is a 3D plot of the correlation output ofthe multiple-human-face detection using the JTCwith an uncompressed human face reference, andFigs. 11(b) and 11(c) illustrate the correlation outputsof the JTC using the compressed reference with a QFof 10. It can be seen from Fig. 11(a) that the primarycorrelation peak intensity is higher and sharper thanthat of the secondary peak. When the reference iscompressed, the degradation of the primary peak in-tensity shown in Fig. 11(b) is insignificant comparedwith the secondary peak. However, when the multi-ple target is strongly corrupted by noise, there are noobservable correlation peaks that can be seen fromFig. 11(c).

Figure 12 show the variation of the PSRs as afunction of the QF of the compressed human face

Fig. 11. Experimental results of the multiple human face detec-tion using the proposed JTC. (a) Correlation output using theuncompressed human face reference and correlation outputs usingthe compressed human face reference (QF of 10) in a situation inwhich the target is (b) noise-free and (c) noisy ��2 � 1�.

Fig. 10. PSR of multiple fingerprint detection as a function of theQF of the compressed fingerprint reference.

Fig. 12. PSR of multiple human face detection as a function of theQF of the compressed human face reference.


reference for different multiple-target scenes ob-tained from the experiments. The PSRs of the noise-free and the noisy high-contrast human face withvariance �2 � 0.01 vary by approximately 3 exceptwhen the QF is smaller than 10. In the presence ofstrong noise in the input scene, the PSR reduces toapproximately 1 because the fringes are degenerated.Although the speckle noise is present, the experimen-tal results show that the multiple-human-face detec-tion using the proposed JTC can be done for a widerange of compressions. This is in agreement with thesimulation result.9

4. Conclusions

We have verified experimentally the JTC by usingJPEG-compressed reference images, where high-contrast fingerprint and human face images were usedas the test scenes. The experimental results confirmthe feasibility of implementing the JTC with com-pressed reference images. However, unlike the simu-lation results,8,9 the effect of additive noise on thedetection performance of the proposed JTC is moresevere than that of compression. This may be causedby the speckle noise that is inherently generated as aresult of light scattering and multiple internal reflec-tions that come from the EASLM and the CCD sensor.

This work was supported by the Institute of Re-search and Development, Suranaree University ofTechnology, under grant SUT 2548.

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Documents

Experimental verifications of a joint transform correlator using compressed reference images