- Email: [email protected]
Multiplexing of volume holographic wavelet correlation processor
15 March 2000
Optics Communications 176 Ž2000. 49–59 www.elsevier.comrlocateroptcom
Multiplexing of volume holographic wavelet correlation processor Wenyi Feng ) , Yingbai Yan 1, Guofan Jin, Minxian Wu, Qingsheng He State Key Laboratory of Precision Measurement Technology and Instruments, Department of Precision Instruments, Tsinghua UniÕersity, Beijing 100084, China Received 30 September 1999; received in revised form 1 December 1999; accepted 6 December 1999
Abstract Volume holographic associative memory in a photorefractive crystal provides an inherent mechanism to develop a multi-channel correlation identification system with high parallelism. Wavelet transform is introduced to improve discrimination of the system. We first investigate parameters of the system for parallelism enhancement, and then study multiplexing of the system on input objects and wavelet filters. A general volume holographic wavelet correlation processor has a single input-object channel and a single wavelet-filtering channel. In other words, it can only process one input object with one wavelet filter at a same time. Based on the fact that a volume holographic correlator is not a shift-invariant system, multiplexing of input objects is proposed to improve parallelism of the processor. As a result, several input objects can be recognized simultaneously. Multiplexing of wavelet filters with different wavelet parameters is also achieved by a Dammann grating. Wavelet correlation outputs with different filters are synthesized to improve recognition accuracy of the processor. Corresponding experimental results in human face recognition are given. The combination of the input object multiplexing and the wavelet filter multiplexing is also described. q 2000 Elsevier Science B.V. All rights reserved. Keywords: Volume holographic storage; Wavelet transform; Correlation identification; Parallel processing; Human face recognition
1. Introduction Volume holographic storage in a photorefractive material is used to construct optical wavelet transform system recently w1x. On the other hand, the associative memory characteristic of the technique is adopted to realize optical wavelet correlation identification more frequently w2,3x. Wavelet transform is introduced to improve the quality of correlation outputs, and as a result, the accuracy of identification. The conventional correlation of images converts to )
Corresponding author. Tel.: q86-10-6278-1204; fax: q86-106278-4691; e-mail: [email protected] 1 E-mail: [email protected].
the correlation of main features extracted by a same wavelet filter. A sharp correlation peak with little sidelobes and robust to noise is obtained w4,5x. The attractive advantages of volume holographic storage for wavelet transform processing are its high diffractive efficiency, large storage capacity, and real time response w6–8x. It was reported that 10 000 images have been recorded and restored in a single crystal w9x. The inherent parallel processing nature offers a suitable mechanism for pattern recognition. Once all the patterns are stored in a crystal, it can be employed as a database for pattern recognition or other processing. A certain reference beam can recover a stored pattern. An input image can also be compared with all the stored patterns by the object beam. For
0030-4018r00r$ - see front matter q 2000 Elsevier Science B.V. All rights reserved. PII: S 0 0 3 0 - 4 0 1 8 Ž 9 9 . 0 0 7 6 6 - X
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W. Feng et al.r Optics Communications 176 (2000) 49–59
example, all the patterns are recorded as angle-multiplexing holograms. When the object beam modulated by an input image is used to read out the holograms, a set of ‘reference beams’ with different transmitting angles will be restored. The intensity of each beam stands for the correlation between the input image and the corresponding recorded pattern. The correlation peaks between the input image and all the stored patterns are obtained simultaneously. The input image can be identified by the energy distribution of the correlation peaks. The multi-channel correlation processor based on volume holographic storage and wavelet transform is described at first in Section 2. Parallelism of the processor, which is defined as the number of correlation channels in a single output, is studied in Section 3 as a base for multiplexing. To simplify the problem, we suppose that the dynamic range of the photorefractive crystal is large enough. Therefore, parallelism is mainly determined by geometrical parameters of the system. The main parameters relative to parallelism, such as the scanning interval and the dynamic scope of the reference beam, are analyzed. A general volume holographic wavelet correlation processor has one input-object channel and one wavelet-filtering channel, which can only process one input object with one wavelet filter at a same time w10x. Multi-input channels are needed to improve the speed in many applications such as human face identification. Several faces are recognized one by one sequentially if there is only one input channel, but they can be recognized simultaneously in a multi-input channel system. It is concluded that a correlation system based on volume holograms is no longer fully shift-invariant. However, various methods have been proposed to compensate the shortcoming w11,12x. We utilize the characteristic to construct a novel volume holographic correlation system with multi-input channels in Section 4. Simulations and experiments on shift invariance are performed to obtain conditions of realizing multi-input channel processing in a volume holographic wavelet correlation system. On the other hand, wavelet filters with different parameters are needed in many situations of pattern recognition w13x. Features of some patterns are very similar to each other in some wavelet-filtering channels, where wavelet correlation peaks are near and hard to distinguish. However, they are
different and can be distinguished in other channels. Hence, it is effective to synthesize the correlation outputs in different wavelet-filtering channels for high recognition accuracy. Based on the idea, a processor with multi-wavelet channels is proposed and constructed in Section 5. Wavelet transform results of all the patterns with different wavelet filters are stored in the crystal. That of an input image can be used to obtain wavelet correlation outputs between the image and all the patterns in different wavelet-filtering channels simultaneously. Multiplexing techniques of the processor on input objects and wavelet filters are testified by its application to human face recognition, and promising experimental results are obtained. In Section 6, the combination of the input object multiplexing and the wavelet filter multiplexing is described so that the two multiplexing techniques can be performed simultaneously for a higher parallel processing. Finally, some conclusions are given.
2. Volume holographic wavelet correlation processor If two images are f Ž x, y . and sŽ x, y ., respectively, their wavelet correlation can be defined as f Ž x , y . m haŽ x , y . m sŽ x , y . m haŽ x , y . q`
s
q`
Hy` Hy` F Ž u, Õ . H
)
Ž a x u, a y Õ . S ) Ž u, Õ .
=H Ž a x u, a y Õ . exp i2 p Ž xu q yÕ . d u dÕ
Ž 1. where ‘m’ is the correlation operator, h aŽ x, y . s Ž1rŽ a x a y . 0.5 . hŽŽ xra x ., Ž yra y .. is the wavelet filter, a s Ž a x , a y . is the dilation factor of the wavelet function, and F Ž u, Õ ., SŽ u, Õ . and H Ž a x u, a y Õ . are the Fourier transforms of f Ž x, y ., sŽ x, y . and h aŽ x, y .. Mexican-hat wavelet function is adopted in the system to fabricate the filter because it is quadratic differential of a Gaussian function and also one of the most useful edge detection functions. In the frequency domain, the function is w14x H Ž u, Õ . s 4 p 2 Ž u 2 q Õ 2 . exp y2 p Ž u 2 q Õ 2 .
Ž 2.
W. Feng et al.r Optics Communications 176 (2000) 49–59
It is a real positive function, which is benefit for filter fabrication. According to the expression Ž1. and the achievement of volume holographic correlators, wavelet correlation can be realized as below. First, we record multiplexing wavelet-filtered spectrum holograms of all the patterns in a crystal. Second, wavelet-filtered spectrum of an input image is used to read out the holograms. Finally, wavelet correlation outputs of the input image and all the stored patterns will be detected on the output plane. A volume holographic wavelet correlation processor based on the mechanism is shown in Fig. 1. The linear polarized light generating from a laser is expanded, filtered and collimated by a microscope lens BL, a pinhole PH, a beam-expanding lens EL, and a diaphragm D. Passing through a half wave plate HP1 and a polarized beam-splitting prism BS, the light is divided into two parts as a reference beam and an object beam. A proper power distribution between the reference beam and the object beam will be implemented by rotating the plate HP1. A beam scanning setup made up of lens L 1 and L 2 controls the reference beam before it projects on the crystal. To ensure there is an interference region of the two beams, we should make the size and position of the reference beam motionless on the
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recording plane, and only permit the alteration of its direction. It is realized by letting the recording plane at the imaging place of the laid the lens L 1 and the recording plane satisfy imaging relation to the lens L 2 . Spherical reference beam is used for a more compact structure. According to the diffractive theories, correlation outputs are detected on the convergent plane of the spherical beams. An extra lens is needed to make inverse Fourier transforms for the read out beams if a plane wave is used as the reference beam. The input pattern on the SLM is Fourier transformed by the lens FL, filtered by the wavelet filter WF, and imaged onto the crystal by the lens IL. The half wave plate HP2 is used to adjust polarization of the object beam. The two beams interfere to form a volume hologram in the crystal. Moving the lens L 1 to alter the transmitting angle of the reference beam and replacing the input pattern at the same time, we can record angle-multiplexing holograms in the crystal. When all the patterns are recorded in the crystal, the system is ready for recognition. The object beam is needed only in recognition. The image for identification is fed to the system whose spectrum is filtered by the wavelet filter and imaged onto the crystal to read out the holograms. Multi-channel wavelet correlation outputs are captured by a CCD camera and transferred
Fig. 1. Schematic drawing of the volume holographic wavelet correlation processor.
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W. Feng et al.r Optics Communications 176 (2000) 49–59
Fig. 2. Contrastive experimental results between conventional correlation and wavelet correlation with No.1 face as the input image.
to a computer for post-processing. The input image can be identified according to the energy distribution of the correlation outputs. The whole process is arranged by a personal computer. Because the time-consuming recording process is a priori and the recognition process is implemented instantly, the processor can be used for real-time pattern recognition. Contrastive experiments of 30 human face recognition are made between conventional correlation and wavelet correlation. Fig. 2 shows the experimental results with No. 1 face as the input image. The above figure is the conventional correlation output, and the bottom one is the wavelet correlation output. Let’s check the conventional situation first. There is a large background noise, and strong correlation peaks appear not only at the position of No. 1 face but also at the positions of No. 5, 15, 21, 25 and 30
faces. Hence, it is difficult to identify the input face from all the patterns. Contrarily, there is almost no background noise in the output of the wavelet correlation. The strong correlation peak only appears at the position of the corresponding pattern, No. 1 face. The input face can be identified easily and accurately.
3. Parallelism of the system Principal drawing of the system above is shown in Fig. 3. More patterns recorded in the crystal, more correlation peaks will be obtained on the output plane, and also higher parallelism is realized. We define parallelism of the system as the number of correlation peaks N in a single system output. By simulation and experiments, we have concluded that
Fig. 3. Principal drawing of the volume holographic wavelet correlation processor.
W. Feng et al.r Optics Communications 176 (2000) 49–59
cross-talk noise of multi-channel volume holographic correlation is reduced significantly with the introduction of wavelet pre-filtering w15x. Two-dimensional scanning can be used to record angle-multiplexing holograms, and parallelism of the system is improved. Correspondingly, a two-dimensional correlation peak array will appear on the output plane. With the system, any input image will be corresponding to a correlation intensity vector. We can identify the input image by finding position of the correlation peak with maximum intensity or calculating the minimum distance between the vector of the input image and that of patterns. Correlation peaks on the output plane are arranged as a two-dimensional array, which is convenient for being captured by a CCD camera. If intervals of neighboring correlation peaks are D x and D y , size of rectangular output region is L x = L y , we have N s INT
Lx
Ly
ž / ž / Dx
INT
Dy
Ž 3.
where INTŽ a. is to choose an integer just less than a. Apparently, smaller intervals of neighboring correlation peaks and larger size of the rectangular output region, higher parallelism of the system. Therefore, parameters relative to parallelism of the system can be divided into two groups. Some affect intervals of neighboring correlation peaks, including scanning interval of the reference beam and size of the correlation facula. Others affect size of the rectangular output region, including scanning scope of the reference beam and valid detection region of the CCD camera.
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Intervals of neighboring correlation peaks should permit distinctness of different correlation peaks. They are mainly determined by the scanning intervals of the lens L 1. If the scanning intervals on x and y directions are d x and d y , intervals of neighboring correlation peaks on x and y directions will be
Dx s Dy s
f2 l1 y f 1 y f 2 f2 l1 y f 1 y f 2
dx , dy
Ž 4.
where f 1 and f 2 are focal lengths of L 1 and L 2 , l 1 is the distance between L 1 and L 2 . The choice of d x and d y is affected by the size of correlation faculas, which is relative to the recording time and determined by experiments. Furthermore, the scanning angle-intervals D ux and D u y should be bigger than Bragg angle of volume holograms. They are D ux s D uy s
l1 y f 2 f1 f2 l1 y f 2 f1 f2
dx , dy
Ž 5.
Size of rectangular output region is limited by scanning scope of the reference beam and valid detection region of the CCD camera. The relations between the scanning beam and the lens L 1 , L 2 , and the CCD camera are shown in Fig. 4. D 1 and D 2 are diameters of L 1 and L 2 ; D 3x and D 3y are length and width of the detection region; B1 and B2 are diame-
Fig. 4. Relations between scanning beam and Ža. Lens L1; Žb. lens L2; Žc. valid detection area of CCD.
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W. Feng et al.r Optics Communications 176 (2000) 49–59
ters of the reference beam on them; B3 is diameter of correlation faculas; m x and m y are scanning-step numbers on x and y directions. Three conditions must be satisfied: Ž1. Shift of lens L 1 cannot exceed the caliber of the input beam; Ž2. Movement of the scanning beam on the lens L 2 cannot exceed the caliber of the lens L 2 ; Ž3. Correlation outputs should contain in the valid detection region of the CCD camera. Using the conditions above, parameters of the system can be adjusted to obtain higher parallelism. 4. Multiplexing of input objects The volume holographic wavelet correlation system described above has only a single input-object channel. Multi-input channels can be obtained by simply shifting the image on the input plane. For example, Fig. 5 shows a system with four input-object channels. One channel is opened at any time in recording while other channels are closed. All the patterns are stored in the channel by scanning along y direction. The reference beam is restored on y direction and moved a scanning interval on x direction while channels are switched. Similar angle-multiplexing holograms of all the patterns are stored in this channel. The process is going on until all the patterns in all the input-object channels are stored. In our system, all the patterns are recorded in each channel in a same order. Positions of correlation peaks corresponding to patterns and input-object channels on the output plane are shown in Fig. 6, where the row and the column are corresponding to
Fig. 5. Principal drawing of a system with four input-object channels.
Fig. 6. Positions of correlation peaks corresponding to patterns and input-object channels.
input-object channels and patterns. The image in each input-object channel can be identified by the energy distribution of the correlation peaks in the corresponding row. The realization of multi-input channels is based on the characteristic that a volume holographic correlation system is not fully shift-invariant. The shift
Fig. 7. Shift invariance of the system: Ža. x direction; Žb. y direction.
W. Feng et al.r Optics Communications 176 (2000) 49–59
invariance of the system is studied to get conditions of realizing multi-input channel processing. In our
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system, relative parameters are wavelength l s 0.6328 mm, focal length f s 250 mm, thickness of
Fig. 8. Input images and their system outputs: Ža. No. 1 face in channel 1; Žb. No. 1 face in channel 2; Žc. No. 1 face in channel 3; Žd. No. 1 face in channel 4; Že. No. 1, 9, 20, 30 faces in four channels.
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W. Feng et al.r Optics Communications 176 (2000) 49–59
the crystal t s 3 mm, size of the input image L = L s 4.8 = 4.8 mm2 . Using a human face to study the shift invariance, we get the simulated and experimental curves about correlation intensity affected by shift along x and y directions as shown in Fig. 7. It can be concluded that the shift invariance on x direction is much better than that on y direction, but both of them are smaller than L, which is the shift distance to form multi-input channels. Condition of realizing multi-input channels is that the shift distance for invariance should be smaller than that for multi-input channels. Hence, the correlation outputs generated by shift can be distinguished with those generated by different input-object channels. Several researches have concluded that the shift invariance would be improved if the focal length of the Fourier transform lens is enlarged w16x. The focal length should be chosen carefully to satisfy the condition of realizing multi-input channels and also ensure limited shift invariance. 30 human faces and 4 input-object channels are recorded in the crystal as a pattern database in the experiment. Feeding No. 1 face in different channels and No. 1, 9, 20, 30 faces in four channels, we obtain their system outputs as shown in Fig. 8. Fig. 8a is checked as an example, and the correlation peak with maximum intensity appears at first row and first column. Similarly, the correlation peaks with maximum intensity at different rows appear at the 1st, 9th, 20th and 30th columns in Fig. 8e. The validity of the system is testified. 5. Multiplexing of wavelet filters The volume holographic wavelet correlation system described above has also only a single waveletfiltering channel. Correlation results with different wavelet filters are needed to improve recognition accuracy of the system. Multi-wavelet correlation processing can be implemented by altering the wavelet filter sequentially. But it is a time-consuming process, and the restoration of a wavelet filter is difficult to perform. A parallel-processing mechanism based on volume holographic storage is proposed to solve the problem. Multiplexing of wavelet-filtering channels is realized by adding a Dammann grating to the object beam as shown in Fig. 9. A special baffle is used to
Fig. 9. Principal drawing of a system with two wavelet-filtering channels.
open one channel at any time in recording while other channels are blocked. All the patterns are stored in the channel by scanning along y direction. The reference beam is restored on y direction and moved a scanning interval on x direction while moving the baffle to switch wavelet-filtering channels. Similar angle-multiplexing holograms of all the patterns are stored in this channel. The process is going on until all the patterns are stored in all the wavelet-filtering channels. In recognition, the baffle is removed and an input image is filtered by a set of wavelet filters to read out the holograms in the crystal. While all the patterns are recorded in a same order in each channels, positions of correlation peaks corresponding to patterns and wavelet-filtering channels on the output plane are same as Fig. 6, where the row and the column are corresponding to wavelet-filtering channels and patterns. The input image can be identified by synthesizing the correlation peaks in different rows along column. The Dammann grating is added between the lens FL and the wavelet filters. The distance between wavelet channels can be adjusted by moving the Dammann grating. The adjustment should satisfy two conditions. One is that all the spectrums are separated on the filtering plane as shown in Fig. 10a. Hence, the baffle can allow only one channel pass through. Another is that all the filtered spectrums Žobject beams. imaged onto the crystal must have interference regions with the reference beam on the recording plane, as shown in Fig. 10b. The real line stands for the object beam in the current channel. The dashed line stands for object beams in the blocked channels. Usually, only several waveletfiltering channels are needed, and the reference beam
W. Feng et al.r Optics Communications 176 (2000) 49–59
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Fig. 10. Ža. Relation between spectrums and wavelet filters on the filtering plane; Žb. relation between reference beam and object beams in different channels on the recording plane.
can cover object beams in all of channels. Otherwise, a more complex scanning setup is needed for the reference beam. The addition of a Dammann grating only alters the spectrum distribution of the input image. Main structure parameters of the system are maintained. 30 human faces and 2 wavelet-filtering channels are recorded in the crystal as a pattern database in the experiment. Two wavelet filters used in the experiment are shown in Fig. 11a. Fig. 11b shows the system outputs with No. 6 human face as the input image. The dashed frames separate different wavelet correlation outputs. There are two clear correlation peaks at the positions of two wavelet-filtering channels of No. 6 pattern channel. An additional correlation peak appears at the position of No. 1 wavelet-filtering channel of No. 15 pattern channel.
Pixel by pixel multiplication of correlation outputs in different rows along column Ždifferent wavelet-filtering channels of a same pattern channel. is adopted for integration. The normalized final output is shown in Fig. 11c. The additional correlation peak is eliminated, and the correlation peak at the corresponding position becomes more distinctive. Higher recognition accuracy is obtained.
6. Combination of the input object multiplexing and the wavelet filter multiplexing The input object multiplexing and the filter multiplexing above can be performed simultaneously for a higher parallel processing if their combination is necessary in a practical application. The combination
Fig. 11. Ža. Two wavelet filters with different coefficients; Žb. system output with No. 6 face as the input image; Žc. final result by multiplication pixel-by-pixel.
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W. Feng et al.r Optics Communications 176 (2000) 49–59
Fig. 12. Positions of correlation peaks corresponding to patterns, wavelet-filtering channels, and input-object channels.
can be implemented by simply using multi-input objects Žshown in Fig. 5. in a multi-wavelet filtering system Žshown in Fig. 9.. The recording order of patterns in different input object channels and wavelet-filtering channels can be arranged like this. Only one input-object channel and one waveletfiltering channel are opened while other channels are closed in recording, and all the patterns are stored in the combined channel by scanning along y direction. The reference beam is restored on y direction and moved a scanning interval on x direction while we switch the wavelet-filtering channel and maintain the input-object channel. Similar angle-multiplexing holograms of all the patterns are stored in this combined channel. The sub-process is going on until all the patterns are stored in all the wavelet-filtering channels and the same input-object channel. Then the input-object channel is switched, and similar recording is completed in the new input-object channel and all the wavelet-filtering channels. The process continues until all the input-object channels are passed. As a result, positions of correlation peaks on the output plane, corresponding to patterns, waveletfiltering channels, and input-object channels, are shown in Fig. 12. Synthesizing the correlation outputs in different wavelet-filtering channels and a same input-object channel can identify the image in a corresponding input-object channel. 7. Conclusions Multiplexing of the volume holographic wavelet correlation processor on input objects, wavelet fil-
ters, and both are proposed and constructed to improve parallelism or recognition accuracy of the general system with a single processing channel. The scanning of the reference beam is skillfully designed. Simulation and experiments testify the feasibility and validity of the ideas in human face recognition. The realization of multi-input channels is just based on the characteristic that the volume holographic correlation system is not fully shift-invariant. The realizing condition is that the shift distance for invariance should be smaller than that for multi-input channels. The focal length of the Fourier transform lens must be chosen carefully to satisfy the condition. A Dammann grating is adopted to achieve multiplexing of wavelet filters. Higher recognition accuracy is obtained by synthesizing the correlation outputs in different wavelet channels of a same pattern channel. Furthermore, the multiplexing above will reduce the number of patterns for correlation from two dimensions to one dimension. However, the pattern number in one dimension is enough for many applications owing to the large capacity of volume holographic storage. Further researches will be done for a more practical system.
Acknowledgements We appreciate the financial supports of the National Natural Science Foundation of China Ž69877007. and the High Technology Research and Development Program of China Ž863-307-14-4..
References w1x J. Joseph, T. Oura, T. Minemoto, Optical implementation of a wavelet transform by the use of dynamic holographic recording in a photorefractive material, Appl. Opt. 34 Ž1995. 3997–4003. w2x M. Wen, S. Yin, P. Purwardi, F.T.S. Yu, Wavelet matched filtering using a photorefractive crystal, Opt. Commun. 99 Ž1993. 325–330. w3x Y. Yan, G. Huang, W. Feng, G. Jin, M. Wu, Multichannel wavelet correlators for fingerprint identification by the use of associative storage in a photorefractive material, Proc. SPIE 3458 Ž1998. 259–266. w4x D. Roberge, Y. Sheng, Optical wavelet matched filter, Appl. Opt. 33 Ž1994. 5287–5294.
W. Feng et al.r Optics Communications 176 (2000) 49–59 w5x J. Li, Y. Zhang, J. Hu, Object recognition with a wavelet transform based joint transform correlator, Opt. Eng. 35 Ž1996. 775–777. w6x J.P. van Heerden, Theory of optical information storage in solids, Appl. Opt. 2 Ž1963. 393–400. w7x J. Heanue, M. Bashaw, L. Hesselink, Volume holographic storage and retrieval of digital data, Science 265 Ž1994. 749–752. w8x B.J. Goertzen, P.A. Mitkas, Volume holographic storage for large relational databases, Opt. Eng. 35 Ž1996. 1847–1853. w9x C.W. Burr, F.H. Mok, D. Psaltis, Large scale volume holographic storage in the long interaction length architecture, Proc. SPIE 2297 Ž1994. 402–414. w10x W. Feng, G. Huang, Y. Yan, G. Jin, Multichannel wavelet correlators by the use of associative storage in a photorefractive material, Proc. SPIE 3554 Ž1998. 149–154.
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w11x F.T.S. Yu, S. Wu, A.W. Mayers, S. Rajan, Wavelength multiplexed reflection matched spatial filters using LiNbO 3 , Opt. Commun. 81 Ž1991. 343–347. w12x C. Gu, J. Hong, S. Campbell, 2-D shift-invariant volume holographic correlator, Opt. Commun. 88 Ž1992. 309–314. w13x R.A. Maestre, J. Garcia, C. Ferreira, Pattern recognition using sequential matched filtering of wavelet coefficients, Opt. Commun. 133 Ž1997. 401–414. w14x I. Ouzieli, D. Mendlovic, Two-dimensional wavelet processor, Appl. Opt. 35 Ž1996. 5839–5846. w15x W. Feng, Research on optical wavelet parallel processing, PhD thesis, Tsinghua University, Beijing, China, 1999. w16x F.T.S. Yu, S. Yin, Bragg diffraction-limited photorefractive crystal-based correlation, Opt. Eng. 34 Ž1995. 2224–2231.
Optics Communications 176 Ž2000. 49–59 www.elsevier.comrlocateroptcom
Multiplexing of volume holographic wavelet correlation processor Wenyi Feng ) , Yingbai Yan 1, Guofan Jin, Minxian Wu, Qingsheng He State Key Laboratory of Precision Measurement Technology and Instruments, Department of Precision Instruments, Tsinghua UniÕersity, Beijing 100084, China Received 30 September 1999; received in revised form 1 December 1999; accepted 6 December 1999
Abstract Volume holographic associative memory in a photorefractive crystal provides an inherent mechanism to develop a multi-channel correlation identification system with high parallelism. Wavelet transform is introduced to improve discrimination of the system. We first investigate parameters of the system for parallelism enhancement, and then study multiplexing of the system on input objects and wavelet filters. A general volume holographic wavelet correlation processor has a single input-object channel and a single wavelet-filtering channel. In other words, it can only process one input object with one wavelet filter at a same time. Based on the fact that a volume holographic correlator is not a shift-invariant system, multiplexing of input objects is proposed to improve parallelism of the processor. As a result, several input objects can be recognized simultaneously. Multiplexing of wavelet filters with different wavelet parameters is also achieved by a Dammann grating. Wavelet correlation outputs with different filters are synthesized to improve recognition accuracy of the processor. Corresponding experimental results in human face recognition are given. The combination of the input object multiplexing and the wavelet filter multiplexing is also described. q 2000 Elsevier Science B.V. All rights reserved. Keywords: Volume holographic storage; Wavelet transform; Correlation identification; Parallel processing; Human face recognition
1. Introduction Volume holographic storage in a photorefractive material is used to construct optical wavelet transform system recently w1x. On the other hand, the associative memory characteristic of the technique is adopted to realize optical wavelet correlation identification more frequently w2,3x. Wavelet transform is introduced to improve the quality of correlation outputs, and as a result, the accuracy of identification. The conventional correlation of images converts to )
Corresponding author. Tel.: q86-10-6278-1204; fax: q86-106278-4691; e-mail: [email protected] 1 E-mail: [email protected].
the correlation of main features extracted by a same wavelet filter. A sharp correlation peak with little sidelobes and robust to noise is obtained w4,5x. The attractive advantages of volume holographic storage for wavelet transform processing are its high diffractive efficiency, large storage capacity, and real time response w6–8x. It was reported that 10 000 images have been recorded and restored in a single crystal w9x. The inherent parallel processing nature offers a suitable mechanism for pattern recognition. Once all the patterns are stored in a crystal, it can be employed as a database for pattern recognition or other processing. A certain reference beam can recover a stored pattern. An input image can also be compared with all the stored patterns by the object beam. For
0030-4018r00r$ - see front matter q 2000 Elsevier Science B.V. All rights reserved. PII: S 0 0 3 0 - 4 0 1 8 Ž 9 9 . 0 0 7 6 6 - X
50
W. Feng et al.r Optics Communications 176 (2000) 49–59
example, all the patterns are recorded as angle-multiplexing holograms. When the object beam modulated by an input image is used to read out the holograms, a set of ‘reference beams’ with different transmitting angles will be restored. The intensity of each beam stands for the correlation between the input image and the corresponding recorded pattern. The correlation peaks between the input image and all the stored patterns are obtained simultaneously. The input image can be identified by the energy distribution of the correlation peaks. The multi-channel correlation processor based on volume holographic storage and wavelet transform is described at first in Section 2. Parallelism of the processor, which is defined as the number of correlation channels in a single output, is studied in Section 3 as a base for multiplexing. To simplify the problem, we suppose that the dynamic range of the photorefractive crystal is large enough. Therefore, parallelism is mainly determined by geometrical parameters of the system. The main parameters relative to parallelism, such as the scanning interval and the dynamic scope of the reference beam, are analyzed. A general volume holographic wavelet correlation processor has one input-object channel and one wavelet-filtering channel, which can only process one input object with one wavelet filter at a same time w10x. Multi-input channels are needed to improve the speed in many applications such as human face identification. Several faces are recognized one by one sequentially if there is only one input channel, but they can be recognized simultaneously in a multi-input channel system. It is concluded that a correlation system based on volume holograms is no longer fully shift-invariant. However, various methods have been proposed to compensate the shortcoming w11,12x. We utilize the characteristic to construct a novel volume holographic correlation system with multi-input channels in Section 4. Simulations and experiments on shift invariance are performed to obtain conditions of realizing multi-input channel processing in a volume holographic wavelet correlation system. On the other hand, wavelet filters with different parameters are needed in many situations of pattern recognition w13x. Features of some patterns are very similar to each other in some wavelet-filtering channels, where wavelet correlation peaks are near and hard to distinguish. However, they are
different and can be distinguished in other channels. Hence, it is effective to synthesize the correlation outputs in different wavelet-filtering channels for high recognition accuracy. Based on the idea, a processor with multi-wavelet channels is proposed and constructed in Section 5. Wavelet transform results of all the patterns with different wavelet filters are stored in the crystal. That of an input image can be used to obtain wavelet correlation outputs between the image and all the patterns in different wavelet-filtering channels simultaneously. Multiplexing techniques of the processor on input objects and wavelet filters are testified by its application to human face recognition, and promising experimental results are obtained. In Section 6, the combination of the input object multiplexing and the wavelet filter multiplexing is described so that the two multiplexing techniques can be performed simultaneously for a higher parallel processing. Finally, some conclusions are given.
2. Volume holographic wavelet correlation processor If two images are f Ž x, y . and sŽ x, y ., respectively, their wavelet correlation can be defined as f Ž x , y . m haŽ x , y . m sŽ x , y . m haŽ x , y . q`
s
q`
Hy` Hy` F Ž u, Õ . H
)
Ž a x u, a y Õ . S ) Ž u, Õ .
=H Ž a x u, a y Õ . exp i2 p Ž xu q yÕ . d u dÕ
Ž 1. where ‘m’ is the correlation operator, h aŽ x, y . s Ž1rŽ a x a y . 0.5 . hŽŽ xra x ., Ž yra y .. is the wavelet filter, a s Ž a x , a y . is the dilation factor of the wavelet function, and F Ž u, Õ ., SŽ u, Õ . and H Ž a x u, a y Õ . are the Fourier transforms of f Ž x, y ., sŽ x, y . and h aŽ x, y .. Mexican-hat wavelet function is adopted in the system to fabricate the filter because it is quadratic differential of a Gaussian function and also one of the most useful edge detection functions. In the frequency domain, the function is w14x H Ž u, Õ . s 4 p 2 Ž u 2 q Õ 2 . exp y2 p Ž u 2 q Õ 2 .
Ž 2.
W. Feng et al.r Optics Communications 176 (2000) 49–59
It is a real positive function, which is benefit for filter fabrication. According to the expression Ž1. and the achievement of volume holographic correlators, wavelet correlation can be realized as below. First, we record multiplexing wavelet-filtered spectrum holograms of all the patterns in a crystal. Second, wavelet-filtered spectrum of an input image is used to read out the holograms. Finally, wavelet correlation outputs of the input image and all the stored patterns will be detected on the output plane. A volume holographic wavelet correlation processor based on the mechanism is shown in Fig. 1. The linear polarized light generating from a laser is expanded, filtered and collimated by a microscope lens BL, a pinhole PH, a beam-expanding lens EL, and a diaphragm D. Passing through a half wave plate HP1 and a polarized beam-splitting prism BS, the light is divided into two parts as a reference beam and an object beam. A proper power distribution between the reference beam and the object beam will be implemented by rotating the plate HP1. A beam scanning setup made up of lens L 1 and L 2 controls the reference beam before it projects on the crystal. To ensure there is an interference region of the two beams, we should make the size and position of the reference beam motionless on the
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recording plane, and only permit the alteration of its direction. It is realized by letting the recording plane at the imaging place of the laid the lens L 1 and the recording plane satisfy imaging relation to the lens L 2 . Spherical reference beam is used for a more compact structure. According to the diffractive theories, correlation outputs are detected on the convergent plane of the spherical beams. An extra lens is needed to make inverse Fourier transforms for the read out beams if a plane wave is used as the reference beam. The input pattern on the SLM is Fourier transformed by the lens FL, filtered by the wavelet filter WF, and imaged onto the crystal by the lens IL. The half wave plate HP2 is used to adjust polarization of the object beam. The two beams interfere to form a volume hologram in the crystal. Moving the lens L 1 to alter the transmitting angle of the reference beam and replacing the input pattern at the same time, we can record angle-multiplexing holograms in the crystal. When all the patterns are recorded in the crystal, the system is ready for recognition. The object beam is needed only in recognition. The image for identification is fed to the system whose spectrum is filtered by the wavelet filter and imaged onto the crystal to read out the holograms. Multi-channel wavelet correlation outputs are captured by a CCD camera and transferred
Fig. 1. Schematic drawing of the volume holographic wavelet correlation processor.
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Fig. 2. Contrastive experimental results between conventional correlation and wavelet correlation with No.1 face as the input image.
to a computer for post-processing. The input image can be identified according to the energy distribution of the correlation outputs. The whole process is arranged by a personal computer. Because the time-consuming recording process is a priori and the recognition process is implemented instantly, the processor can be used for real-time pattern recognition. Contrastive experiments of 30 human face recognition are made between conventional correlation and wavelet correlation. Fig. 2 shows the experimental results with No. 1 face as the input image. The above figure is the conventional correlation output, and the bottom one is the wavelet correlation output. Let’s check the conventional situation first. There is a large background noise, and strong correlation peaks appear not only at the position of No. 1 face but also at the positions of No. 5, 15, 21, 25 and 30
faces. Hence, it is difficult to identify the input face from all the patterns. Contrarily, there is almost no background noise in the output of the wavelet correlation. The strong correlation peak only appears at the position of the corresponding pattern, No. 1 face. The input face can be identified easily and accurately.
3. Parallelism of the system Principal drawing of the system above is shown in Fig. 3. More patterns recorded in the crystal, more correlation peaks will be obtained on the output plane, and also higher parallelism is realized. We define parallelism of the system as the number of correlation peaks N in a single system output. By simulation and experiments, we have concluded that
Fig. 3. Principal drawing of the volume holographic wavelet correlation processor.
W. Feng et al.r Optics Communications 176 (2000) 49–59
cross-talk noise of multi-channel volume holographic correlation is reduced significantly with the introduction of wavelet pre-filtering w15x. Two-dimensional scanning can be used to record angle-multiplexing holograms, and parallelism of the system is improved. Correspondingly, a two-dimensional correlation peak array will appear on the output plane. With the system, any input image will be corresponding to a correlation intensity vector. We can identify the input image by finding position of the correlation peak with maximum intensity or calculating the minimum distance between the vector of the input image and that of patterns. Correlation peaks on the output plane are arranged as a two-dimensional array, which is convenient for being captured by a CCD camera. If intervals of neighboring correlation peaks are D x and D y , size of rectangular output region is L x = L y , we have N s INT
Lx
Ly
ž / ž / Dx
INT
Dy
Ž 3.
where INTŽ a. is to choose an integer just less than a. Apparently, smaller intervals of neighboring correlation peaks and larger size of the rectangular output region, higher parallelism of the system. Therefore, parameters relative to parallelism of the system can be divided into two groups. Some affect intervals of neighboring correlation peaks, including scanning interval of the reference beam and size of the correlation facula. Others affect size of the rectangular output region, including scanning scope of the reference beam and valid detection region of the CCD camera.
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Intervals of neighboring correlation peaks should permit distinctness of different correlation peaks. They are mainly determined by the scanning intervals of the lens L 1. If the scanning intervals on x and y directions are d x and d y , intervals of neighboring correlation peaks on x and y directions will be
Dx s Dy s
f2 l1 y f 1 y f 2 f2 l1 y f 1 y f 2
dx , dy
Ž 4.
where f 1 and f 2 are focal lengths of L 1 and L 2 , l 1 is the distance between L 1 and L 2 . The choice of d x and d y is affected by the size of correlation faculas, which is relative to the recording time and determined by experiments. Furthermore, the scanning angle-intervals D ux and D u y should be bigger than Bragg angle of volume holograms. They are D ux s D uy s
l1 y f 2 f1 f2 l1 y f 2 f1 f2
dx , dy
Ž 5.
Size of rectangular output region is limited by scanning scope of the reference beam and valid detection region of the CCD camera. The relations between the scanning beam and the lens L 1 , L 2 , and the CCD camera are shown in Fig. 4. D 1 and D 2 are diameters of L 1 and L 2 ; D 3x and D 3y are length and width of the detection region; B1 and B2 are diame-
Fig. 4. Relations between scanning beam and Ža. Lens L1; Žb. lens L2; Žc. valid detection area of CCD.
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ters of the reference beam on them; B3 is diameter of correlation faculas; m x and m y are scanning-step numbers on x and y directions. Three conditions must be satisfied: Ž1. Shift of lens L 1 cannot exceed the caliber of the input beam; Ž2. Movement of the scanning beam on the lens L 2 cannot exceed the caliber of the lens L 2 ; Ž3. Correlation outputs should contain in the valid detection region of the CCD camera. Using the conditions above, parameters of the system can be adjusted to obtain higher parallelism. 4. Multiplexing of input objects The volume holographic wavelet correlation system described above has only a single input-object channel. Multi-input channels can be obtained by simply shifting the image on the input plane. For example, Fig. 5 shows a system with four input-object channels. One channel is opened at any time in recording while other channels are closed. All the patterns are stored in the channel by scanning along y direction. The reference beam is restored on y direction and moved a scanning interval on x direction while channels are switched. Similar angle-multiplexing holograms of all the patterns are stored in this channel. The process is going on until all the patterns in all the input-object channels are stored. In our system, all the patterns are recorded in each channel in a same order. Positions of correlation peaks corresponding to patterns and input-object channels on the output plane are shown in Fig. 6, where the row and the column are corresponding to
Fig. 5. Principal drawing of a system with four input-object channels.
Fig. 6. Positions of correlation peaks corresponding to patterns and input-object channels.
input-object channels and patterns. The image in each input-object channel can be identified by the energy distribution of the correlation peaks in the corresponding row. The realization of multi-input channels is based on the characteristic that a volume holographic correlation system is not fully shift-invariant. The shift
Fig. 7. Shift invariance of the system: Ža. x direction; Žb. y direction.
W. Feng et al.r Optics Communications 176 (2000) 49–59
invariance of the system is studied to get conditions of realizing multi-input channel processing. In our
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system, relative parameters are wavelength l s 0.6328 mm, focal length f s 250 mm, thickness of
Fig. 8. Input images and their system outputs: Ža. No. 1 face in channel 1; Žb. No. 1 face in channel 2; Žc. No. 1 face in channel 3; Žd. No. 1 face in channel 4; Že. No. 1, 9, 20, 30 faces in four channels.
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W. Feng et al.r Optics Communications 176 (2000) 49–59
the crystal t s 3 mm, size of the input image L = L s 4.8 = 4.8 mm2 . Using a human face to study the shift invariance, we get the simulated and experimental curves about correlation intensity affected by shift along x and y directions as shown in Fig. 7. It can be concluded that the shift invariance on x direction is much better than that on y direction, but both of them are smaller than L, which is the shift distance to form multi-input channels. Condition of realizing multi-input channels is that the shift distance for invariance should be smaller than that for multi-input channels. Hence, the correlation outputs generated by shift can be distinguished with those generated by different input-object channels. Several researches have concluded that the shift invariance would be improved if the focal length of the Fourier transform lens is enlarged w16x. The focal length should be chosen carefully to satisfy the condition of realizing multi-input channels and also ensure limited shift invariance. 30 human faces and 4 input-object channels are recorded in the crystal as a pattern database in the experiment. Feeding No. 1 face in different channels and No. 1, 9, 20, 30 faces in four channels, we obtain their system outputs as shown in Fig. 8. Fig. 8a is checked as an example, and the correlation peak with maximum intensity appears at first row and first column. Similarly, the correlation peaks with maximum intensity at different rows appear at the 1st, 9th, 20th and 30th columns in Fig. 8e. The validity of the system is testified. 5. Multiplexing of wavelet filters The volume holographic wavelet correlation system described above has also only a single waveletfiltering channel. Correlation results with different wavelet filters are needed to improve recognition accuracy of the system. Multi-wavelet correlation processing can be implemented by altering the wavelet filter sequentially. But it is a time-consuming process, and the restoration of a wavelet filter is difficult to perform. A parallel-processing mechanism based on volume holographic storage is proposed to solve the problem. Multiplexing of wavelet-filtering channels is realized by adding a Dammann grating to the object beam as shown in Fig. 9. A special baffle is used to
Fig. 9. Principal drawing of a system with two wavelet-filtering channels.
open one channel at any time in recording while other channels are blocked. All the patterns are stored in the channel by scanning along y direction. The reference beam is restored on y direction and moved a scanning interval on x direction while moving the baffle to switch wavelet-filtering channels. Similar angle-multiplexing holograms of all the patterns are stored in this channel. The process is going on until all the patterns are stored in all the wavelet-filtering channels. In recognition, the baffle is removed and an input image is filtered by a set of wavelet filters to read out the holograms in the crystal. While all the patterns are recorded in a same order in each channels, positions of correlation peaks corresponding to patterns and wavelet-filtering channels on the output plane are same as Fig. 6, where the row and the column are corresponding to wavelet-filtering channels and patterns. The input image can be identified by synthesizing the correlation peaks in different rows along column. The Dammann grating is added between the lens FL and the wavelet filters. The distance between wavelet channels can be adjusted by moving the Dammann grating. The adjustment should satisfy two conditions. One is that all the spectrums are separated on the filtering plane as shown in Fig. 10a. Hence, the baffle can allow only one channel pass through. Another is that all the filtered spectrums Žobject beams. imaged onto the crystal must have interference regions with the reference beam on the recording plane, as shown in Fig. 10b. The real line stands for the object beam in the current channel. The dashed line stands for object beams in the blocked channels. Usually, only several waveletfiltering channels are needed, and the reference beam
W. Feng et al.r Optics Communications 176 (2000) 49–59
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Fig. 10. Ža. Relation between spectrums and wavelet filters on the filtering plane; Žb. relation between reference beam and object beams in different channels on the recording plane.
can cover object beams in all of channels. Otherwise, a more complex scanning setup is needed for the reference beam. The addition of a Dammann grating only alters the spectrum distribution of the input image. Main structure parameters of the system are maintained. 30 human faces and 2 wavelet-filtering channels are recorded in the crystal as a pattern database in the experiment. Two wavelet filters used in the experiment are shown in Fig. 11a. Fig. 11b shows the system outputs with No. 6 human face as the input image. The dashed frames separate different wavelet correlation outputs. There are two clear correlation peaks at the positions of two wavelet-filtering channels of No. 6 pattern channel. An additional correlation peak appears at the position of No. 1 wavelet-filtering channel of No. 15 pattern channel.
Pixel by pixel multiplication of correlation outputs in different rows along column Ždifferent wavelet-filtering channels of a same pattern channel. is adopted for integration. The normalized final output is shown in Fig. 11c. The additional correlation peak is eliminated, and the correlation peak at the corresponding position becomes more distinctive. Higher recognition accuracy is obtained.
6. Combination of the input object multiplexing and the wavelet filter multiplexing The input object multiplexing and the filter multiplexing above can be performed simultaneously for a higher parallel processing if their combination is necessary in a practical application. The combination
Fig. 11. Ža. Two wavelet filters with different coefficients; Žb. system output with No. 6 face as the input image; Žc. final result by multiplication pixel-by-pixel.
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Fig. 12. Positions of correlation peaks corresponding to patterns, wavelet-filtering channels, and input-object channels.
can be implemented by simply using multi-input objects Žshown in Fig. 5. in a multi-wavelet filtering system Žshown in Fig. 9.. The recording order of patterns in different input object channels and wavelet-filtering channels can be arranged like this. Only one input-object channel and one waveletfiltering channel are opened while other channels are closed in recording, and all the patterns are stored in the combined channel by scanning along y direction. The reference beam is restored on y direction and moved a scanning interval on x direction while we switch the wavelet-filtering channel and maintain the input-object channel. Similar angle-multiplexing holograms of all the patterns are stored in this combined channel. The sub-process is going on until all the patterns are stored in all the wavelet-filtering channels and the same input-object channel. Then the input-object channel is switched, and similar recording is completed in the new input-object channel and all the wavelet-filtering channels. The process continues until all the input-object channels are passed. As a result, positions of correlation peaks on the output plane, corresponding to patterns, waveletfiltering channels, and input-object channels, are shown in Fig. 12. Synthesizing the correlation outputs in different wavelet-filtering channels and a same input-object channel can identify the image in a corresponding input-object channel. 7. Conclusions Multiplexing of the volume holographic wavelet correlation processor on input objects, wavelet fil-
ters, and both are proposed and constructed to improve parallelism or recognition accuracy of the general system with a single processing channel. The scanning of the reference beam is skillfully designed. Simulation and experiments testify the feasibility and validity of the ideas in human face recognition. The realization of multi-input channels is just based on the characteristic that the volume holographic correlation system is not fully shift-invariant. The realizing condition is that the shift distance for invariance should be smaller than that for multi-input channels. The focal length of the Fourier transform lens must be chosen carefully to satisfy the condition. A Dammann grating is adopted to achieve multiplexing of wavelet filters. Higher recognition accuracy is obtained by synthesizing the correlation outputs in different wavelet channels of a same pattern channel. Furthermore, the multiplexing above will reduce the number of patterns for correlation from two dimensions to one dimension. However, the pattern number in one dimension is enough for many applications owing to the large capacity of volume holographic storage. Further researches will be done for a more practical system.
Acknowledgements We appreciate the financial supports of the National Natural Science Foundation of China Ž69877007. and the High Technology Research and Development Program of China Ž863-307-14-4..
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