Optics Communications 284 (2011) 5093–5099

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Optics Communications

j ourna l homepage: www.e lsev ie r.com/ locate /optcom

Optical display of magnified, real and orthoscopic 3-D object images bymoving-direct-pixel-mapping in the scalable integral-imaging system

Miao Zhang, Yongri Piao ⁎, Eun-Soo Kim3D Display Research Center, Department of Electronic Engineering, Kwangwoon University, Republic of Korea

⁎ Corresponding author. Tel.: +82 2 940 5520; fax: +E-mail addresses: chaodashuier@gmail.com (Y. Piao)

0030-4018/$ – see front matter. Crown Copyright © 20doi:10.1016/j.optcom.2011.07.022

a b s t r a c t

a r t i c l e i n f o

Article history:Received 7 April 2011Received in revised form 9 July 2011Accepted 12 July 2011Available online 27 July 2011

Keywords:Scalable integral-imagingMoving array lenslet techniquePseudoscopic-to-orthoscopic conversionMoving-direct-pixel-mapping

In this paper, we proposed a novel approach for reconstruction of the magnified, real and orthoscopic three-dimensional (3-D) object images by using the moving-direct-pixel-mapping (MDPM) method in the MALT(moving-array-lenslet-technique)-based scalable integral-imaging system. In the proposed system, multiplesets of elemental image arrays (EIAs) are captured with the MALT, and these picked-up EIAs arecomputationally transformed into the depth-converted ones by using the proposed MDPM method. Then,these depth-converted EIAs are combined and interlaced together to form an enlarged EIA, from which amagnified, real and orthoscopic 3-D object images can be optically displayed without any degradation ofresolution. Good experimental results finally confirmed the feasibility of the proposed method.

Crown Copyright © 2011 Published by Elsevier B.V. All rights reserved.

1. Introduction

Since integral imagingwas invented by G. Lipmann in 1908 [1], it hasbeen regarded as one of the most promising three-dimensional (3-D)display techniques, because it canprovide a full-parallax and continuous-viewing3-D imagewithout any convergence–accommodation conflict aswell as it can work with an incoherent light [2–6].

Basically, the conventional integral imaging system consists of twoprocesses: pickup and reconstruction. In the pickup process, the rayinformation emanating from a 3-D object can be optically captured byusing a two-dimensional (2-D) image sensor through a lenslet array.Here, a set of picked-up object images having different perspectives ofthe 3-D object is called an elemental image array (EIA). In thereconstructionprocess, 3-Dobject images canbeoptically reconstructedfrom the picked-up EIA by combined use of the display panel and lensletarray [7–10].

However, the conventional integral imaging technique has beensuffered from several problems including small depth of field [11–14],low image-resolution [15–20], narrow viewing-angle [21–23], depthreversion [24–32] and scalability [33–40], so that numerous studieshave been done in order to alleviate these problems. Among them,depth reversion occurred in the reconstructed 3-D images has beenconsidered as a primary problem of the conventional integral-imagingsystem, because it may causes the displayed 3-D images to bepseudoscopic.

82 2 941 5523., eskim@kw.ac.kr (E.-S. Kim).

11 Published by Elsevier B.V. All rig

Thus far, various kinds of optical or computational approaches toperform the pseudoscopic-to-orthoscopic (PO) conversion of thereconstructed 3-D image have been presented [24–29]. H. E. Ivesproposed an optical two-step integral photography [24]. But, in thismethod, a significant degree of image degradation occurs due to thediffractioneffect and thepixilated structure of the opticaldevices causedby two-step recording. Several other optical approaches [25–29] werealso proposed, but they have been suffered from the limited availabilityof the optical devices and the image degradation due to the diffractioneffect of the employed optical devices.

Accordingly, to avoid these problems of the optical approaches, anumber of computational PO conversion methods were proposed. B.Javidi et al. presented the smart pixel-mapping (SPM) method forcomputational depth conversion in the conventional integral-imagingsystem [30]. Y. Piao et al. also proposed the direct pixel-mapping(DPM) method to reconstruct the real and orthoscopic 3-D images inthe curving-effect integral-imaging (CEII) system [31].

In addition to the depth reversion problem, reconstruction of a high-resolution and scalable 3-D image has been also regarded as another hotissue in the integral imaging system, so that various scalable methodshave been investigated [33–40]. Basically, resolution of the reconstructed3-D image might be highly dependent on the number of elementalimages, so that an increase of the number of elemental images shouldbe required for reconstruction of high-resolution and scalable 3-Dimages [38–40].

One approach is based on the repositioning and scaling of elementalimages to reconstruct 3-D images without distortion when the lensletarrays having different specifications are considered between thepickup and display processes[34]. Another approach is based on thedepthmap extracted from the picked-up elemental images, with which

hts reserved.

Fig. 1. MALT-based scalable integral-imaging system: (a) pickup process and (b) reconstruction process.

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scaled elemental images for display can be generated [36]. Furthermore,a moving-array-lenslet technique (MALT) was presented for pickup ofmany time-multiplexed elemental images instead of modification ofelemental images [38,39]. In this method, the scaling could beaccomplished by controlling the spatial sampling rate in the pick-upprocess. However, even though this MALT-based scalable integral-imaging system can provide a good performance in reconstruction ofhigh-resolution and scalable 3-D images, it still shows the samedrawback of the conventional integral-imaging system providingobserverswith a depth-reversed3-D image.Moreover, the conventionaldepth conversion methods of SPM and DPM cannot be applied to thisMALT-based scalable integral-imaging system.

Therefore, in this paper,wepropose a novel approach to reconstruct amagnified orthoscopic 3-D image in MALT-based scalable integral-imaging systems by newly employing the MDPM (moving direct pixelmapping) method. In the proposed system, multiple sets of the EIA arepicked-up with the MALT and they can be computationally transformedinto the depth-converted EIAs by using the proposed MDPM method.Then, from these depth-converted EIAs amagnified, real and orthoscopic3-D object image can be reconstructed without any degradation ofresolution. Some experiments are performed to confirm the feasibility ofthe proposed depth-conversion method of MDPM and the results arediscussed.

2. MALT-based scalable integral-imaging system

In order to overcome the resolution limitation caused by theNyquistsampling theorem in the conventional integral-imaging system, aMALT(moving array lenslet technique) was proposed [39]. In the MALTsystem, the pickup lenslet array is vibrated in the horizontal and verticaldirections to increase the spatial sampling rate. ThisMALT could beusedfor magnification of 3-D object images with a uniform scaling ofhorizontal and vertical coordinates.

Fig. 2. System structure of the proposed system: (a) pick-up process

Fig. 1 shows the MALT-based scalable integral-imaging system, inwhich magnification can be accomplished just by increasing the spatialsampling rate in the pickup process. As we can see in Fig. 1, thereconstructed 3-D images can be enlarged with the uniform magnifi-cation of horizontal and vertical coordinates.

Assume a magnification of a 3-D object image n-times. Then, n×narrays of EIA of a 3-D object should be picked up at the n×n samplingpoints, in which the displacement step of the pickup lenslet arrayshould be satisfied by δ=p/n. The parameter p is the pitch of thelenslet array in the lateral dimensional. Then, all these picked-up EIAsare combined and interlaced together with a ratio of 1:n to form anenlarged EIA and, fromwhich a 3-D object image magnified n-times isfinally reconstructed through a stationary display lenslet array.

Although the MALT-based scalable integral-imaging system hasthe merit of magnifying the reconstructed 3-D image, it also inheritsthe drawback from the conventional II system that provides observerswith real, pseudoscopic images, that is, with depth-reversed recon-structed images. Therefore, a new method needs to be developed forsolving the depth reversion problem occurred in the MALT-basedscalable integral-imaging system.

3. Proposed depth conversion method

Fig. 2 shows the structure of the proposed system, which is largelycomposed of three processes; pickup, depth conversion and recon-struction. In this system, a moving direct pixel-mapping (MDPM)method is newly presented for effective reconstruction of magnified,real and orthoscopic 3-D images in the MALT-based scalable integralimaging system.

For explanation of the proposed scheme, here we employ the MALTto capture n×n arrays of EIA in the pick-up process of Fig. 2(a). Then,applying the proposed MDPM on each picked-up EIA, n×n arrays ofdepth-converted EIAs are obtained as shown in Fig. 2(b). Then, these

, (b) depth-conversion process, and (c) reconstruction process.

Fig. 3. Ray mapping process of the proposed MDPM method.

Fig. 4. Pixel mapping diagram for analysis of the empty pixels occurred in the depth-converted EIA.

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depth-converted EIAs are combined and interlaced together to form anew EIAwhich is enlarged n-times. From this enlarged EIA, amagnified,real andorthoscopic 3-Dobject image can befinally reconstructed in thereconstruction process as shown in Fig. 2(c).

Fig. 5. An enlarged EIA generated from 4 sets of depth-converted EIA: (a)

3.1. Pick-up of multiple sets of EIA

In the pick-up process of Fig. 2(a), n×n arrays of EIA of a 3-D objectare captured on the n×n sampling points by using theMALT. Here, weassume that each picked-up EIA consists of M×M elemental images,in which an elemental image is composed of N×N pixels. For a simpleexample of the proposed system, we consider a case that 4 sets of EIAsare captured with the MALT on the 2×2 sampling points, in which thetotal number of the elemental images per EIA and the total number ofpixels per elemental image are assumed to be M×M=5×5 andN×N=5×5, respectively.

3.2. Depth conversion of the picked-up EIAs with MDPM

Fig. 3 illustrates amappingprocess of theproposedMDPMmethod. Tounderstand the MDPM process in details, here we consider a 1-D pixel-mapping case, because its extension to the 2-D case is straightforward.

To avoid the typical aliasing problem in pixel-mapping, aneffective distance of MDPM is necessary to be satisfied

d = Ng = n; ð1Þ

where g is the distance between EIA and lenslet array.In order to be more explicit to describe the mapping procedure of

MDPM, here we consider MDPM as a two-step process. In the firststep, we only consider those pixels transmitted through the centers of

2×2 array of depth-converted EIAs and (b) Enlarged EIA (2-times).

Fig. 6. Experimental setup for pick-up of multiple sets of EIA with MALT.

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the pinholes and at the same time properly mapped into thecorresponding pixel positions of the depth-converted EIA. In thesecond step, mapping for the mismatched pixels left over from thefirst step is considered.

Here, we consider 4 sets of picked up EIAs, which are denoted asthe EIA Set-1, Set-2, Set-3, Set-4, respectively. And now a mappingbetween the pixels of the picked up EIAs and the corresponding pixelpositions of the depth-converted EIAs by MDPM is considered.

The pixel order in each elemental image is denoted by b=0, ±1,…,±(N−1)/2, where b=0 means the center pixel in each elementalimage. Fig. 3(a) shows a mapping process for the first step of MDPM.

Let us consider a ray coming from the 0th pixel of the ath elementalimage of the ‘EIA Set-1’, where a=0, ±1,…, ±(M−1)/2, and a=0means the center elemental imageof the ‘EIASet-1’. As shown in Fig. 3(a),the 0th pixel of the 0th elemental image, E0(0) ismapped to the 0th pixelof the 0th depth-converted elemental image, D0(0), and the 1st pixel ofthe 1st elemental image, E1(1) is mapped to the −2nd pixel of the 0thdepth-converted elemental image, D0(−2). Similarly, the −1st pixel ofthe−1stelemental image,E−1(−1) ismapped to the2ndpixel of the0thdepth-converted elemental image, D0(2).

Aswe can see in the procedurementioned above, amapping rule forgenerationof the 0thdepth-convertedelemental imageof the ‘EIA Set-1’can be given by Dk uð Þ = Ea=0; uuj j k−n + 1ð Þ b = − u × nð Þ% n + 1ð Þð Þ,where u means the pixel position of the depth-converted elementalimageof the ‘EIASet-1’, and kmeans thepositionof thedepth-convertedelemental image of the ‘EIA Set-1’. A similarmapping processmay occuraccording to the abovemapping rulewhen the pixels in other elementalimages are to be mapped to the corresponding depth-converted pixels.

Fig. 7. 4 Sets of originally picked-up and depth-converted EIAs: (a) pick

Next,we consider amapping for themismatchedpixels left over fromthe first step. Fig. 3(b) illustrates a procedure for resolving the matchingproblem for the mismatched pixels, in which the concept of MALT isemployed for moving the virtual pinhole array. Based on δ=p/n, thedisplacement step of the virtual pinhole array is given by δ=p/2.

As we can see in Fig. 3(b), the missed pixels in the mappingprocess of the ‘EIA Set-1’, E1(−2) and E−1(2) are mapped to the−1stpixel of the 0th depth-converted elemental image, D0(−1) and 1stpixel of the 0th depth-converted elemental image, D0(1) from another‘EIA Set-2’, respectively. Accordingly, a mapping for the missed pixelsof the 0th depth-converted elemental image of the ‘EIA Set-1’ can begiven by Dk uð Þ = Ea= u

uj j k−n + 1ð Þ b = u × nð Þ% n + 1ð Þð Þ. A similar map-ping processmay also occur when themixed pixels in other elementalimages are to be mapped.

Therefore, it is straightforwardly concluded that the MDPMalgorithm for the 1-D case can be expressed as

Dk uð Þ = Ea bð Þ: ð2Þ

And, a and b given by

a =0 ; if u = 0uuj j k−n + 1ð Þ;Others ; and b =

u × nð Þ% n + 1ð Þ;u is odd

− u × nð Þ% n + 1ð Þ;u is even;

(8<:

ð3Þ

where Ea(b) is the bth pixel of the ath elemental image in EIA, Dk(u) isthe uth pixel of the kth elemental image in the depth-converted EIA, inwhich a=0, ±1,…, ±(M−1)/2, and b=0, ±1,…, ±(N−1)/2.

Now, we analyze the number of empty pixels occurred in thedepth-converted EIA. Fig. 4 shows the pixel mapping process betweenthe picked-up and the depth-converted EIA. In the MALT-basedscalable system, n has to be greater than 1, which means that thedistance of MDPM has to be less than Ng.

That is, according to Eq. (1), the effective distance of MDPM mayvary depending on the sampling points of n in the MALT-basedintegral-imaging system, so that mismatching must be occurred. Inother words, as the sampling points increases, the correspondingmapping interval also increases, which results in raising the numberof empty pixels. Here, the number of empty pixels in the depth-converted EIA depends on the mapping interval φ(d).

ed-up EIAs with the MALT and (b) depth-converted EIAs by MDPM.

Fig. 9. Optical setup for reconstruction of the magnified 3-D object image from theenlarged EIAs of Fig. 8(a) and (b).

Fig. 8. Enlarged EIAs generated from (a) 4 sets of originally picked-up EIAs and (b) 4 sets of depth-converted EIAs.

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In Fig. 4, the mapping interval always satisfies Eq. (4) as follows

tan α =φ dð Þg

=pd: ð4Þ

Here, based on the Eq. (1), the pixel mapping interval φ(d) can berepresented by

φ dð Þ = gpd

=gp

Ng=n=

pN ⋅ n = Δ⋅ n; ð5Þ

where Δ is the pixel size.From Eq. (5), it is concluded that n is always greater than 1, so that

the interval between two pixels of the depth-converted EIA dependson the sampling points of n. For example, when n=2, one empty pixel(one missing pixel) appears following every other pixel.

After performingMDPMon each picked-up EIA, n×n sets of depth-converted EIAs can be obtained.

3.3. Reconstruction of a magnified, real and orthoscopic 3-D image

To reconstruct amagnified, real andorthoscopic 3-D image,n×n setsof depth-converted EIA obtained from theMDPMprocess are combinedand interlaced to form a new EIA which is enlarged n-times in size.

For the case of n=2, 2×2 arrays of depth-converted EIA can begenerated from the 4 sets of originally picked-up EIAs through theoperation of MDPM, which are shown in Fig. 5(a).

Then, the enlarged EIA S(i, j) with a ratio of 1:2 can be formed byinterlacing 4 sets of depth converted EIAs of Fig. 5(a) in the directionsof x and yaxes, and diagonally.

Here, the 2-D interlacing algorithm [28] can be formulated as follow

S i; jð Þ = Dk;l u; vð Þ;where k = i%nl = j%n

; and u = i = n½ �v = j = n½ � ;

��ð6Þ

where i=1,…,k×u and j=1,…,l×v, u×v is the size of each depth-converted EIA.

Thefinally enlarged EIA from4 sets of depth converted EIA of Fig. 5(a)by using the interlacing algorithm of Eq. (6) is shown in Fig. 5(b).

4. Experimental results

To demonstrate the feasibility of the proposed method, opticalexperiments with a test object are carried out. Fig. 6 illustrates theexperimental setup for picking up the multiple sets of EIAs of the testobjectwith theMALT.Here, the test object is assumed tobe composed oftwo 2-D images of the Arabic number ‘3’ and the Alphabetical letter ‘D’

having a resolution of 900×900, which are longitudinally located at33 m and 39 mm from the lenslet array, respectively. The lenslet arrayused for pick-up is composed of 30×30 lenslets, in which the focallength and the diameter of each lenslet are given by3 mmand1.08 mm,respectively. Hence, the pitch of the lenslet is given by p≈1.0 mm.

With the experimental setup of Fig. 6, 4 sets of EIAs for the test objectare obtained. That is, as the pickup lenslet array is vibrated with thedisplacement step of p/n≈5 mm, 4 sets of EIA are picked up and theyare shown in Fig. 7(a). Then, these 4 sets of EIAs are transformed into 4sets of depth-converted EIAs by using the proposed MDPM method asdescribed in Eqs. (2) and (3), and the results are shown in Fig. 7(b).

Fig. 8(a) shows an enlarged EIA generated by interlacing 4 sets oforiginally picked-up EIA of Fig. 7(a)with the ratio 1:2. For comparison, in

5098 M. Zhang et al. / Optics Communications 284 (2011) 5093–5099

the experiment, another is also shown in Fig. 8(b) shows an EIA enlarged2-times in size by combining and interlacing 4 sets of depth-convertedEIA of Fig. 7(b) according to the interlacing algorithm of Eq. (6).

Fig. 9 shows an experimental setup for reconstruction of the 3-Dobject image from the enlarged EIA of Fig. 8(b), whichwas generated bycombining and interlacing 4 sets of depth-converted EIA. For compar-ison, another 3-D object image is also reconstructed from the enlargedEIA of Fig. 8(a), which was generated by 4 sets of EIA originally picked-up with the MALT.

Fig. 10. Optically reconstructed 3-D object images: (a) Pseudoscopic 3-D object images of thescalable system, and (c) magnified orthoscopic 3-D object images of the proposed system.

Here,weuse the EPSONprojector (EMP-820) composed of three colorpanels for projecting elemental images, in which each panel consists of1024×768 pixels with a pixel pitch of 18 μm. Moreover, the employedlenslet array is composed of 60×60 lenslets, inwhich the focal length andthe diameter of each lenslet is given by 3 mm and 1.08 mm, respectively.The distance between the lenslet array and the relay optics isapproximately given by 48 cm.

Then, these optically reconstructed 3-D object images, areobserved through 5 different viewing angles: center position, right

conventional system, (b) magnified pseudoscopic 3-D object images of theMALT-based

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and left positions rotated by 7° and 15° from the center, respectivelyto confirm the depth-reversion of the reconstructed 3-D images. Here,it must be noted that the object of ‘3’was originally located in front ofthe object of ‘D’ in the pickup process as shown in Fig. 6.

Fig. 10(a), (b) and (c) shows the 3-D object images opticallyreconstructed from the conventional, MALT-based, and proposedsystem, respectively. Each of them has been observed from 5 differentviewing angles of ‘Center’, ‘Left 7°’, ‘Left 15°’, ‘right 7°’ and ‘right 15°’.

Fig. 10(b) shows the magnified, real and pseudoscopic 3-D objectimages reconstructed from the enlarged EIA of Fig. 8(a). For comparison,3-D object images reconstructed from the conventional integral-imagingsystem by using one of the originally picked-up EIAs of Fig. 7(a) are alsoshown in Fig. 10(a). From Fig. 10(a) and (b), we can easily observed thatas the viewing angle increases, the horizontal displacement of the objectimages of ‘D’ become larger than those of the object images of ‘3’ relativeto the optical axis of the central lenslet. These observation resultsconfirmed that the object of ‘D’ is displayed in front of the object of ‘3’dueto the pseudoscopic reconstruction of the 3-D object image both in theconventional and MALT-based scalable integral-imaging system. How-ever, even though theMALT-based scalable integral-imaging system canprovide a good performance in reconstruction of magnified 3-D imagesthan the conventional integral imaging system, it still shows the samedrawback of the conventional integral-imaging system providingobservers with a pseudoscopic 3-D image.

On the other hand, Fig. 10(c) shows the magnified, real andorthoscopic 3-D object images reconstructed from the depth-convertedand enlarged EIA of Fig. 8(b). As we can see in Fig. 10(c), as the viewingangle deviates from the optical axis to the degrees of −15° and +15°,the horizontal displacement of the object image of ‘D’ becomes smallerthan that of the object image of ‘3’ relative to the optical axis of thecentral lenslet. These observations might reveal that the object of ‘D’ isbehind the object of ‘3’ just like the pickup situation of Fig. 6, so that wecan finally see the magnified, real and orthoscopic 3-D object imagesvery naturally in the proposed scalable integral-imaging system.

5. Conclusions

In this paper, a novel approach for reconstruction of amagnified, realand orthoscopic 3-D object image has been proposed by using theMDPMmethod in the scalable integral-imaging system.Multiple sets ofpicked up EIA are computationally transformed into the depth-converted ones by using the MDPM method. Then, from the depth-converted and enlarged EIA, a magnified, real and orthoscopic 3-Dobject image has been reconstructed without any degradation ofresolution. Successful experimental results have confirmed the feasi-bility of the proposed method.

Acknowledgement

This research was supported by the MKE (Ministry of KnowledgeEconomy), Korea, under the ITRC (Information Technology ResearchCenter) support program supervised by the NIPA (National IT IndustryPromotion Agency) (NIPA-2011-C1090-1111-0002).

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