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Adapted all-numerical correlator for face recognition applications

M. Elbouz,1 F. Bouzidi,1,2 A. Alfalou,1,* C. Brosseau,3 I. Leonard,1 and B.- E. Benkelfat 4 (1) ISEN Brest, Groupe Vision, L@bISEN, 20 rue Cuirassé Bretagne, CS 42807, 29228 Brest Cedex 2, France.

(2) University of Sfax, Ecole Nationale d’Ingénieurs de Sfax, Electronics and Information Technology Laboratory, route de Soukra, Sfax, Tunisie.

(3) Université Européenne de Bretagne, Université de Brest, Lab-STICC (UMR CNRS 6285), CS 93837, 6 avenue Le Gorgeu, 29238 Brest Cedex 3, France.

(4) Institut Télécom –Télécom Sud Paris, SAMOVAR (UMR CNRS-INT 5157), Département Electronique et Physique, 9 rue Charles Fourier, 91011 Evry Cedex, France.

*[email protected]

ABSTRACT

In this study, we suggest and validate an all-numerical implementation of a VanderLugt correlator which is optimized for face recognition applications. The main goal of this implementation is to take advantage of the benefits (detection, localization, and identification of a target object within a scene) of correlation methods and exploit the reconfigurability of numerical approaches. This technique requires a numerical implementation of the optical Fourier transform. We pay special attention to adapt the correlation filter to this numerical implementation. One main goal of this work is to reduce the size of the filter in order to decrease the memory space required for real time applications. To fulfil this requirement, we code the reference images with 8 bits and study the effect of this coding on the performances of several composite filters (phase-only filter, binary phase-only filter). The saturation effect has for effect to decrease the performances of the correlator for making a decision when filters contain up to nine references. Further, an optimization is proposed based for an optimized segmented composite filter. Based on this approach, we present tests with different faces demonstrating that the above mentioned saturation effect is significantly reduced while minimizing the size of the learning data base. Keywords: Correlation, VLC, FFT, optical Fourier transform, Fraunhofer, diffraction, face recognition.

1. INTRODUCTION

The rapid progress in face recognition has given rise to many fields of application. One important example is security near strategic sites, e.g. airports. For that purpose, it remains crucial to be able to identify target subjects. Automatic video surveillance technologies constitute major challenges in image processing. However, the study of robust and discriminating systems for recognizing faces is still the focus of intense research [1-5]. Most of the face recognition algorithms require intense computation time with weak recognition rates. Optical correlation is a promising route to deal with these challenges [1-4]. However numerical methods are simpler to implement than the optical ones. We have recently suggested numerical correlation schemes based either on graphics processor unit (GPU) [5], or field-programmable gate array (FPGA) [6]. We have also considered a hybrid technique using independent component analysis (ICA) and correlation methods [7]. Interest in optical and/or numerical correlation techniques has been also addressed in the literature [8-12]. In this work, we present a numerical implementation of a correlator based on a numerical version of the Fourier transform (FT) [13-14]. For that purpose we consider a Vanderlugt correlator (VLC) and implement numerically the optical FT (NO_FT) via the Fraunhofer diffraction [13]. A comparison of the results obtained with a VLC using the fast FT (FFT) algorithm confirms the good performances of the correlator based on a numerical implementation of NO_FT.

2. NUMERICAL IMPLEMENATION OF A VLC BASED ON THE FRAUNHOFER DIFFRACTION AND NUMERICAL IMPLEMENTATION OF THE OPTICAL FT

Before embarking in the presentation of the results, it is worth providing some details on the principle of the VLC [13].

Optical Pattern Recognition XXIV, edited by David Casasent, Tien-Hsin Chao, Proc. of SPIE Vol. 8748, 874807 · © 2013 SPIE · CCC code: 0277-786X/13/$18 · doi: 10.1117/12.2014383

Proc. of SPIE Vol. 8748 874807-1

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As illustrated in Fig. 1(a), the optical setup of the VLC has three planes, the input plane P1, the Fourier plane P2, and the correlation plane P3. Passing from one plane to the other is done through two convergent lenses (L1 and L2 with focal length f and aperture 2w; L1: P1to P2, L2: P2 to P3) which realize the FT of P1 and P2. The second one is performed after the multiplication of the target image spectrum with a correlation filter.

Fig. 1: Illustrating the principle of OCT (optical correlator technique) and numerical implementation of the VLC

(N_VLC).

Consequently, the numerical algorithm of the VLC is shown in Fig. 1(b). In [14], we have applied this procedure based on Fraunhofer diffraction. The two-dimensional FT of the input plane at point (u,v) reads as

dxdyvyuxz

jyxPyxUvuz

kjjkz

jkzvuU i ))(2exp(),(),()(2

exp()exp(),( 022 +−+= ∫∫ λ

π

(1)

where 2k λ= π denotes the wave vector, λ is the wavelength of the incident wave illuminating the transparency. If we suppose that z is chosen to be so large that the phase factor P(x,y)=1 over the entire region of the (x,y) plane in which Uo(x,y) is non-zero, Ui(u,v) is just the two-dimensional FT of the aperture Uo(x,y), except for a multiplicative phase factor

preceding the integral and which does not affect the intensity of the diffracted light, at frequencies ,u vz zλ λ

⎛ ⎞⎜ ⎟⎝ ⎠

.

3. CORRELATION RESULTS BASED ON NO_FT AND FRAUNHOFER

DIFFRACTION

In this paper, we consider the special case of a circular aperture with diameter lw given by the pupil function

2 2( , ) circ

l

x yP x y

w

⎛ ⎞+⎜ ⎟=⎜ ⎟⎝ ⎠

, (2)

where the circle function circ(x)=1 if x<1, =1/2 if x=1, and 0 if x>1. A MATLAB function can compute the Fraunhofer diffraction pattern using the algorithm discussed in [13-14] with lw denoting the circular aperture of the lens (Fig.1(a)) illuminated with light of wavelength 633 nm. In order to show the impact of these parameters on the correlation results, we consider a face recognition application with horizontal rotation angles ranging from -45° to 45° and vertical rotation angles from -10 ° to 10°, test samples (Fig. 2) from the Pointing Head Pose Image Database (PHPID [11]. We make use of the receiver operating characteristic (ROC) curve obtained from the peak-to-correlation energy (PCE) calculations [1]. Furthermore, a phase-only filter (POF) [1], fabricated from the face framed in red in Fig. 2, is assumed in the VLC architecture [13].

Identification

Correlation Filter (Fn)

No

Yes EndTarget image FT

Target Image

spectrum

Correlation Plane

-1FT

(a)

(b)



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[14], ML ≤size, and f deby the values

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Corr

W=0.0

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W=

Fig. 3:

Case 1: W=6

ase used for t

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here M is the al length of thmeters.

relation obtaiNO_FT alg

0125m, L=0.3

AUC=0.7(a)

relation obtai

NO_FT alg0.05m, L=1.2

AUC=0.(c)

Correlation r

6.25mm, f=0.1

tests. The im

urve (AUC) c

number of pihe lens. It is ea

ined with theorithm mm, f=0.001m

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=0.5591 (d)

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The 4f setup (Fig. 4(a)) is used to reconstruct the input plane with this set of parameters. Figure 4(b) shows the reconstructed image at the output using NO_FT (Eq. (1)). The face is limited by the aperture 2W which takes a smaller value than the size of the input plane. Hence, the reconstructed image does contain only partly the input image.

Fig. 4: Reconstructed image using a 4f setup with W=6.25mm, f=0.125m, M=250, and L=0.625mm.

Application of this scheme leads to erroneous correlation results. This can be seen in Fig. 5 for several target and reference images. The autocorrelation plane presented in Fig. 5(a), while the correlation results corresponding to a target image and its variant rotated of 45° contains a central peak which looks like a correlation peak. However, the peak height shown in Fig. 5(b) is still large. This is counterintuitive since the target and reference images are significantly different. In like fashion, this peak is present in Fig. 5(c) and Fig. 5(d). It should be noted that this peak is related to the circular aperture (Fig. 4(b)).

f f f f

L L

2w

(b)(a)



n.::¡ae¿np

bi:;edineprCi

target image (P1) reference image

(a)


(b) target image (P2) reference image

(c)


(d) Fig. 5 : Correlation results between target and reference images when 2L W≥ .

3.2. Case 2: W=17.975 mm, f=0.125m, M=250, and L=0.625mm. To overcome the aperture issue, we assume now that 2L W≤ as shown in Fig. 6; a same requirement is made for the other lens. It should be noted that the length of the diagonal of the input plane is equal to the pupil’s aperture. Application of the proposed reconstruction scheme leads to disappearance of the circular pattern shown in Fig. 5(c). The corresponding correlation results are now shown in Fig. (7). Figure 7(a) shows the autocorrelation with a numerical implementation of the optical FT (NO_FT). As expected from a POF, it is characterized by a narrow and sharpened peak. Other panes in Fig. 7, i.e. Fig.7(b), Fig. 7(c), and Fig. (d), do not possess any correlation peak. In the following simulations, we take W=17.975 mm, f=0.125m, M=250, and L=0.625mm.



Fig. 6: Reconstruction of a input plane case when 2L W≤ .

Target image reference image

(a)


(b)


(c)


(d)

Fig. 7: Correlation results for two subjects of PHPID. W=17.975mm, L=0.625mm, f=0.125m, and M=250.

f f f f

L L

(c)(b)2WL

(a)



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4. DISCUSSION

In this brief section, we compare the VLC performances using either the FFT algorithm or the NO_FT algorithm. The tests consider the correlation of subject P2 having a close resemblance subject P1. The results, obtained with a specific threshold of the PCEs [1-3], are shown in Fig. 8. The NO_FT algorithm has for effect to decrease the false alarm rate and to increase the good decisions since in that case we obtain an AUC= 0.88 which is significantly larger than that obtained with the FFT algorithm (AUC= 0.75).

Correlation obtained with FFT

AUC=0.7558

(a)

Correlation obtained with the NO_FT algorithm W=17.975 mm, L=0.625mm, and f=0.125m

AUC= 0.8827

(b)

Fig. 8: Comparison between correlation results obtained with FFT and the algorithm (NO_FT), with subject P1 and P2.

5. CONCLUSION

In conclusion, the NO_FT procedure has been implemented numerically in a VLC. We have tested our approach by varying quantities of interest and found that the best performances correspond to the equality of the input plane size with the aperture of the lens. Based on these numerical calculations, we demonstrated that the NO_FT is robust and highly discriminating. Furthermore, a comparison with the correlation results obtained with FFT indicates that the discrimination is significantly improved.

REFERENCES [1] A. Alfalou and C. Brosseau, “Understanding Correlation Techniques for Face Recognition: From Basics to Applications,” Face Recognition Book, Milos Oravec (Ed.) INTECH, 354-380 (2010). ISBN: 978-953-307-060-5. http://sciyo.com/articles/show/title/understanding-correlation-techniques-for-face-recognition-from-basics-to-applications [2] P. Katz, A. Alfalou, C. Brosseau, and M. S. Alam, “Correlation and Independent Component Analysis Based Approaches for Biometric Recognition ,” in Face Recognition: Methods, Applications and Technology, A. Quaglia and C. M. Epifano (Editors), Chap 11, 201-229 (2012). ISBN: 978-1-61942-663-4. https://www.novapublishers.com/catalog/product_info.php?products_id=28370 [3] I. Leonard, A. Alfalou, and C. Brosseau, “Face recognition based on composite correlation filters: analysis of their performances” in Face Recognition: Methods, Applications and Technology, A. Quaglia and C. M. Epifano (Editors), Chap 3, 57-80 (2012). ISBN: 978-1-61942-663-4. https://www.novapublishers.com/catalog/product_info.php?products_id=28370



[4] M. Elbouz, A. Alfalou, and C. Brosseau, "Fuzzy logic and optical correlation-based face recognition method for patient monitoring application in home video surveillance", Opt. Eng. 50, 067003 (2011). [5] Y. Ouerhani, M. Jridi, A. Alfalou, and C. Brosseau, ”Graphics Processor Unit Implementation of Correlation Technique using a Segmented Phase Only Composite Filter,” Opt. Commun. 289, 33–44 (2013). [6] Special Issue on: “Field-Programmable Technology", J. Real-Time Image Proc. 2, (2011). [7] A. Alfalou and C. Brosseau, "Robust and discriminating method for face recognition based on correlation technique and independent component analysis model," Opt. Lett. 36, 645-647 (2011) [8] Eriko Watanabe, Kanami Ikeda, and Kashiko Kodate, "High-speed holographic correlation system by a time-division recording method for copyright content management on the internet", Proc. SPIE 8498, Optics and Photonics for Information Processing VI, 84980A (October 15, 2012). doi:10.1117/12.929690. [9] Mrs. Hemlata Patel, Pallavi Asrodia, “Fingerprint Matching Using Two Methodes,” IJERA 2, 857-860 (2012). [10] S. G. Bhele, V. H. Mankar, “A Review Paper on Face Recognition Techniques,” IJARCET 1, 339-646 (2012). [11] N. Gourier, D. Hall, and J. L. Crowley, “Estimating Face Orientation from Robust Detection of Salient Facial Features,” Proc. of Pointing 2004, ICPR, International Workshop on Visual Observation of Deictic Gestures (2004). [12] A Alfalou, M Elbouz, A Mansour, and G Keryer, “New spectral image compression method based on an optimal phase coding and the RMS duration principle,” J. Opt. 12, 115403 (2010). [13] A. Alfalou, C. Brosseau, B.-E. Benkelfat, S. Qasmi, and I. Léonard, “Towards all-numerical implementation of correlation,” Proc. SPIE 8398, Optical Pattern Recognition XXIII, 839809 (April 23, 2012); doi:10.1117/12.919378. [14] D. G. Voelz, Computational Fourier Optics: A MATLAB Tutorial, SPIE Tutorial Texts TT89 (SPIE Press, Bellingham, WA, 2011). See also J. Goodman, Introduction to Fourier Optics (McGraw-Hill, San Francisco, 1968). [15] J. P. Egan, Signal Detection Theory and ROC Analysis (Academic Press Series in Cognition and Perception, New York, 1975).



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