An Image-encoded Mach-Zehnder Joint Transform Correlator for Polychromatic Pattern Recognition with Multi-level Quantized Reference Functions

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1 Proceeding of the International MultiConference of Engineer and Computer Scientit 008 Vol I IMECS 008, 19-1 March, 008, Hong Kong An Image-encoded Mach-Zehnder Joint Tranform Correlator for Polychromatic Pattern Recognition with Multi-level Quantized Reference Function Chungcheng Lee, Chulung Chen, Chunmin Wang, and Chiehpo Chang Abtract The concept of uing image-encoded input repreentation in a Mach-Zehnder joint tranform correlator ytem with multi-level quantized reference function baed on the HSV color pace for polychromatic pattern recognition i propoed, in which we preent that the large zero order term can be removed in only one tep by the Stoke relation. By the image-encoding technique, the ize of the liquid crytal patial light modulator will be le with interlaced rearrangement of hue, aturation and value color component. Simultaneouly, multi-level quantized reference function (MQRF) which including finite quantization level are utilized to deign the input reference function. Since the reference function i real-valued in the patial domain, the LCSLM device in the image-encoded Mach-Zehnder joint tranform correlator require only real-valued modulation. Conequently, a reflective LCSLM device (RLCSLM) alo can be utilized to achieve the only real-valued modulation. Computed numerical reult are hown to verify the performance of thi ytem. Index Term image-encoded Mach-Zehnder joint tranform correlator, multi-level quantized reference function, polychromatic pattern recognition, reflective liquid crytal patial light modulator. I. INTRODUCTION Increaed attention ha been focu on liquid crytal patial light modulator (LCSLM) in the optical pattern recognition literature in recent year. There are many advantage of uing optical technique with LCSLM, e.g. capability of high-peed parallel operation, broad-bandwidth, non-crotalk interconnection, and real-time ignal proceing. Thee are ueful information for pattern recognition in which a great quantity of data need to be proceed. Accordingly, optical correlator have been implemented for pattern recognition. There were two well-known optical correlator for pattern Manucript received December 1, 007. Thi work wa upported by the National Science Council in Taiwan, under Grant No. NSC E MY3. Chungcheng Lee i with the department of Electrical Engineering, Yuan Ze univerity, 135 Yung Tung Road, Taoyuan 306, Taiwan. phone: ext 46; fax: ; chulung@ aturn.yzu.edu.tw. recognition, which are the VanderLugt (or matched filter baed) correlator (VLC) [1] and joint tranform correlator (JTC) []. Compared with the VLC, becaue the JTC ytem doe not have the tringent filter-alignment problem, the JTC i more robut in term of environment diturbance and more uitable for real-time proceing than VLC. However, the claical JTC ha a diadvantage. That i a large zero-order term in the correlation output. The recognition ability of thi ytem will be decreaed by the zero-order term. The deired cro-correlation peak were almot overhadowed and the output detector wa often aturated. To remove the zero-order term, many method have been propoed to accomplih the nonzero order JTC (NOJTC): for intance, phae-hifting technique [3] and joint tranform power pectrum (JTPS) ubtraction trategy [4]. Neverthele, the removal of the zero-order term in the NOJTC require more time-conuming tep. To improve thi, Cheng et al. [5] propoed a method that utilized a Mach-Zehnder configuration in the NOJTC (MZJTC), which can remove the zero-order term directly in only one tep. Beide, thi ytem doe not need to tore the Fourier pectra of both the target and reference image in the computer. Accordingly, everal reearch group have tudied to improve the performance of JTC [6]-[8]. For pattern recognition, color i alo an importance type in viual information. A a reult of the importance of color information, the multi-channel ingle-output NOJTC [9] ytem ha been propoed by Deutch et al. and the color pattern i eparated into the RGB multi-channel. In thi article, we uing a MZJTC correlator ytem with RLCSLM and image encoding technique baed on the HSV color pace for polychromatic pattern recognition. The minimum average correlation energy (MACE) [10] method i alo utilized to deign the reference function in the input patial domain [11]. The concept of image encoding lead to the ize of the RLCSLM will be mall by the interlaced rearrangement of hue, aturation and value color component. However, the MACE filter i complex-valued and require large dynamic range, which i hard to be implemented with preently available RLCSLM. Conequently, we alo utilize the multi-level quantized reference function (MQRF) filter [1] to deign the input reference function, which i a patial domain filter with finite quantization level. The both technique can yield harp ISBN: IMECS 008

2 Proceeding of the International MultiConference of Engineer and Computer Scientit 008 Vol I IMECS 008, 19-1 March, 008, Hong Kong correlation peak. At lat, the imulation numerical reult are obtained to verify our performance of the ytem. II. ANALYSIS The MZJTC uing image encoding technique (IEMZJTC) architecture with RLCSLM i now ued in optical image proceing. The implementation etup with interlaced canned color component i hown in Fig.1. It conit of a laer a a ource, a collimated len (CL), beam plitter (BS), 3 RLCSLM, 3 Fourier lene (FL), 3 CCD camera, 1 electronic Subtractor (ES) to remove the zero-order term of JTPS, and a PC to control the whole ytem. The RLCSLM conit of a polarizing beam plitter (PBS), a half wave plate (), a quarter wave plate (), and a LC modulator. The RLCSLM1 and RLCSLM can diplay the graycale image of color component for the encoded reference image and the encoded target image, which are denoted by e( xd, y) and t( x d, y), repectively. Here d i the ditance of the reference channel and target channel away from the horizontal central line of the RLCSLM. The model correpond better to how people experience color than the RGB color pace doe. Let mall capital letter h, and v denote, repectively, the normalized hue, aturation, and value channel in the HSV pace, with color value normalized to 1 for full intenity. The HSV color pace ued to be called the hexcone color model, which i hown in Fig.. In general, the ytem repreentation of digital color i 8-bit per component. Therefore, digital RGB value are with a range between 0 and 55. Each component can be regarded a a graycale image. In optic, the component value are normalized, with full intenity, 55, equal to 1.0 for convenience. Let mall capital letter r, g and b denote, repectively, the normalized R, G, and B channel in the RGB pace. We can tranfer the RGB to HSV color pace a the following equation: h if if bg bg 1 ( r g) ( r b) 1/ ( rg ) ( rg )( gb ) with =co, max( r, g, b) min( r, g, b), () max( r, g, b) and v max( r, g, b), (3) where max and min operator elect the maximum and (1) minimum value of the operand, repectively. We can ee that the tranformation from RGB to HSV i a non-linear operation. Next, the h,, and v component will be utilized in our IEMZJTC ytem with image encoding technique for color image. In thi method, thee graycale image are organized a a new encoded image, a hown in Fig., which i diplayed on a ingle, monochromatic, input plane. The proce i lited a follow: 1. Let h1 1 v1 h h,, and v v, (4) hn n vn where h,, and v repreent the matrice of hue, aturation, value image, repectively; n denote the number of the maximum row vector.. Inert one by one repectively each h,, and v row vector to a matrix. h1 1 v1 e. (5) hn n v n Hence, the new matrix e i an encoding image, which include all color element. Thi method i different from multi-channel ingle-output JTC. The encoding image can repreent the combination of hue, aturation, and value graycale image at the input plane. The ytem could be maller ince the channel number of input image ha reduced to a ingle channel. The encoded reference image and the encoded target image are put into RLCSLM1 and RLCSLM, repectively. A collimated coherent beam illuminate both the RLCSLM1 and RLCSLM, and pa through the FL. We can repreent the light field H1 and H in term of the reflected and tranmitted component in thi IEMZJTC a follow: H (, ) E(, ) exp{ j ( d)} and 1 1 T (, ) exp{ j ( d)} H (, ) T (, ) exp{ j ( d)} where and E(, ) exp{ j ( d)}, 1 (6) (7) denote the tranmiion and reflection coefficient of the BS, repectively; E (, ) and T(, ) are ISBN: IMECS 008

3 Proceeding of the International MultiConference of Engineer and Computer Scientit 008 Vol I IMECS 008, 19-1 March, 008, Hong Kong the Fourier tranform of e( x, y) and t( x, y ), repectively; andare mutually independent frequency domain variable. Both of the output of CCD1 and CCD are connected to an ES. The reultant output of the ES due to the quare-law detection i IH (, ) H 1(, ) ( 1 1 ) T (, ) exp[ j ( d)] T (, ) exp[ j ( d)] ( ) E(, ) exp[ j ( d)] E(, ) exp[ j ( d)] * * ( 1 1 ) T (, ) exp[ j ( d)] E(, ) exp[ j ( d)] * * ( 1 1 ) E(, ) exp[ j ( d)] T (, ) exp[ j ( d)]. According to Stoke relation [13], let 1, 1 1, and. We can obtain I E (, ) T (, ) co{ [ d] (, ) (, )}, E where i the phae of ; E and T are the phae of E (, ) and T (, ) repectively. Finally, the MZJTPS can be obtained without the zero-order term. Then, we diplay I in RLCSLM3. Finally, we can obtain the intenity ditribution without auto-correlation term at the output correlation plane via the CCD3 detector, which i I ( x, y) c( x, y) ( x d, y), (10) c( x, y) ( x d, y) where c( x, y) e ( x, y) t ( x, y) i the complex cro-correlation between e and t ; and denote the correlation and convolution operation, repectively. Furthermore, we can minimize the average correlation energy for all training image by uing the Lagrange multiplier method and contrain the correlation peak to be a deired value P. The optimum olution can be depicted a the following equation. 1 * T 1 1 * E D T [( T ) D T] P. T (8) (9) (11) The olution in (11) i a vector repreentation in the frequency domain. After the column vector E i rearranged a a quare matrix E (, ), e( x, y) can be obtained by invere Fourier tranform of E (, ) ; that i e x y 1, { E, }. (1) Moreover, the MQRF i ued to obtain the quantized function with finite level in thi IEMZJTC ytem. The tranmittance i controlled with digital voltage and i therefore quantized becaue the commercial LCD circuit i deigned with digital IC technology. Finally, the Eq. (1) with MQRF can be expreed a 1 1 [ E (, )] Q e( x, y) Round ( ), Q M where M i the maximum of (13) 1 [ E (, )] ; Q i the amplitude quantization parameter; Round(K) function round K to the nearet integer. Since the reference function i real-valued in the patial domain, the RLCSLM device in the IEMZJTC require real-valued only modulation. III. SIMULATION RESULTS The performance of the IEMZJTC baed on the HSV color pace i invetigated with the MQRF. We choe a colorful fih image with pixel a the tet image, which i hown a Fig.. Furthermore, we utilize the combination of h,, and v graycale image to form an encoded image with pixel. Furthermore, we utilize the combination of h,, and v graycale image to form an encoded image with pixel. The training et alo contain 5 color image with different angle of in-plane rotation for implicity. The rotational ditortion range from -4 to 4 i conidered (in tep of ). Next, we yntheize the reference image from training image et with the method of Lagrange multiplier and the MQRF. The computed reference function for training encoded image with MQRF i put in the RLCSLM1. We chooe the 0 rotated image to be the target image, and put the HSV channel of target image in the LCSLM. The three-dimenional correlation intenity profile for the 1t, nd, and 5th order quantization level are illutrated in Fig. 3(a), 3(b), and 3(c), repectively. Accordingly, we can oberve the variation of idelobe under quantization level Q=1, Q=, and Q=5. From the three-dimenional output profile, we can ee that the deired harp correlation peak can be een clearly. Therefore, the ytem with IEMZJTC baed on the HSV color pace with quantization method can yield acceptable reult to recognize color pattern. IV. CONCLUSIONS In thi paper, we have preented a novel optoelectronic ytem with image encoding technique for invariant color pattern recognition baed on the HSV color pace. Compared to multi-channel JTC in the joint input plane, the propoed IEMZJTC could be eaier and the ytem could be maller ince the channel of input image can be reduced to a ingle channel. Beide, the IEMZJTC ytem can remove the zero-order term in one tep without two or more redundant procedure. For real-time proceing, the joint input plane i diplayed on the RLCSLM with the MQRF technique to deign the reference k ISBN: IMECS 008

4 Proceeding of the International MultiConference of Engineer and Computer Scientit 008 Vol I IMECS 008, 19-1 March, 008, Hong Kong function for color pattern recognition. The MQRF with a limited number of dicrete level can be implemented in current available RLCSLM. Beide, we have proved that the deigned reference function i a real-valued function. Meanwhile, ome RLCSLM device are utilized to achieve real-valued only modulation. In the tet, the algorithm i robut to the real-time proce and ditortion invariance. It i expected that the propoed method i promiing in practical application. Beide, the IEMZJTC baed on the HSV color pace with MQRF ha quite good performance for polychromatic pattern recognition. To ummarize, the overall performance of thi IEMZJTC ytem uing MQRF are good, which offer an attractive alternative for polychromatic pattern recognition. REFERENCES [1] A. VanderLugt, Signal detection by complex patial filtering, IEEE Tran. Inf. Th., vol. IT-10, 1964, pp [] C. S. Weaver and J. W. Goodman, A technique for optically convolving two function, Appl. Opt., vol. 5, 1966, pp [3] G. Lu, Z. Zhang, S. Wu, and F. T. S. Yu, Implementation of a nonzero order joint tranform correlator by ue of phae hifting technique, Appl. Opt., vol. 36, 1997, pp [4] C. Li, S. Yin and F. T. S. Yu, Nonzero-order joint tranform correlator, Opt. Eng., vol. 37, 1998, pp [5] C. Cheng and H. Tu, Implementation of a nonzero-order joint tranform corelator uing interferometric technique, Opt. Rev., vol. 9, 00, pp [6] B. Javidi and C. J. Kuo, Joint tranform image correlation uing a binary patial light modulator at the Fourier plane, Appl. Opt., vol. 7, 1988, pp [7] F. T. S. Yu, G. Lu, M. Lu, and D. Zhao, Application of poition encoding to complex joint tranform correlator, Appl. Opt., vol. 34, 1995, pp [8] C. Wu, C. Chen, and J. Fang, Linearly contraint color pattern recognition with a nonzero order joint tranform correlator, Opt. Commun., vol. 14, 00, pp [9] M. Deutch, J. Garcia, and D. Mendlovic, Multi-channel ingle-output color pattern recognition by ue of a joint-tranform correlator, Appl. Opt., vol. 35, 1996, pp [10] A. Mahalanobi, B. V. K. V. Kumar, and D. Caaent, Minimum average correlation energy filter, App. Opt., vol. 6, 1987, pp [11] C. Chen, C. Chen, C. Lee, and C. Chen, Contrained optimization on the nonzero order joint tranform correlator contructed with the Mach-Zehnder configuration, Opt. Commun., vol. 31, 004, pp [1] J. Fang and C. Chen, Non-zero order joint tranform correlator with multi-level quantized reference function, Opt. Commun., vol. 0, 003, pp [13] E. Hecht, Optic, Reading, Ma., 4th edition, Addion-Weley,00, pp Laer BS1 CL BS PBS3 CCD3 PBS1 PBS FL3 RLCSLM1 BS3 RLCSLM3 RLCSLM FL FL1 CCD ES CCD1 PC Fig. 1. The chematic diagram of an IEMZJTC ytem with RLCSLM. ISBN: IMECS 008

5 Proceeding of the International MultiConference of Engineer and Computer Scientit 008 Vol I IMECS 008, 19-1 March, 008, Hong Kong h e Original color image v Graycale image (b) Encoded image Fig.. Image encoding proceing with HSV color pace in the IEMZJTC (a) (b) (C) Fig. 3. The 3D correlation intenity profile with (a) Q=1, (b) Q=, and (c) Q=5. ISBN: IMECS 008