Frequency Domain Approach for Face Recognition Using Optical Vanderlugt Filters

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1 Optics and Photonics Jounal, 016, 6, Published Online August 016 in SciRes. Fequency Domain Appoach fo Face Recognition Using Optical Vandelugt Filtes Faanak Heidai, Hassan Kaatuzian, Amin Alizadeh Photonics Reseach Lab (PRL), Electical Engineeing Depatment, Amikabi Univesity of Technology, Tehan, Ian Received 30 May 016; accepted 1 August 016; published 5 August 016 Abstact In this pape human face machine identification is expeienced using optical coelation techniques in spatial fequency domain. This appoach is tested on ORL dataset of faces which includes face images of 40 subjects, each in 10 diffeent positions. The examined optical setup elies on optical coelation based on developing optical Vandelugt filtes and its basics ae descibed in this aticle. With the limitation of face database of 40 pesons, the ecognition is examined successfully with nealy 100% of accuacy in matching the input images with thei espective Vandelugt synthesized filtes. Softwae simulation is implemented by using MATLAB fo face identification. Keywods Face Recognition, Optical Filtes, Optical Coelation, Optical Image Pocessing, Vande Lugt Filtes, Image Pocessing 1. Intoduction When we talk to someone, we usually look at his face. Face ecognition not only plays an impotant ole in social inteactions but also is cucial fo secuity check and human machine inteface. In compaison with fingepint o iis data which need complex devices, face pictues can easily and inteactively be gatheed by a simple camea. Theefoe face ecognition has advantages ove othe biometics. It has been a challenging subject fo ove 50 yeas and yet many eseaches ae investigating on methods to solve its complicated poblems. Filteing images fo image pocessing puposes involving face ecognition has been investigated in two main categoies. One is to use optical coelatos in which face images ae consideed as a whole and the othe is to use digital methods in which pixel computations unde the concept of digital image pocessing ae concened [1] []. Using optical filtes to measue similaity between images is being consideed fo decades [3]. Since optical filteing basically ely on using spatial Fouie tansfom of images in fequency domain, pactically it can be achieved by use of simple optical elements such as conveging lenses [4]. Futhemoe, egading to the paallel natue of optical pocessing; since light waves tavel in paallel, all the infomation of an image can be seached at the speed of light and it can be consideed as eal-time pocessing. A eview on optical image pocessing using Vandelugt filteing and its calculations which ae the basics of How to cite this pape: Heidai, F., Kaatuzian, H. and Alizadeh, A. (016) Fequency Domain Appoach fo Face Recognition Using Optical Vandelugt Filtes. Optics and Photonics Jounal, 6,

2 ou investigation is pesented in Section. Section 3 will cove a desciption on the dataset which we used and ou investigation on it with the Vandelugt coelato. Conclusion is pesented in Section 4.. A Review on Optical Image Pocessing Using Vandelugt Filtes Seveal methods fo optical image pocessing exist which ely on simila concepts. One of the basic methods is to pocess images by means of Vandelugt spatial filteing [5]. Based on that, -D Fouie tansfom infomation of an object can be ecoded on a photo-sensitive film. Using Vandelugt filteing and a coelation setup called 4f o Fequency Plane Optical Coelato; FPC, optical image pocessing and patten ecognition in images can be accomplished..1. 4f Coelato Setup A simple and effective setup fo optical image pocessing called 4f setup is illustated in Figue 1. This system povides the coelation between two images. One image is placed on the input plane and the filteed fom of anothe image is settled in the Fouie plane position. As can be seen, a lase beam passes though the fist image and the fist optic lens and shapes Fouie tansfomed fom of the fist image on the Fouie plane. Vandelugt filte of the second image which contains its fequency domain infomation intefees with the Fouie tansfomed of the fist image. As the intefeence passes though the second optical lens, pactically an invese Fouie tansfom is applied. Theefoe the invese Fouie tansfom of the multiplication of Vandelugt filte and input image in the fequency domain will fom on the output plane egaded as the coelation between the two images. By sensing the intensity of the coelation and compaing it to the auto-coelation of images, the similaity between two images can be measued [6]... Poviding Vandelugt Filte of an Image Figue shows a schematic setup to synthesize spatial fequency Vandelugt filte of an image on a film. The L 1 lens emit paallel light on P 1 plane which has the image on it with the spatial impulse esponse of h( x1, y 1). When the image light passes though L lens, in the distance of focal length of L, spatial Fouie tansfom of 1 x y the image foms on the P plane. Theefoe we will have H,? on the P plane. A photo-sensitive plane can be substituted instead of P. Also, the P pism, diectly guides a pat of the souce light towads the P plane, thus this light and the light coming fom the L lens intefee on the P plane. So the intefeence of souce light and the Fouie tansfom of the image will be ecoded on the film placed instead of the P plane. If the tilted plane wave incident fom the pism poduces a field distibution U ( x, y ) at the P plane as below: Figue 1. a 4f coelato setup [1]. 95

3 Figue. Vandelugt filte synthesis setup [4]. whee U ( x, y ) =.exp( j πα y ) (1) 0 sinθ α =, then the intefeence model on P will be as: λ 1 x y gx (, y).exp( j y) H(, ) = 0 πα + ( Since a photo-sensitive film is only sensitive to the intensity of light, the model is squaed in the Equation (. By manipulating the Equation (, gx (, y will be as: 1 x y 0 x y gx (, y = 0 + H(, ) + H(, ).exp( j πα y x y H (, ).exp( j πα y 0 + As the final stage fo the synthesis of the image s spatial fequency Vandelugt filte, the film would ecod a tanspaent pictue whee its amplitude; tx (, y, is elated to the intensity of the light coming fom both the image and the souce t( x, y + 0 H H.exp( j πα y H.exp( j πα y + + (4) The thid tem in Equation (4) is exactly the Fouie tansfom of the impulse esponse of the image and thus can be used fo optical pocessing in spatial fequency domain puposes..3. Image Pocessing by Means of the Vandelugt Filte Synthesized Vandelugt filte can be eplaced by the Fouie plane of Figue 1. If the input image to be filteed 1 x y is shown by gx ( 1, y 1), its spatial fequency distibution will be equal to G,?. Regading to the Equation (4), optical signal eceived on the Fouie plane of the 4f coelato depicted in Figue 1 will be as: U G + H G+ H. G.exp( j πα y H. G.exp( j πα y (5) U is the multiplication of the Vandelugt filte and the Fouie tansfom of the input image in the fequency domain. When this intefeence passes though the second lens of the 4f coelato, afte taveling as fa as the focal length of the lens, invese Fouie tansfom is applied and U 3 will fom on the output plane. (3) 96

4 1 U3 0. g( x3, y3) + [ h( x 3, y3) h ( x3, y3) g( x3, y3)] [ h( x, y ) g( x, y ) ( x, y α)] δ [ h ( x3, y3) g( x3, y3) δ ( x3, y3 α)] The thid tem of the Equation (6) is the convolution between h and g which will occu at an aea cen- 0, α on the output plane. The fouth tem can be witten as, teed at ( ) (, ) (, ) (, ) = h x3 y3 g x3 y3 δ x3 y3 α + (, ). (, 3 + ) g ϕ η h ϕ x η y α dϕdη which is the coelation between h and g which will occu at an aea centeed at ( 0, α ) + on the output plane. Thus, if the light souce makes the sufficiently lage angle with the P plane duing the Vandelugt filte synthesis, the convolution and coelation aeas would be fa fom each othe enough on the output plane of the 4f coelato. This leads to the possibility of spatial high-pass filteing the output plane in ode to achieve to the coelation and convolution between the input image and the Vandelugt filte sepaately. Note that spatial high-pass filteing means to allow passing pat of the optical signal which is away fom the cente of the plane. Also note that the fist and the second tems of the Equation (6) which occu aound the cente of the output plane, have the least effect on the desied output and as they will be spatially filteed by the high-pass filte, they will be neglected fo the simulation as well. In Figue 3, the output plane of the 4f coelato is illustated. The place of the convolution and the coss coelation can be seen as descibed. If the maximum spatial width of h and g is egaded as maximum value of the discussed fou tems will be as below: 1 0 gx3 y3 W g W h and (6) (7) W espectively, then the possible g 1:. (, ) : max (8) : [ h( x3, y3) h ( x3, y3) g( x3, y3) ( Wh + Wg):max (9) 0 3: [ h( x 3, y3) g( x3, y3) δ ( x3, y3 + α)] ( Wh + Wg):max (10) Figue 3. Locations of the coelato output tems [4]. 97

0 4: [ h ( x 3, y3) g( x3, y3) δ ( x3, y3 α)] ( Wh Wg):max + (11) So to be able to sepaate the fou tems on the output plane spatially, α and θ should meet the limitations of Equation (1 and Equation

5 0 4: [ h ( x 3, y3) g( x3, y3) δ ( x3, y3 α)] ( Wh Wg):max + (11) So to be able to sepaate the fou tems on the output plane spatially, α and θ should meet the limitations of Equation (1 and Equation (13). 1 3W h sinθ α ( + Wg ) ( α = ) (1 λ 3 W h W g θ + ( if sin ) f f θ θ (13) It is of significant impotance to conside that since natually in a 4f setup the spatial impulse esponse of a desied image will be computed and ecoded automatically with the speed of light, thee will be no need fo complex and time consuming computations as in digital systems is equied. Moe impotant, the Vandelugt filte ecods both the amplitude and the phase of a Fouie tansfomed image on the same film with high esolution so thee will be no need to ecod the amplitude and the phase infomation sepaately. 3. Ou Investigation In yea 00 an investigation was done on English alphabet ecognition at ou Photonics Reseach Laboatoy; PRL, and the designed system was successfully implemented as a hybid optical-digital pocesso with simple optical elements and a pesonal compute [7]. It motivated us to simulate a simila pocess fo face ecognition which demands moe pecise calculations due to the moe complex natue of face images. The investigation is done on the ORL face database collected fom 40 subjects each with 10 diffeent vaiations in thei pose [8]. An oveview of the data set is pesented in Figue 4. The poblem was to ecognize an input subject among the 400 images of diffeent 40 people using the Vandelugt filteing and 4f coelato. Fist a database of Vandelugt filtes of all the images in the dataset had to be ceated. This has been done by numeically implementing the Equation ( fo the MATLAB softwae. This implementation may be a little ticky due to the high sensitivity of discimination between diffeent subjects Vandelugt filtes to the accuacy of the implementation. All the paametes and constants should be consideed pecisely to obtain a esolution nea the eal optical setup; othewise the coelation simulation will fail. In Figue 5 two images fom ORL data set and thei calculated Vandelugt filtes ae pesented. The next step is to apply each intended face image to the 4f coelato and coelate it with all the Vandelugt filtes of the images in the data set. Fo this means, Fouie tansfom of each of the input images is multiplied by the Vandelugt filtes and the esult ae invese Fouie tansfomed to obtain the optical coelation on the Figue 4. Pat of the ORL dataset which was used [8]. 98

output plane. Now the maximum value of the output plane is used as a measue of similaity. Thus the moe this value is, the moe the input image should be simila to that Vandelugt filte.

It means that the input image exactly matches with its Vandelugt filte as they have the highest optical coelation among all.

6 output plane. Now the maximum value of the output plane is used as a measue of similaity. Thus the moe this value is, the moe the input image should be simila to that Vandelugt filte. Fist we have simulated this setup fo all the 400 pictues and ou system ecognized the input image nealy eoless and with about 100% accuacy. It means that the input image exactly matches with its Vandelugt filte as they have the highest optical coelation among all. In Figue 6 ba chats fo six subjects ae pesented which show the nomalized optical coelation between the fist images of six diffeent subjects fom the dataset and all the 400 Vandelugt filtes of the whole dataset. As can be conducted, the coelation of the input image with its espective Vandelugt filte is the highest among all with a consideable diffeence to othes, leading to a high confidence on the ecognition output. Second peak and next high numbes ae fo the same subject with diffeent positions. Although some of them failed to match bette than othe subjects with the input image. In Figue 6, each 10 bas elate to diffeent positions of an individual subject. Figue 5. Subject 1 and its Vandelugt in the above ow, subject 6 and its Vandelugt in the bottom ow. Figue 6. The optical coelation between the fist image of six subjects and the Vandelugt filtes fo all the 400 ORL face. 99

7 4. Conclusion Face ecognition poblems ae divided in two majo subsets as face identification (identifying a peson among a set of people) and face veification (veifying that a peson is who he claims). In ou suvey ou focus was on face identification. As showed in pevious sections, pocessing images using a eal optical setup especially fo coelation is faste than the digital pocesses as pocesses hee take place at the speed of light. This appoach can be highly beneficial to use in secuity check stations, e.g. in aipots. A database of suspects Vandelugt filtes can be made and fo each in sufficient diffeent positions and the coelation will immediately be eady. Although this appoach can fail when the subject s pose diffeence inceases, vaieties of subjects poses can be added to the Vandelugt database without losing the speed due to the eal-time natue of this optical setup. Futhemoe, as secuity check usually takes place in contolled situations, woies about the pose diffeence of the subject and its image in the Vandelugt data base can be neglected and identification can be achieved with nealy 100% accuacy. To expand the usage of this appoach and to add moe flexibility to the situations in which it will wok accuate, an optical coelato can be combined with a digital pocesso. The digital pocesso can help in applying pepocessing on the input image in ode to eliminate spatial and illumination noises and occlusions which can affect the optical coelato output quality. Refeences [1] Kaatuzian, H. (009) Photonics, Volume. nd Edition, Amikabi Univesity Pess, Tehan. (In Pesian) [] Napoleon, T. and AlFalou, A. (014) Local Binay Pattens Pepocessing fo Face Identification/Veification Using the VandeLugt Coelato. Poc. of SPIE, [3] Goodman, J.W. (1988) Intoduction to Fouie Optics. nd Edition, McGaw-Hill, New Yok. [4] Watanabe, E., et al. (008) Ultahigh-Speed Optical Coelation System Using Hologaphic Disc. The Japan Society of Applied Physics, Japan. [5] Alfalou, A. and Bosseau, C. (010) Undestanding Coelation Techniques fo Face Recognition: Fom Basics to Applications. In: Oavec, M., Ed., Face Recognition, InTech. [6] Stewad, E.G. (1987) Fouie Optics, nd Edition, Dove Publications, Mineola, New Yok. [7] Alizadeh, A.(00 Simulation, Design and Implementation of a Hybid Optical Pocesso fo Pocessing Images. M.Sc. Thesis, Amikabi Univesity of Technology, Ian. [8] AT&T Laboatoies Cambidge (1994) ORL Face Database. Submit o ecommend next manuscipt to SCIRP and we will povide best sevice fo you: Accepting pe-submission inquiies though , Facebook, LinkedIn, Twitte, etc. A wide selection of jounals (inclusive of 9 subjects, moe than 00 jounals) Poviding 4-hou high-quality sevice Use-fiendly online submission system Fai and swift pee-eview system Efficient typesetting and poofeading pocedue Display of the esult of downloads and visits, as well as the numbe of cited aticles Maximum dissemination of you eseach wok Submit you manuscipt at: 100

Journal of World s Electrical Engineering and Technology J. World. Elect. Eng. Tech. 1(1): 12-16, 2012

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