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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 17, Iss. 24 — Nov. 23, 2009
  • pp: 21738–21747

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Multi-sample parallel estimation in volume holographic correlator for remote 
sensing image recognition

Shunli Wang, Qiaofeng Tan, Liangcai Cao, Qingsheng He, and Guofan Jin  »View Author Affiliations


Optics Express, Vol. 17, Issue 24, pp. 21738-21747 (2009)
http://dx.doi.org/10.1364/OE.17.021738


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Abstract

Based on volume holographic correlator, a multi-sample parallel estimation method is proposed to implement remote sensing image recognition with high accuracy. The essential steps of the method including image preprocessing, estimation curves fitting, template images preparation and estimation equation establishing are discussed in detail. The experimental results show the validity of the multi-sample parallel estimation method, and the recognition accuracy is improved by increasing the sample numbers.

© 2009 OSA

1. Introduction

Based on high-density holographic storage technology, multichannel volume holographic correlator (VHC) has the characteristics of high-speed, high parallelism and multichannel processing [1

G. W. Burr, F. H. Mok, and D. Psaltis, “Large-scale volume holographic storage in the long interaction length architecture,” Proc. SPIE 2297, 402–414 ( 1994). [CrossRef]

,2

Y. Takashima and L. Hesselink, “Media tilt tolerance of bit-based and page-based holographic storage systems,” Opt. Lett. 31(10), 1513–1515 ( 2006). [CrossRef] [PubMed]

]. It may have the potential applications in the area requiring high speed, real time, high-capacity correlation calculations, such as associative retrieval [3

G. W. Burr, S. Kobras, H. Hanssen, and H. Coufal, “Content-addressable data storage by use of volume holograms,” Appl. Opt. 38(32), 6779–6784 ( 1999). [CrossRef] [PubMed]

,4

B. J. Goertzen and P. A. Mitkas, “Volume holographic storage for large relational databases,” Opt. Eng. 35(7), 1847–1853 ( 1996). [CrossRef]

], pattern recognition [5

L. Hesselink, S. S. Orlov, and M. C. Bashaw, “Holographic Data Storage Systems,” in Proceedings of IEEE Conference on Digital Object Identifier (Institute of Electrical and Electronics Engineers, New York, 2004), pp. 1231–1280.

], target tracking [6

A. Heifetz, J. T. Shen, J. K. Lee, R. Tripathi, and M. S. Shahriar, “Translation-invariant object recognition system using an optical correlator and a superparallel holographic random access memory,” Opt. Eng. 45(2), 1–5 ( 2006). [CrossRef]

], navigation [7

A. Pu, R. Denkewalter, and D. Psaltis, “Real-time vehicle navigation using a holographic memory,” Opt. Eng. 36(10), 2737–2746 ( 1997). [CrossRef]

], and so on. It has been reported that 4000 correlation spots can be parallelly retrieved from a single location in a crystal [8

K. Ni, Z. Y. Qu, L. C. Cao, P. Su, Q. S. He, and G. F. Jin, “High accurate volume holographic correlator with 4000 parallel correlation channels,” Proc. SPIE 6827, 6827J ( 2007).

]. The phase-modulated multi-group method has been used in the VHC to further increase the number of the retrieved correlation spots [9

K. Ni, W. Ren, Z. Y. Qu, L. C. Cao, Q. S. He, and G. F. Jin, “Phase-modulated multigroup volume holographic correlator,” Opt. Lett. 33(10), 1144–1146 ( 2008). [CrossRef] [PubMed]

]. Random modulation [10

C. Ouyang, L. C. Cao, Q. S. He, Y. Liao, M. X. Wu, and G. F. Jin, “Sidelobe suppression in volume holographic optical correlators by use of speckle modulation,” Opt. Lett. 28(20), 1972–1974 ( 2003). [CrossRef] [PubMed]

] has been implemented to extract inner product of the correlation results, and interleaving technology [11

K. Ni, Z. Y. Qu, L. C. Cao, P. Su, Q. S. He, and G. F. Jin, “Improving accuracy of multichannel volume holographic correlators by using a two-dimensional interleaving method,” Opt. Lett. 32(20), 2972–2975 ( 2007). [CrossRef] [PubMed]

] has been adopted to eliminate “pattern dependent behavior”. Thus the accuracy of the multichannel VHC is greatly improved.

The remote sensing image recognition is widely used in space exploration, guided cruise, target tracking, and so on. The remote sensing image recognition is to locate of the target image in the reference remote sensing image [12

J. Capon, “A Probabilistic Mode for Run Length Coding of Picture,” IEEE Trans. Inf. Theory 5(4), 157–163 ( 1959). [CrossRef]

,13

“S. Fumihiko, “Image template matching based on edge-spin correlation,” Electr. Eng. 153, 1592–1596 ( 2005).

]. In the template matching recognition, as shown in Fig. 1 , the reference image with K × L pixels is divided vertically and horizontally into a set (M × N) of template images, each of which has same P × Q pixels as the target image and same vertical and horizontal segmentation interval Δ 1, Δ 2. So the locations of template images in the reference image are exactly known. The matching recognition process is that the correlations between the target image and all of the template images are calculated, and the template image with the maximum inner product value corresponding to the brightest spot is determined to be the target image.

Fig. 1 The schematic diagram of the segmentation of the remote sensing image.

VHC can be used to realize such correlation parallelly. When Δ 1 = Δ 2 = 1, and if M × N template images divided from the reference image can be all recorded in VHC, the remote sensing image can be perfectly recognized. However K and L are generally too large and then the VHC cannot record all template images with Δ 1 = Δ 2 = 1. Δ 1 and Δ 2 should be large enough to ensure M × N template images to be all recorded in VHC. Now if the brightest spot is only used to determine the location of the target image in reference image, the recognition accuracy is sharply decreased to Δ 1 and Δ 2. Furthermore, VHC should be precisely adjusted to ensure the correlation accuracy. However for remote sensing image recognition, the system may work under the real-time, high speed condition, and precise adjustment is very hard to maintain. The influence of noise should be considered and new technology should be adopted.

In statistics, the spatial grayscale distribution g(x, y) of most remote sensing images is approximately a stationary random process [14

S. D. Wei and S. H. Lai, “Robust and efficient image alignment based on relative gradient matching,” IEEE Trans. Image Process. 15(10), 2936–2943 ( 2006). [CrossRef] [PubMed]

,15

T. S. Huang, “PCM Picture Transmission,” IEEE Spectr. 2, 57–63 ( 1965).

]. A large number of project practices show that any point in the remote sensing image has some relevance with the points around it, and the correlation function R of the image can be expressed as [16

L. E. Franks, “A Mode for the Random Video Process,” Bell Syst. Tech. J. 45, 609–630 ( 1966).

]
R(Δx,Δy)=E[g(x,y)g(x+Δx,y+Δy)]                =a×exp(−α|Δx|−β|Δy|)+b,
(1)
where E[·] expresses the mathematic expectation, and a, b are the constant, determined by the variance and mean of the image grayscale respectively. And Δx, Δy represent horizontal and vertical coordinate difference respectively. And α, β are also constant, whose reciprocal values are called correlation lengths, determined by the characteristics of the horizontal and vertical spatial grayscale distributions respectively. A remote sensing image and its correlation function are shown in Fig. 2 . According to the characteristic of the stationary random process, the correlation value of any two points is only determined by the coordinate difference Δx and Δy, but independent of the absolute coordinate of the points.

Fig. 2 A remote sensing image and its correlation function.

For a remote sensing image without any preprocessing, the typical one-dimensional correlation curve is shown in Fig. 3 . The brightness of the correlation spots corresponding to the template images adjacent to each other have small difference. Misjudgement usually happens because of the noise effect if we use the brightest spot to estimate the location of the target and the recognition accuracy is decreased. Since the VHC is able to extract the inner product of the correlation results parallelly, more spots besides the brightest spot can be used to determine the target image location in reference image with higher accuracy.

Fig. 3 A typical correlation curve of remote sensing image without preprocessing.

In the VHC, thermal noise and shot noise of the detector and amplifier are Gaussian distributed, while the statistic property of optical signal is subject to Poisson distribution [17

H. Andrew, Jazwinskl, Stochastic process and filtering theory (New York and London,1970).

]. However, many experimental measurements show that the difference is very small to use the same Gaussian distribution to approximate the noise distribution of the light intensity of a single point [18

P. M. Lundquist, C. Poga, R. G. Devoe, Y. Jia, W. E. Moerner, M.-P. Bernal, H. Coufal, R. K. Grygier, J. A. Hoffnagle, C. M. Jefferson, R. M. Macfarlane, R. M. Shelby, and G. T. Sincerbox, “Holographic digital data storage in a photorefractive polymer,” Opt. Lett. 21(12), 890–892 ( 1996). [CrossRef] [PubMed]

]. According to the probability theory and multiple estimation theory [19

M.-P. Bernal, H. Coufal, R. K. Grygiel, J. A. Hoffnagle, C. M. Jefferson, R. M. Macfarlane, R. M. Shelby, G. T. Sincerbox, P. Wimmer, and G. Wittmann, “A precision tester for studies for holographic optical storage materials and recording physics,” Appl. Opt. 35(14), 2360–2374 ( 1996). [CrossRef] [PubMed]

,20

R. V. Hogg, and A. T. Craig, Introduction to Mathematical Statistics (The Macmillan Company, 1959).

], if the noise of each observed sample has the same distribution and is independent of each other, then multiple samples can be used to improve the accuracy. The multiple correlation spots in the VHC accord well with the request of the probability theory and multiple estimation theory. In this paper, we introduce a multi-sample parallel estimation method, which can be used to estimate the location of the target image with high accuracy, and the characteristics of high speed, high parallelism, multichannel processing can also be exploited sufficiently. Furthermore the system has higher tolerance and can work without precise adjustment.

2. Multi-sample parallel estimation method (MPE)

The MPE method with the VHC has the essential steps of image preprocessing, estimation curves fitting, template images preparation and estimation equation establishing.

Suppose the actual coordinate of the target image in the reference image is (x 1, y 1) and the recognized coordinate of the target image is (x 2, y 2), the recognition accuracy can be determined by error radius ρ, and
ρ= d x2+d y2,
(2)
where dx= x2− x1,dy= y2− y1.

Image preprocessing, which can be used to adjust the correlation length of the image and reduce the redundancy correlation (which is mean of the image grayscale) between the target image and the template images, is an important step to implement MPE for remote sensing image recognition. Without image preprocessing, which is shown in Fig. 3, the redundancy correlation is so much and the brightness of them will be mostly the same. There are two categories of the image preprocessing [21

A. Baraldi and F. Paramiggiani, “An investigation of the textural characteristics associated with gray level co-occurrence matrix statistical parameters,” IEEE Trans. Geosci. Rem. Sens. 3, 293–304 ( 1993).

], including feature-based and gray-scale-based methods. The mathematical morphology [22

C. Rafael, Gonzalez, Digital image processing (New York, 2005).

], the gray-level co-occurrence matrix [23

R. M. Haralick, K. Shanmugan, and I. H. Dinstein, “Textural features for image classification,” IEEE Trans. Syst. Man Cybern. 3(6), 610–621 ( 1973). [CrossRef]

] and thinning algorithm [21

A. Baraldi and F. Paramiggiani, “An investigation of the textural characteristics associated with gray level co-occurrence matrix statistical parameters,” IEEE Trans. Geosci. Rem. Sens. 3, 293–304 ( 1993).

] are actual examples of image preprocessing.

Thinning algorithm can narrow the width of the lines but maintain the basic skeleton of the image. The correlation length can be adjusted with the width of the lines changing and the characteristic of the stationary random process is determined by the skeleton of the remote sensing image. Then, as shown in Fig. 4 , the thinning algorithm can adjust the correlation length but maintain the characteristic of the stationary random process, which well satisfies the need of MPE. When lots of lines are narrowed to 1-2 pixels, then more times thinning gives no help to narrow the correlation length, which is shown in Fig. 5 .

Fig. 4 Typical correlation curves of remote sensing image using different times of thinning algorithm, (a) once; (b) three times; (c)six times.
Fig. 5 Remote sensing image after different times of thinning algorithm. (a) Without preprocessing; (b) once; (c) three times; (d)six times.

The reference image needs to be segmented into a set of template images, which has been mentioned above. The segmentation intervals Δ1 and Δ2 should be in consideration. According to the characteristics of the stationary random process, for the remote sensing image, if the distance between two points exceeds the correlation length, the points will have little relevance to each other. Then to use multiple template images, the segmentation intervals must be less than the correlation length. The choice of the segmentation interval is not only determined by the accuracy requested, but also determined by the limited storage capacity of the holographic correlator, the scope of the recognized remote image and the noise of the system. The bigger size of the segmented template images, which gives better characteristic of the stationary random, would be benefit to the MPE, but it also should match the size of the SLM.

The schematic diagram of one-dimensional MPE of remote sensing image recognition is shown in Fig. 6 . For sake of convenience, three template images n-1, n and n + 1 with the interval Δ being less than the correlation length, are used to determine the location of target image around nth template image. For a target image, between the template images n-1 and n, is correlated with the template images n-1, n and n + 1 simultaneously, and the detected brightness of the correlation spots are respectively a 1 at n-1, a 2 at n and a 3 at n + 1. To get the location of the target image, the estimation function fn -1, fn and fn +1 should be used to establish the estimation equations. According to the ergodic characteristic of the stationary random process and the relationship of the template images, the estimation function can be expressed by the same function form as
fn(Δx,Δy)= R2(Δx,Δy)= ( a× e −α|Δx|−β|Δy|+b)2.
(3)
Seen from the Eq. (3), the Eq. (3) is the square of the Eq. (1). The reason is that the f n(x,y) represents the brightness of the spots and the R(x,y) represents the complex amplitude. Any image, whose size is the same as the target image, in the reference image is correlated with the reference image to fit Eq. (3). Then the estimation equations are given as
{ fn(x+Δ)= a1 fn(x)= a2 fn(x−Δ)= a3,
(4)
and the location x of the target can be obtained. Generally, the parameters in Eq. (3) should be determined according to the reference image.

Fig. 6 The schematic diagram of one-dimensional MPE of remote sensing image recognition.

According to the obtained correlation length and considering the storage capacity of the VHC, the scope of the remote sensing image and the noise of the system, the interval Δ1 and Δ2 can be chosen to segment the reference image. The template images are all stored in the VHC. Generally Δ1 = Δ2 = Δ. When the target image is input into the VHC, the correlation spots can be parallelly detected. And the estimation equations can be established by using the brightness of different correlation spots. Now the number of the correlation spots used in the estimation should be decided. The number of the estimation spots is g (line p, row q, g = p × q). As shown in Fig. 7 , the location of the target image can be determined by the variable x, y. Then the estimation equation is
F(x,y)= { m 11= f 11(x,y) m 12= f 12(x,y) ... m uv= f uv(x,y) ... m pq= f pq(x,y),
(5)
where f 11(x,y), f 12(x,y),…, f pq(x,y) are the estimation functions, and F(x,y) expresses the function group composed of the estimation functions above, and m 11, m 12,…,mpq are the brightness of the used correlation spots. If the template image with sequences u and v is chosen as the benchmark image, according to the relationship of the template images, the other estimation functions can all be expressed by f uv(x,y), i.e.
F(x,y)= { m 11= f uv(x+(u−1)Δ,y+(v−1)Δ) m 12= f uv(x+(u−2)Δ,y+(v−1)Δ) ... m uv= f uv(x,y) ... m pq= f uv(x+(u−p)Δ,y+(v−q)Δ),
(6)
Equation (6) can be solved with g equations and 2 unknowns x and y (g≥2), and the accuracy of x and y can be improved by increasing the number of the correlation spots, which is proved by the following experimental results.

Fig. 7 The schematic diagram of estimation equation of correlation spots

3. Experimental results

The experimental setup is shown in Fig. 8 , which is the same as the apparatus in literature [11

K. Ni, Z. Y. Qu, L. C. Cao, P. Su, Q. S. He, and G. F. Jin, “Improving accuracy of multichannel volume holographic correlators by using a two-dimensional interleaving method,” Opt. Lett. 32(20), 2972–2975 ( 2007). [CrossRef] [PubMed]

]. The light source is a diode-pumped solid-state laser (DPSSL, λ = 532 nm). A diffuser with 0.2° scattering angle is placed behind the SLM. The holograms are angle fractal multiplexed in a Fe: LiNbO3 crystal. A CCD camera (MINTRON MTV-1881EX) is used to detect the correlation spots. The thickness of the recording medium is 15mm and the thickness of volume grating in the recording medium is about 6mm.

Fig. 8 Experiment setup for test the MPE method used in the VHC. PBS, polarizing beam splitter; SLM, spatial light modulator; S, shutter; L1, L2, L3 and L4 lenses; M, mirror; λ/2, half-wave-plate.

A remote sensing reference image with size of 787 × 543 is used to test the MPE method. The template image has size of 640 × 480 limited by the SLM. The reference image after preprocessing (after three times thinning) is shown in Fig. 9 . The parameters in estimation function Eq. (3) are derived by doing the self-correlation of the reference image, and we get α = 0.122, β = 0.160, a = 0.453, b = 0.491. The segmentation interval Δ1 and Δ2 are chosen to be 3. And 1100 (50 × 22) template images are derived and then stored into the VHC. When a white image is input into the VHC, the correlation spots are detected by the CCD, as shown in Fig. 10(a) .When the target image is input into the VHC, the correlation spots are detected by the CCD, as shown in Fig. 10(b).

Fig. 9 An actual example of remote sensing image recognition. (a) Reference image and a sample of the template image; (b) preprocessing of the reference image.
Fig. 10 The experiment of the multiple sample estimation. (a) Detected correlation spots by inputting white image; (b) detected correlation spots by inputting the target image;(c) 16(4 × 4) sample spots to be used.

The top left corner of the reference image is chosen to be the coordinate origin (1, 1) and a random target image with coordinate (83, 33) is input into the VHC, which locates between the template images. Coordinate (X, Y) means the top left corner of the target image is X-1 pixels and Y-1 pixels apart from the coordinate origin along horizontal and vertical directions, respectively. The coordinate of the brightest spot is derived as (85, 31) and the error radius ρ is 2.8. Around the brightest spot, we choose 4 × 4 spots (sampling number is 16) to estimate the location of the input target image, as shown in Fig. 10(c). The correlation result of the white image in Fig. 10(a) is used to be the base for the normalizing the brightness. And the normalized brightness of 4 × 4 spots is

[ 0.3212 0.5324 0.5429 0.0198 0.2135 0.6035 0.8789 0.3869 0.1206 0.7878 0.6057 0.4108 0.4293 0.6512 0.1213 0.3909].

The image with brightness 0.3212 is chosen to be the benchmark image with coordinate (79, 28). The relationship of the estimation function can be inferred by the template images. And then the final equation can be written as
[ f 11(x,y)=0.3212 f 11(x−3,y)=0.5324 f 11(x−6,y)=0.5429 f 11(x−9,y)=0.0198 f 11(x,y−3)=0.2135 f 11(x−3,y−3)=0.6035 f 11(x−3,y−3)=0.8789 f 11(x−9,y−3)=0.3869 f 11(x,y−6)=0.1206 f 11(x−3,y−6�=0.7878 f 11(x−6,y−6)=0.6057 f 11(x−9,y−6)=0.4108 f 11(x,y−9)=0.4293 f 11(x−3,y−6)=0.6512 f 11(x−6,y−6)=0.1213 f 11(x−9,y−9)=0.3909].
(7)
Usually, the location of the target image is determined by the real-time location of the remote sensing image system. Sometimes the location of the target image may coincide with the integer pixel of the reference image but sometimes may be inter-pixel. So we use the fraction coordinate to denote the location of the target image.

After solving Eq. (7), x = 4.3 and y = 4.4. Since the coordinate of benchmark image is (79, 28), the location of the target image is (83.3, 32.4) and the error radius ρ is 0.7, one forth of that determined only by the brightest spot. In other words, using the MPE method, the recognition accuracy has been improved by about four times. For sixteen sampling correlation spots arbitrarily extracted around the brightest spot, the accuracy is approximately the same level.

Another random target image with the coordinate (34, 58), the same as one of the template images, is input. The coordinate of the brightest spot is derived as (37, 58) and the error radius ρ is 3.0. The normalized brightness of 4 × 4 spots around the brightest spot is

[ 0.4816 0.5971 0.2231 0.4541 0.5608 0.6329 0.6221 0.4645 0.7736 0.7071 0.8141 0.5524 0.3122 0.4902 0.5751 0.3389].

In the similar manner, the image with brightness 0.4816 is chosen to be the benchmark image with coordinate (31, 52). Also we use the final equation and derive the result (34.5, 56.7). The error radius ρ is 1.4, which is half of that obtained only by the brightest spot.

217 random target images are input into the VHC to test the estimation error of different sample numbers in statistics. One part of data is shown in Table 1 . The statistical error radius distribution can be obtained from the 217 groups of the correlation results, as shown in Fig. 11 . As is shown in Table 1, for one group observation, the accuracy cannot be always improved by increasing the sample number because of the gross error of the individual spots. In statistics, the larger the sample number is, the smaller the maximum error radius and the higher the recognition accuracy are, which agrees with the probability theory and multiple estimation theory. As is shown in the Fig. 11, the sample number is from 1,4,16 to 36, and the maximum error radius is from 8, 6.2, 4.6 to 4. Then the curve of the relationship between the accuracy and the sample number is nearly as the reciprocal of the square root and it will approach the horizontal with the number increasing, which is shown in Fig. 12 . Thus the accuracy can be improved by increasing the sample number, but it cannot be increased unlimitedly, which fits the theory simulation very well. In our experiment, the sample number 36(6 × 6) is nearly enough, and a larger sample number does not mean a higher accuracy.

Table 1  The error radius with different sample number.
The coordinate of the input image The error radius of the brightest spot Sample number 4(2*2) Sample number 16(4*4) Sample number 36(6*6)
[15,8]2.72.01.91.2
[58 10,]3.53.31.30.6
[147,6]1.31.00.80.5
[12,33]4.44.22.11.2
[58,35]3.12.91.20.8
[130,36]4.23.72.61.0
[14,52]1.51.61.10.9
[88,60]1.81.20.90.8
[144,58]5.32.93.11.7
[14,12]6.25.33.82.1
[72 9,]7.85.64.22.8
Fig. 11 The error radius distribution with different sample number. (a) Only with the brightest spot; sample number is (b) 4(2 × 2); (c) 16(4 × 4) and (d) 36(6 × 6).
Fig. 12 Curve of relationship between the accuracy and increasing number.

4. Conclusions

The MPE method is proposed to increase the remote sensing image recognition accuracy under the VHC, which makes good use of the characteristics of the high speed, high parallelism, multi-channel processing of the VHC and the characteristic of the stationary random of the remote sensing image. The image preprocessing, estimation curves fitting, template images preparation and the estimation equation establishing are important steps to accomplish the MPE method. The segmentation interval must be less than the correlation length. Most of these steps can be completed before the system begins to work. During the real-time correlation, only the preprocessing of target image and the simple estimation computation are needed, which cost little time and can meet the need of the high-speed application. The experimental results verify that the MPE method can improve the recognition accuracy of the remote sensing image. Furthermore the requirement of the storage capacity of the VHC is relaxed. Generally speaking, the larger the sample number is, the higher the recognition accuracy is. Because of the slope of the correlation curve and limited dynamic range of the CCD detector, more sampling spots can hardly narrow the error radius in a practical VHC system. The optimization of the MPE method should be in consideration in future.

Acknowledgment

This work is sponsored by National Project 973 (No.2009CB72400701), National Natural Science Foundation of China (No.60677037) and National Natural Science Foundation of China (No. 60807005).

References and links

1.

G. W. Burr, F. H. Mok, and D. Psaltis, “Large-scale volume holographic storage in the long interaction length architecture,” Proc. SPIE 2297, 402–414 ( 1994). [CrossRef]

2.

Y. Takashima and L. Hesselink, “Media tilt tolerance of bit-based and page-based holographic storage systems,” Opt. Lett. 31(10), 1513–1515 ( 2006). [CrossRef] [PubMed]

3.

G. W. Burr, S. Kobras, H. Hanssen, and H. Coufal, “Content-addressable data storage by use of volume holograms,” Appl. Opt. 38(32), 6779–6784 ( 1999). [CrossRef] [PubMed]

4.

B. J. Goertzen and P. A. Mitkas, “Volume holographic storage for large relational databases,” Opt. Eng. 35(7), 1847–1853 ( 1996). [CrossRef]

5.

L. Hesselink, S. S. Orlov, and M. C. Bashaw, “Holographic Data Storage Systems,” in Proceedings of IEEE Conference on Digital Object Identifier (Institute of Electrical and Electronics Engineers, New York, 2004), pp. 1231–1280.

6.

A. Heifetz, J. T. Shen, J. K. Lee, R. Tripathi, and M. S. Shahriar, “Translation-invariant object recognition system using an optical correlator and a superparallel holographic random access memory,” Opt. Eng. 45(2), 1–5 ( 2006). [CrossRef]

7.

A. Pu, R. Denkewalter, and D. Psaltis, “Real-time vehicle navigation using a holographic memory,” Opt. Eng. 36(10), 2737–2746 ( 1997). [CrossRef]

8.

K. Ni, Z. Y. Qu, L. C. Cao, P. Su, Q. S. He, and G. F. Jin, “High accurate volume holographic correlator with 4000 parallel correlation channels,” Proc. SPIE 6827, 6827J ( 2007).

9.

K. Ni, W. Ren, Z. Y. Qu, L. C. Cao, Q. S. He, and G. F. Jin, “Phase-modulated multigroup volume holographic correlator,” Opt. Lett. 33(10), 1144–1146 ( 2008). [CrossRef] [PubMed]

10.

C. Ouyang, L. C. Cao, Q. S. He, Y. Liao, M. X. Wu, and G. F. Jin, “Sidelobe suppression in volume holographic optical correlators by use of speckle modulation,” Opt. Lett. 28(20), 1972–1974 ( 2003). [CrossRef] [PubMed]

11.

K. Ni, Z. Y. Qu, L. C. Cao, P. Su, Q. S. He, and G. F. Jin, “Improving accuracy of multichannel volume holographic correlators by using a two-dimensional interleaving method,” Opt. Lett. 32(20), 2972–2975 ( 2007). [CrossRef] [PubMed]

12.

J. Capon, “A Probabilistic Mode for Run Length Coding of Picture,” IEEE Trans. Inf. Theory 5(4), 157–163 ( 1959). [CrossRef]

13.

“S. Fumihiko, “Image template matching based on edge-spin correlation,” Electr. Eng. 153, 1592–1596 ( 2005).

14.

S. D. Wei and S. H. Lai, “Robust and efficient image alignment based on relative gradient matching,” IEEE Trans. Image Process. 15(10), 2936–2943 ( 2006). [CrossRef] [PubMed]

15.

T. S. Huang, “PCM Picture Transmission,” IEEE Spectr. 2, 57–63 ( 1965).

16.

L. E. Franks, “A Mode for the Random Video Process,” Bell Syst. Tech. J. 45, 609–630 ( 1966).

17.

H. Andrew, Jazwinskl, Stochastic process and filtering theory (New York and London,1970).

18.

P. M. Lundquist, C. Poga, R. G. Devoe, Y. Jia, W. E. Moerner, M.-P. Bernal, H. Coufal, R. K. Grygier, J. A. Hoffnagle, C. M. Jefferson, R. M. Macfarlane, R. M. Shelby, and G. T. Sincerbox, “Holographic digital data storage in a photorefractive polymer,” Opt. Lett. 21(12), 890–892 ( 1996). [CrossRef] [PubMed]

19.

M.-P. Bernal, H. Coufal, R. K. Grygiel, J. A. Hoffnagle, C. M. Jefferson, R. M. Macfarlane, R. M. Shelby, G. T. Sincerbox, P. Wimmer, and G. Wittmann, “A precision tester for studies for holographic optical storage materials and recording physics,” Appl. Opt. 35(14), 2360–2374 ( 1996). [CrossRef] [PubMed]

20.

R. V. Hogg, and A. T. Craig, Introduction to Mathematical Statistics (The Macmillan Company, 1959).

21.

A. Baraldi and F. Paramiggiani, “An investigation of the textural characteristics associated with gray level co-occurrence matrix statistical parameters,” IEEE Trans. Geosci. Rem. Sens. 3, 293–304 ( 1993).

22.

C. Rafael, Gonzalez, Digital image processing (New York, 2005).

23.

R. M. Haralick, K. Shanmugan, and I. H. Dinstein, “Textural features for image classification,” IEEE Trans. Syst. Man Cybern. 3(6), 610–621 ( 1973). [CrossRef]

OCIS Codes
(070.4550) Fourier optics and signal processing : Correlators
(090.7330) Holography : Volume gratings

ToC Category:
Fourier Optics and Signal Processing

History
Original Manuscript: August 27, 2009
Revised Manuscript: October 22, 2009
Manuscript Accepted: November 9, 2009
Published: November 12, 2009

Citation
Shunli Wang, Qiaofeng Tan, Liangcai Cao, Qingsheng He, and Guofan Jin, "Multi-sample parallel estimation in volume holographic correlator for remote 
sensing image recognition," Opt. Express 17, 21738-21747 (2009)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-24-21738


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References

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  23. R. M. Haralick, K. Shanmugan, and I. H. Dinstein, “Textural features for image classification,” IEEE Trans. Syst. Man Cybern. 3(6), 610–621 (1973). [CrossRef]

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