Analysis of image distortion based on light ray field by multi-view and horizontal parallax only integral imaging display

doi:10.1364/OE.20.023755

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Analysis of image distortion based on light ray field by multi-view and horizontal parallax only integral imaging display

Hee-Seung Kim, Kyeong-Min Jeong, Sung-In Hong, Na-Young Jo, and Jae-Hyeung Park »View Author Affiliations

Optics Express, Vol. 20, Issue 21, pp. 23755-23768 (2012)
http://dx.doi.org/10.1364/OE.20.023755

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▸ Article Outline
– Abstract
1. Introduction
2. Light ray field
3. Analysis of image distortion
4. Experimental verification
5. Conclusion
– References and links

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Abstract

Three-dimensional image distortion caused by mismatch between autostereoscopic displays and contents is analyzed. For a given three-dimensional object scene, the original light ray field in the contents and deformed one by the autostereoscopic displays are calculated. From the deformation of the light ray field, the distortion of the resultant three-dimensional image is finally deduced. The light ray field approach enables generalized distortion analysis across different autostereoscopic display techniques. The analysis result is verified experimentally when multi-view contents are applied to a multi-view display of non-matching parameters and a horizontal parallax only integral imaging display.

1. Introduction

Autostereoscopic displays provide observers with three-dimensional(3D) images without requiring special glasses [1

T. Okoshi, “Three-dimensional displays,” Proc. IEEE 68(5), 548–564 (1980). [CrossRef]

P. Benzie, J. Watson, P. Surman, I. Rakkolainen, K. Hopf, H. Urey, V. Sainov, and C. von Kopylow, “A survey of 3DTV display: techniques and technologies,” IEEE Trans. Circ. Syst. Video Tech. 17(11), 1647–1658 (2007). [CrossRef]

]. Active researches have been conducted on autostereoscopic displays at many research groups. Among various autostereoscopic display techniques, multi-view(MV) display is broadly considered as the most practical method. MV display provides observers with high quality 3D images at several pre-defined viewpoints through a special ray guiding optics such as parallax barrier or lenticular lens sheet [3

J. Hong, Y. Kim, H.-J. Choi, J. Hahn, J.-H. Park, H. Kim, S.-W. Min, N. Chen, and B. Lee, “Three-dimensional display technologies of recent interest: principles, status, and issues [Invited],” Appl. Opt. 50(34), H87–H115 (2011). [CrossRef] [PubMed]

]. Many contents and products have been manufactured for MV display. Integral imaging(InIm) is another type of autostereoscopic display technique. InIm display generates 3D images by reconstructing spatio-angular ray distribution using a lens array [3

–7

K. Yamamoto, T. Mishina, R. Oi, T. Senoh, and M. Okui, “Cross talk elimination using an aperture for recording elemental images of integral photography,” J. Opt. Soc. Am. A 26(3), 680–690 (2009). [CrossRef] [PubMed]

]. While MV display is designed to provide different views to different viewpoints, InIm display is designed to reconstruct ray distribution in the observer space. This difference leads to distinguishable characteristics of InIm display including natural and continuous motion parallax. Motivated by these advantages of InIm display, considerable efforts have been recently made to commercialize InIm display. Due to insufficient panel resolution, however, these approaches usually make compromise by abandoning vertical parallax and reducing the number of rays per each display cell to the level comparable to that of MV displays. With these compromises, the horizontal parallax only(HPO) InIm display is now considered as another autostereoscopic display technique with a practical value.

Image distortion is one of the primary issues in autostereoscopic displays. Only when image contents captured with correct geometry are applied to the corresponding display, the 3D images can be presented without distortion. In practice, however, the contents capturing condition using multiple cameras or computer graphic techniques can deviate from the ideal one, resulting in distortion of the displayed 3D images. The situation becomes worse when HPO InIm display is considered. Since the InIm display requires orthographic image contents, usual perspective image contents captured using cameras cannot be used in principle.

There are considerable prior works on the analysis of the 3D image distortion [8

D. B. Diner and D. H. Fender, Human Engineering in Stereoscopic Viewing Devices (Plenum, 1994).

–13

J.-Y. Son, Y. N. Gruts, K.-D. Kwack, K.-H. Cha, and S.-K. Kim, “Stereoscopic image distortion in radial camera and projector configurations,” J. Opt. Soc. Am. A 24(3), 643–650 (2007). [CrossRef] [PubMed]

]. Camera parameters including capturing distance, spacing, and orientation, and display parameters such as viewing distance and viewpoint separation are considered to find the distortion of the displayed 3D images. However, they use view based approach assuming both the contents and display have pre-defined capturing-point/viewpoint based configuration. Hence they cannot be applied to HPO InIm display which does not have view based configuration. There are significant previous works on 3D image quality of the InIm display but they usually analyze viewing zone [14

V. Saveljev, “Image and observer regions in 3D displays,” J. Inform. Disp. 11(2), 68–75 (2010). [CrossRef]

–17

S.-I. Uehara, T. Horikoshi, C. Kato, T. Koike, G. Hamagishi, K. Mashitani, T. Nomura, K. Taira, A. Yuuki, N. Umezu, N. Watanabe, Y. Hisatake, and H. Ujike, “Characterization of motion parallax on multi-view/integral-imaging displays,” SID Tech. Dig. 41(1), 661–664 (2010). [CrossRef]

], resolution [18

H. Hoshino, F. Okano, H. Isono, and I. Yuyama, “Analysis of resolution limitation of integral photography,” J. Opt. Soc. Am. A 15(8), 2059–2065 (1998). [CrossRef]

, 19

J.-H. Park, Y. Kim, J. Kim, S.-W. Min, and B. Lee, “Three-dimensional display scheme based on integral imaging with three-dimensional information processing,” Opt. Express 12(24), 6020 (2004). [CrossRef] [PubMed]

] or distortion caused by display system misalignment [20

M. Kawakita, H. Sasaki, J. Arai, F. Okano, K. Suehiro, Y. Haino, M. Yoshimura, and M. Sato, “Geometric analysis of spatial distortion in projection-type integral imaging,” Opt. Lett. 33(7), 684–686 (2008). [CrossRef] [PubMed]

] without contents consideration. To the authors’ best knowledge, contents induced 3D image distortion of the HPO InIm display was first analyzed by T. Saishu et al. [21

T. Saishu, K. Taira, R. Fukushima, and Y. Hirayama, “Distortion control in a one-dimensional integral imaging autostereoscopic display system with parallel optical beam groups,” SID Tech. Dig. 35(1), 1438–1441 (2004). [CrossRef]

]. They, however, only provide resultant distortion relation without explicit derivation procedure.

In this paper, we firstly analyze contents induced 3D image distortion using light ray field concept. The light ray field approach enables unified simple analysis of the 3D image distortion both in MV and HPO InIm displays. The proposed light ray field approach has potential to be further extended to various different ray based autostereoscopic displays. In the following sections, the concept of the light ray field and the distortion analysis based on it are presented.

2. Light ray field

2.1 Concept

Light ray field is defined by a spatio-angular distribution of the light rays in a plane L(x, y, θ_x, θ_y; z_r) as shown in Fig. 1 where (x, y) represents spatial position in a reference plane at z = z_r and (θ_x, θ_y) represents propagation angle measured with respect to x and y axis, respectively [22

A. Stern and B. Javidi, “Ray phase space approach for 3-D imaging and 3-D optical data representation,” J. Display Technol. 1(1), 141–150 (2005). [CrossRef]

–24

M. Levoy, R. Ng, A. Adams, M. Footer, and M. Horowitz, “Light field microscopy,” ACM Trans. On Graphics (Proc. SIGGRAPH) 25, 924–934 (2006).

]. Hereafter only (x, θ_x) distribution is considered without (y, θ_y) for simplicity. The reference plane is also assumed to be located at z_r = 0 without loss of generality. Figure 2 shows an example of the light ray field of a single object point at a position (x₁, z₁). As shown in Fig. 2, the corresponding light ray field can be represented by a straight line intersecting the x-axis at x₁ with a slanting angle of −1/z₁ in x-θ_x plot. For general 3D objects composed of 3D object point cloud, the light ray field is given by a collection of the slanted lines.

Fig. 1 Concept of light ray field.

Fig. 2 Light ray field of a single 3D point object.

2.2 Light ray field captured in MV contents

Currently most 3D contents are stereoscopic two view or MV images. Two or multiple cameras are usually located with a uniform spacing Δx_c at a specific distance from the 3D object scene to capture 3D contents. Figure 3 shows the captured rays in the MV contents where x_cn represents lateral position of n-th camera and z_c is the camera distance from the reference plane. The x-θ_x plot of the corresponding light ray field at a reference plane is shown in Fig. 4 . As shown in Fig. 4, a single view image corresponds to a single line with a slanting angle −1/z_c in the light ray field. Therefore MV contents with N views can be represented by N slanted lines in the light ray field. Note that only a small linear portion of the entire light ray field information is included in the MV contents.

Fig. 3 Rays captured at several camera positions.

Fig. 4 Light ray field in the MV contents.

2.3 Light ray field reconstructed by MV and HPO InIm display

MV display and HPO InIm display can be distinguished by their different light ray field reconstruction characteristics. Figure 5 shows ray reconstruction of MV display and HPO InIm display. As shown in Fig. 5, the MV display reconstructs the light ray field such that the reconstructed rays are converging at a few viewpoints while the HPO InIm display reconstructs a few parallel light ray groups with a constant angular spacing Δθ_x.

Fig. 5 Ray reconstruction characteristics.

Figure 6 shows x-θ_x plot of the reconstructed light ray field at the ray guiding optics plane of two display methods. In case of MV display shown in Fig. 6(a), the reconstructed light ray field is represented as a collection of the slanted lines each of which corresponds to the light rays converging at a viewpoint. The slating angle and the x-axis intersection of the lines are given by −1/z_v and x_vn respectively where z_v and x_vn are the distance and the lateral position of the n-th viewpoint. On the other hand, in case of HPO InIm display, the reconstructed light ray field is represented as a collection of the horizontal lines, reflecting parallel ray reconstruction characteristics as shown in Fig. 6(b). Note that ideal 3D display would reconstruct whole plane in x-θ_x plot. Figure 6 shows that MV display and HPO InIm display only reconstruct a few linear portions of entire light ray field. The light ray field portion that is reconstructed depends on the display method and system specifications.

Fig. 6 Reconstructed light ray field.

3. Analysis of image distortion

3.1 Light ray field and image distortion

3D images can be displayed without distortion only when right contents are used for right displays. In terms of the light ray field, it can be stated that distortion can be avoided only when the light ray field captured in the contents is reproduced as it is by the display panel. Figure 7 shows one example. Figure 7(a) shows a light ray field in 4-view image contents captured at a distance z_c and spacing Δx_c. When the 4-view image contents in Fig. 7(a) are supplied to the 4-view MV display with viewing distance z_v = z_c and viewpoint spacing Δx_v = Δx_c, the light ray field is reconstructed correctly as shown in Fig. 7(b) and the 3D image can be observed without distortion at the designed viewpoints. On the other hands, when the specifications of the display deviate from this optimal condition, the light ray field is reconstructed with deformation as shown in Fig. 7(c) and thus the 3D image is distorted accordingly even when the observer is located at the designated viewpoint of the display. In the followings, the distortions are analyzed in detail.

Fig. 7 Light ray field reconstruction by correct and incorrect display panels.

3.2 Image distortion caused by using MV image contents to incorrect MV display panel

Let l(x, θ_x) and l'(x, θ_x) denote original light ray field at the reference plane in the contents and reconstructed one at the panel plane in the display, respectively. In our analysis, it is assumed that the reference plane in the contents capture coincides with the panel plane in the display. Note that there is no loss of generality as the selection of the plane for representing the light ray field is arbitrary. As shown in Fig. 8 , l(x, θ_x) and l'(x, θ_x) are related to originally captured 3D object’s depth slice at a distance z, f(x; z) and reconstructed slice at a distance z′, f'(x; z′) by,

l (x, θ_{x}) = f (x + θ_{x} z; z) .

(1)

l^{'} (x, θ_{x}) = f^{'} (x + θ_{x} z^{'}; z^{'}) .

(2)

The purpose of our analysis is to find the relationship between original object slice f(x; z) and reconstructed 3D image slice f'(x; z′) from the given contents and display panel conditions.

Fig. 8 Light ray field and 3D object.

Figure 9 shows four cases of applying MV contents to MV displays. When the camera position in the capturing process coincides with the designed viewpoints in the display as shown in Fig. 9(a), the light ray field is reconstructed as it is, i.e. l'(x, θ_x) = l(x, θ_x), and thus the 3D image is displayed without distortion, i.e. f'(x; z) = f(x; z).

Fig. 9 Image distortions when MV image contents are applied to non-matching MV display panel.

Next suppose that the designed viewpoints are laterally shifted from the camera position by a as shown in Fig. 9(b). In this case, the light rays collected at a camera position (x_cn, z_c) are actually reconstructed such that they converge at a viewpoint located at a different lateral position (x_vn, z_v) = (x_cn + a, z_c). An original light ray propagating from a position x in the reference plane to a camera position (x_cn, z_c) with an angle (x_cn-x)/z_c is reconstructed as a light ray propagating from the same position x in the reference plane but to a different position (x_vn, z_v) = (x_cn + a, z_c) with an angle (x_vn-x)/z_v = (x_cn-x + a)/z_c. Therefore, in the reference plane, the direction of each light ray is rotated by an angle a/z_c. In the x-θ_x plot of light ray field, this can be represented by shifting each slanted line by a/z_c along θ_x-axis, resulting in l'(x, θ_x) = l(x, θ_x-(a/z_c)). From Eqs. (1) and (2), this leads to

f^{'} (x + θ_{x} z^{'}; z^{'}) = f (x + (θ_{x} - \frac{a}{z_{c}}) z; z) .

(3)

Letting u' = x + θ_xz', we have

f^{'} (u^{'}; z^{'}) = f (u^{'} - \frac{a}{z_{c}} z + θ_{x} (z - z^{'}); z) .

(4)

Since Eq. (4) should hold for all θ_x, we have z = z′ and

f^{'} (x; z) = f (x - \frac{a}{z_{c}} z; z),

(5)

where u′ is replaced by x for better clarity. Equation (5) indicates that each depth slice at z of the original 3D object is reconstructed at the same distance z but with a lateral shift of (a/z_c)z, distorting the reconstructed 3D image along lateral direction. The amount of the distortion is proportional to the object depth z and the position mismatch a between the camera position and viewpoint. The distortion is visualized in the right inset of Fig. 9(b) for a hexahedron object.

Figure 9(c) shows situation where the designed viewpoint distance z_v of the display is shorter than the camera distance z_c of the capture system by a distance b. In this case, a light ray propagating from a position x in the reference plane to a camera position (x_cn, z_c) with an angle (x_cn-x)/z_c is reconstructed as a light ray propagating from the same position x in the reference plane but to a different position (x_vn, z_v) = (x_cn, z_c-b) with an angle (x_vn-x)/z_v = (x_cn-x)/(z_c-b). Therefore light ray field is deformed by

l^{'} (x, θ_{x}) = l (x, \frac{z_{c} - b}{z_{c}} θ_{x})

, giving

l^{'} (x, θ_{x}) = f^{'} (x + θ_{x} z^{'}; z^{'}) = f (x + \frac{z_{c} - b}{z_{c}} θ_{x} z; z),

(6)

where Eqs. (1) and (2) are used. In the same manner as the above case, substituting u' = x + θ_xz' into Eq. (6) gives

f^{'} (u^{'}; z^{'}) = f (u^{'} + θ_{x} (\frac{z_{c} - b}{z_{c}} z - z^{'}); z) .

(7)

In order to make Eq. (7) true for all θ_x, we have z′ = (z_c-b)z/z_c and thus Eq. (7) reduces to

f^{'} (x; z) = f (x; \frac{z_{c}}{z_{c} - b} z),

(8)

where u′ and z′ are replaced by x and z. Equation (8) indicates that each depth slice at z is reconstructed at a different distance (z_c-b)z/z_c, compressing the 3D image longitudinally.

Finally, Fig. 9(d) shows situation that lateral spacing between designed viewpoints Δx_v is wider than camera spacing Δx_c by k. A light ray propagating from a position x in the reference plane to a camera position (x_cn, z_c) = (nΔx_c, z_c) with an angle (nΔx_c-x)/z_c is reconstructed as a light ray propagating from the same position x in the reference plane but to a different position (x_vn, z_v) = (nΔx_v, z_c) = (nkΔx_c, z_c) with an angle (nkΔx_c-x)/z_c, giving a relation

l^{'} (x, \frac{n k Δ x_{c} - x}{z_{c}}) = l (x, \frac{n Δ x_{c} - x}{z_{c}}) .

(9)

Using

θ_{x} = \frac{n k Δ x_{c} - x}{z_{c}}

, Eq. (9) can be written

l^{'} (x, θ_{x}) = l (x, θ_{x} - \frac{(k - 1) n Δ x_{c}}{z_{c}}) = l (x, \frac{1}{k} (θ_{x} - \frac{(k - 1) x}{z_{c}})),

(10)

where

n Δ x_{c} = \frac{z_{c} θ_{x} + x}{k}

is used in the last equality. From Eqs. (1) and (2), we have

l^{'} (x, θ_{x}) = f^{'} (x + θ_{x} z^{'}; z^{'}) = f (x + \frac{1}{k} (θ_{x} - \frac{(k - 1) x}{z_{c}}) z; z) .

(11)

Again, substituting u' = x + θ_xz' into Eq. (11) gives

f^{'} (u^{'}; z^{'}) = f ((1 - \frac{(k - 1) z}{k z_{c}}) u^{'} + θ_{x} (\frac{z}{k} + \frac{(k - 1) z z^{'}}{k z_{c}} - z^{'}); z) .

(12)

Equation (12) is true for all θ_x when

z = \frac{k z^{'}}{1 + (k - 1) z^{'} / z_{c}} .

(13)

By substituting Eq. (13) into Eq. (12), finally we have

f^{'} (x; z) = f ((1 - \frac{(k - 1) z}{z_{c} + (k - 1) z}) x; \frac{k z}{1 + (k - 1) z / z_{c}}),

(14)

where u′ and z′ are replaced by x and z. Equation (14) indicates that the 3D image of hexahedron object is distorted to trapezoidal shape with both longitudinal and lateral deformations.

Note that the results of the distortion analysis using light ray field concept agree well with the results of Woods et al.’s analysis.¹⁴ It confirms the validity of our light ray field based analysis. Our light ray field analysis, however, is more general framework as it can be applied to autostereoscopic displays of different modality. Next section shows distortion analysis when MV image contents are applied to HPO InIm display panel.

3.3 Image distortion caused by using MV image contents to HPO InIm display panel

Unlike MV display, HPO InIm display reconstructs parallel light rays without specific pre-defined viewpoints. Since the MV contents are collection of the light rays converging at several camera positions, it is expected that the 3D image distortion would be severe when the MV contents are used for HPO InIm display without modification.

Figure 10 shows the corresponding light ray field representation. A light ray propagating from a position x in the reference plane to a camera position (x_cn, z_c) with an angle (x_cn-x)/z_c is reconstructed as a light ray emanating from the same position x in the reference plane but with a different constant angle θ_xn, where θ_xn is n-th parallel light ray reconstruction angle of the HPO InIm display. This can be represented by a relation

l^{'} (x, θ_{x n}) = l (x, \frac{x_{c n} - x}{z_{c}}) .

(15)

Assuming θ_xn = nΔθ_x and x_ci = nΔx_c where Δθ_x is the angular ray spacing of the HPO InIm display, and treating the sampled angle θ_xn as a continuous variable θ_x (i.e. θ_xn = nΔθ_x = θ_x, x_cn = nΔx_c = (θ_x/Δθ_x) Δx_c), Eq. (15) becomes

l^{'} (x, θ_{x}) = l (x, \frac{θ_{x} Δ x_{c} - x Δ θ_{x}}{z_{c} Δ θ_{x}}) .

(16)

Again, from Eqs. (1) and (2), we have

l^{'} (x, θ_{x}) = f^{'} (x + θ_{x} z^{'}; z^{'}) = f (x + \frac{θ_{x} Δ x_{c} - x Δ θ_{x}}{z_{c} Δ θ_{}} z; z),

(17)

which reduces to

f^{'} (x; z) = f ((1 - \frac{Δ θ_{x} z}{Δ x_{c} + Δ θ_{x} z}) x; (\frac{z_{c} Δ θ_{x}}{Δ x_{c} + Δ θ_{x} z}) z) .

(18)

Equation (18) indicates that when MV contents are applied to HPO InIm display panel, the 3D images are distorted with depth scaling and depth dependent lateral magnification. Note that Eq. (18) agrees with T. Saishu et al.’s result [21

]. Figure 10 shows visualization of the distortion for a hexahedron object.

Fig. 10 Image distortion when MV image contents are applied to HPO InIm display panel

4. Experimental verification

The analysis was verified experimentally. In experiment, 6-view MV contents and HPO InIm contents were synthesized for two plane objects located at + 20mm and −20mm as shown in Fig. 11 . These contents were loaded to a MV display panel or a HPO InIm display panel, displaying 3D image. In order to check the longitudinal distortion expected from Eqs. (8), (14), and (18), a real cylindrical object was located at different distances in front of the display panel. By comparing motion parallax of the cylindrical object and the displayed 3D image, it is possible to estimate the depth of the displayed image.

Fig. 11 Experimental setup

In the first experiment, 3D image distortion occurring when incorrect MV contents are applied to MV displays was examined. Among lateral and longitudinal distortions, only longitudinal distortion was measured since lateral distortion is much smaller than longitudinal distortion as revealed in Eqs. (8), (14), and (18) and visualized in the rightmost part of Fig. 9. Among three distortion cases shown in Fig. 9, only two cases of viewpoint distance mismatch shown in Fig. 9(c) and viewpoint spacing mismatch shown in Fig. 9(d) were considered because the viewpoint shift shown in Fig. 9(b) does not bring longitudinal distortion.

In the experiment, a MV display panel was implemented using a slanted parallax barrier of a slanting angle tan⁻¹(2/3) measured from the vertical axis. The pixel pitch of the panel was 294μm. The designed viewpoint distance z_v and spacing Δx_v of the MV display were 600mm and 29mm, respectively. For 6-view MV contents, two contents were prepared. One was synthesized with parameters z_c = 2z_v = 1200mm (i.e. b = 600mm) and Δx_c = Δx_v = 29mm (i.e. k = 1) and the other one with z_c = z_v = 600mm (i.e. b = 0mm) and Δx_c = 0.5Δx_v = 14.5mm (i.e. k = 2). For these parameters, Eqs. (8) and (14) indicate that in both cases the depth of the displayed ‘apple’ image will be reduced to around 10mm.

Experimental results are shown in Figs. 12 and 13 . All images in Figs. 12 and 13 were captured at a distance 600mm from the panel. In Fig. 12, the motion parallax of the displayed ‘apple’ image is compared with that of the real cylindrical object located at 20mm in front of the display panel. Note that the horizontal offset of the captured images were adjusted so that the horizontal position of the cylindrical object is maintained in all images. Hence the motion parallax can be observed by comparing the position of the left end of the 'apple' image. From Fig. 12, it can be observed that the motion parallax of the real cylindrical object is larger than that of the displayed ‘apple’ image in two incorrect cases (left and center column in Fig. 12), revealing the depth of the displayed ‘apple’ image is smaller than original depth 20mm. Figure 13 shows the results when the cylindrical object is located at 10mm. Now the motion parallax of the displayed ‘apple’ image in two incorrect cases is the same as that of the real cylindrical object, confirming that the reduced depth of the displayed ‘apple’ object is around 10mm as expected. In the right column of Fig. 13, it can also be observed that the motion parallax of the displayed ‘apple’ image in ideal case is larger than real cylindrical object at 10mm since it is displayed at a original depth 20mm.

Fig. 12 Experimental result: MV contents to MV display, real cylindrical object located at + 20mm.

Fig. 13 Experimental result: MV contents to MV display, real cylindrical object located at + 10mm.

In the second experiment, 3D image distortion occurring when MV contents are applied to HPO InIm display was examined. Again only longitudinal distortion was measured by comparing the motion parallax with real object. In the experiment, the HPO InIm display was implemented using a slanted parallax barrier with the same slanting angle tan⁻¹(2/3) as the MV display panel used in previous experiment. The horizontal spacing between apertures, however, were adjusted so that the display panel has 6 parallel ray directions with Δθ_x = 2.8 degree spacing. For 6-view MV contents, an image content was synthesized with a camera spacing Δx_c = 65/5mm. The contents capturing distance z_c was set to 600mm from the panel. For these parameters, Eq. (18) indicates that the depth of the displayed ‘apple’ image is reduced to 9mm.

Experimental results are shown in Figs. 14 and 15 . In Fig. 14, the motion parallax of the displayed 'apple' image is compared with that of the real cylindrical object located at 20mm. By observing relative shift between the real cylindrical object and the displayed 'apple' image, it can be seen that the real cylindrical object moves larger than the displayed ‘apple’ object in MV image contents of Δx_c = 65/5mm case, which indicates that the displayed ‘apple’ object is reconstructed with reduced depth. On the contrary, in ideal HPO InIm image contents case, the relative motion is negligible, confirming that the ‘apple’ image has similar depth with the cylindrical object. In Fig. 15, the real cylindrical object was located at 9mm. As expected, the relative motion becomes negligible in MV image contents of Δx_c = 65/5mm case, indicating the depth of the 'apple' image is reduced to around 9mm.

Fig. 14 Experimental result: MV contents to HPO InIm display, real cylindrical object located at + 20mm.

Fig. 15 Experimental result: MV contents to HPO InIm display, real cylindrical object located at + 9mm.

5. Conclusion

3D image distortion caused by incorrect contents is analyzed for MV and HPO InIm displays. Unlike previous works which uses view based approach, the light ray field concept is used in our analysis. In the analysis, the light ray field captured in the contents and its deformation by the MV and HPO InIm displays are first identified. From the light ray field deformation, the corresponding distortion of the 3D images is finally deduced. The analysis is verified experimentally when MV image contents are applied to MV display of non-matching parameters and HPO InIm display. The light ray field concept enables unified and simple analysis of the 3D image distortion induced by incorrect contents both in MV and HPO InIm displays. The proposed light ray field based approach is not limited to MV and HPO InIm displays but has potential to be further extended to various different ray based autostereoscopic display techniques.

Acknowledgment

This work was supported by the research grant of LG display Co., LTD. This work was also supported by the research grant of the Chungbuk National University in 2010.

References and links

1.	T. Okoshi, “Three-dimensional displays,” Proc. IEEE 68(5), 548–564 (1980). [CrossRef]
2.	P. Benzie, J. Watson, P. Surman, I. Rakkolainen, K. Hopf, H. Urey, V. Sainov, and C. von Kopylow, “A survey of 3DTV display: techniques and technologies,” IEEE Trans. Circ. Syst. Video Tech. 17(11), 1647–1658 (2007). [CrossRef]
3.	J. Hong, Y. Kim, H.-J. Choi, J. Hahn, J.-H. Park, H. Kim, S.-W. Min, N. Chen, and B. Lee, “Three-dimensional display technologies of recent interest: principles, status, and issues [Invited],” Appl. Opt. 50(34), H87–H115 (2011). [CrossRef] [PubMed]
4.	A. Stern and B. Javidi, “Three-dimensional image sensing, visualization, and processing using integral imaging,” Proc. IEEE 94(3), 591–607 (2006). [CrossRef]
5.	J.-H. Jung, S.- Park, Y. Kim, and B. Lee, “Integral imaging using a color filter pinhole array on a display panel,” Opt. Express 20(17), 18744–18756 (2012). [CrossRef]
6.	J.-H. Park, K. Hong, and B. Lee, “Recent progress in three-dimensional information processing based on integral imaging,” Appl. Opt. 48(34), H77–H94 (2009). [CrossRef] [PubMed]
7.	K. Yamamoto, T. Mishina, R. Oi, T. Senoh, and M. Okui, “Cross talk elimination using an aperture for recording elemental images of integral photography,” J. Opt. Soc. Am. A 26(3), 680–690 (2009). [CrossRef] [PubMed]
8.	D. B. Diner and D. H. Fender, Human Engineering in Stereoscopic Viewing Devices (Plenum, 1994).
9.	A. Woods, T. Docherty, and R. Koch, “Image distortions in stereoscopic video systems,” Proc. SPIE 1915, 36–48 (1993). [CrossRef]
10.	L. M. J. Meesters, W. A. IJsselsteijn, and P. J. H. Seuntiens, “A survey of perceptual evaluations and requirements of three-dimensional TV,” IEEE Trans. Circ. Syst. Video Tech. 14(3), 381–391 (2004). [CrossRef]
11.	K.-H. Lee, M.-J. Lee, Y.-S. Yoon, and S.-K. Kim, “Incorrect depth sense due to focused object distance,” Appl. Opt. 50(18), 2931–2939 (2011). [CrossRef] [PubMed]
12.	C. Ricolfe-Viala, A.-J. Sanchez-Salmeron, and E. Martinez-Berti, “Calibration of a wide angle stereoscopic system,” Opt. Lett. 36(16), 3064–3066 (2011). [CrossRef] [PubMed]
13.	J.-Y. Son, Y. N. Gruts, K.-D. Kwack, K.-H. Cha, and S.-K. Kim, “Stereoscopic image distortion in radial camera and projector configurations,” J. Opt. Soc. Am. A 24(3), 643–650 (2007). [CrossRef] [PubMed]
14.	V. Saveljev, “Image and observer regions in 3D displays,” J. Inform. Disp. 11(2), 68–75 (2010). [CrossRef]
15.	B.-R. Lee, J.-J. Hwang, and J.-Y. Son, “Characteristics of composite images in multiview imaging and integral photography,” Appl. Opt. 51(21), 5236–5243 (2012). [CrossRef] [PubMed]
16.	T. Horikoshi, S.-I. Uehara, T. Koike, C. Kato, K. Taira, G. Hamagishi, K. Mashitani, T. Nomura, A. Yuuki, N. Watanabe, Y. Hisatake, and H. Ujike, “Characterization of 3D image quality on autostereoscopic displays: proposal of interocular 3D purity,” SID Tech. Dig. 41(1), 331–334 (2010). [CrossRef]
17.	S.-I. Uehara, T. Horikoshi, C. Kato, T. Koike, G. Hamagishi, K. Mashitani, T. Nomura, K. Taira, A. Yuuki, N. Umezu, N. Watanabe, Y. Hisatake, and H. Ujike, “Characterization of motion parallax on multi-view/integral-imaging displays,” SID Tech. Dig. 41(1), 661–664 (2010). [CrossRef]
18.	H. Hoshino, F. Okano, H. Isono, and I. Yuyama, “Analysis of resolution limitation of integral photography,” J. Opt. Soc. Am. A 15(8), 2059–2065 (1998). [CrossRef]
19.	J.-H. Park, Y. Kim, J. Kim, S.-W. Min, and B. Lee, “Three-dimensional display scheme based on integral imaging with three-dimensional information processing,” Opt. Express 12(24), 6020 (2004). [CrossRef] [PubMed]
20.	M. Kawakita, H. Sasaki, J. Arai, F. Okano, K. Suehiro, Y. Haino, M. Yoshimura, and M. Sato, “Geometric analysis of spatial distortion in projection-type integral imaging,” Opt. Lett. 33(7), 684–686 (2008). [CrossRef] [PubMed]
21.	T. Saishu, K. Taira, R. Fukushima, and Y. Hirayama, “Distortion control in a one-dimensional integral imaging autostereoscopic display system with parallel optical beam groups,” SID Tech. Dig. 35(1), 1438–1441 (2004). [CrossRef]
22.	A. Stern and B. Javidi, “Ray phase space approach for 3-D imaging and 3-D optical data representation,” J. Display Technol. 1(1), 141–150 (2005). [CrossRef]
23.	J.-H. Park and K.-M. Jeong, “Frequency domain depth filtering of integral imaging,” Opt. Express 19(19), 18729–18741 (2011). [CrossRef] [PubMed]
24.	M. Levoy, R. Ng, A. Adams, M. Footer, and M. Horowitz, “Light field microscopy,” ACM Trans. On Graphics (Proc. SIGGRAPH) 25, 924–934 (2006).

OCIS Codes
(100.2960) Image processing : Image analysis
(100.6890) Image processing : Three-dimensional image processing

ToC Category:
Image Processing

History
Original Manuscript: August 24, 2012
Revised Manuscript: September 21, 2012
Manuscript Accepted: September 22, 2012
Published: October 2, 2012

Citation
Hee-Seung Kim, Kyeong-Min Jeong, Sung-In Hong, Na-Young Jo, and Jae-Hyeung Park, "Analysis of image distortion based on light ray field by multi-view and horizontal parallax only integral imaging display," Opt. Express 20, 23755-23768 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-21-23755

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References

T. Okoshi, “Three-dimensional displays,” Proc. IEEE68(5), 548–564 (1980). [CrossRef]
P. Benzie, J. Watson, P. Surman, I. Rakkolainen, K. Hopf, H. Urey, V. Sainov, and C. von Kopylow, “A survey of 3DTV display: techniques and technologies,” IEEE Trans. Circ. Syst. Video Tech.17(11), 1647–1658 (2007). [CrossRef]
J. Hong, Y. Kim, H.-J. Choi, J. Hahn, J.-H. Park, H. Kim, S.-W. Min, N. Chen, and B. Lee, “Three-dimensional display technologies of recent interest: principles, status, and issues [Invited],” Appl. Opt.50(34), H87–H115 (2011). [CrossRef] [PubMed]
A. Stern and B. Javidi, “Three-dimensional image sensing, visualization, and processing using integral imaging,” Proc. IEEE94(3), 591–607 (2006). [CrossRef]
J.-H. Jung, S.- Park, Y. Kim, and B. Lee, “Integral imaging using a color filter pinhole array on a display panel,” Opt. Express20(17), 18744–18756 (2012). [CrossRef]
J.-H. Park, K. Hong, and B. Lee, “Recent progress in three-dimensional information processing based on integral imaging,” Appl. Opt.48(34), H77–H94 (2009). [CrossRef] [PubMed]
K. Yamamoto, T. Mishina, R. Oi, T. Senoh, and M. Okui, “Cross talk elimination using an aperture for recording elemental images of integral photography,” J. Opt. Soc. Am. A26(3), 680–690 (2009). [CrossRef] [PubMed]
D. B. Diner and D. H. Fender, Human Engineering in Stereoscopic Viewing Devices (Plenum, 1994).
A. Woods, T. Docherty, and R. Koch, “Image distortions in stereoscopic video systems,” Proc. SPIE1915, 36–48 (1993). [CrossRef]
L. M. J. Meesters, W. A. IJsselsteijn, and P. J. H. Seuntiens, “A survey of perceptual evaluations and requirements of three-dimensional TV,” IEEE Trans. Circ. Syst. Video Tech.14(3), 381–391 (2004). [CrossRef]
K.-H. Lee, M.-J. Lee, Y.-S. Yoon, and S.-K. Kim, “Incorrect depth sense due to focused object distance,” Appl. Opt.50(18), 2931–2939 (2011). [CrossRef] [PubMed]
C. Ricolfe-Viala, A.-J. Sanchez-Salmeron, and E. Martinez-Berti, “Calibration of a wide angle stereoscopic system,” Opt. Lett.36(16), 3064–3066 (2011). [CrossRef] [PubMed]
J.-Y. Son, Y. N. Gruts, K.-D. Kwack, K.-H. Cha, and S.-K. Kim, “Stereoscopic image distortion in radial camera and projector configurations,” J. Opt. Soc. Am. A24(3), 643–650 (2007). [CrossRef] [PubMed]
V. Saveljev, “Image and observer regions in 3D displays,” J. Inform. Disp.11(2), 68–75 (2010). [CrossRef]
B.-R. Lee, J.-J. Hwang, and J.-Y. Son, “Characteristics of composite images in multiview imaging and integral photography,” Appl. Opt.51(21), 5236–5243 (2012). [CrossRef] [PubMed]
T. Horikoshi, S.-I. Uehara, T. Koike, C. Kato, K. Taira, G. Hamagishi, K. Mashitani, T. Nomura, A. Yuuki, N. Watanabe, Y. Hisatake, and H. Ujike, “Characterization of 3D image quality on autostereoscopic displays: proposal of interocular 3D purity,” SID Tech. Dig.41(1), 331–334 (2010). [CrossRef]
S.-I. Uehara, T. Horikoshi, C. Kato, T. Koike, G. Hamagishi, K. Mashitani, T. Nomura, K. Taira, A. Yuuki, N. Umezu, N. Watanabe, Y. Hisatake, and H. Ujike, “Characterization of motion parallax on multi-view/integral-imaging displays,” SID Tech. Dig.41(1), 661–664 (2010). [CrossRef]
H. Hoshino, F. Okano, H. Isono, and I. Yuyama, “Analysis of resolution limitation of integral photography,” J. Opt. Soc. Am. A15(8), 2059–2065 (1998). [CrossRef]
J.-H. Park, Y. Kim, J. Kim, S.-W. Min, and B. Lee, “Three-dimensional display scheme based on integral imaging with three-dimensional information processing,” Opt. Express12(24), 6020 (2004). [CrossRef] [PubMed]
M. Kawakita, H. Sasaki, J. Arai, F. Okano, K. Suehiro, Y. Haino, M. Yoshimura, and M. Sato, “Geometric analysis of spatial distortion in projection-type integral imaging,” Opt. Lett.33(7), 684–686 (2008). [CrossRef] [PubMed]
T. Saishu, K. Taira, R. Fukushima, and Y. Hirayama, “Distortion control in a one-dimensional integral imaging autostereoscopic display system with parallel optical beam groups,” SID Tech. Dig.35(1), 1438–1441 (2004). [CrossRef]
A. Stern and B. Javidi, “Ray phase space approach for 3-D imaging and 3-D optical data representation,” J. Display Technol.1(1), 141–150 (2005). [CrossRef]
J.-H. Park and K.-M. Jeong, “Frequency domain depth filtering of integral imaging,” Opt. Express19(19), 18729–18741 (2011). [CrossRef] [PubMed]
M. Levoy, R. Ng, A. Adams, M. Footer, and M. Horowitz, “Light field microscopy,” ACM Trans. On Graphics (Proc. SIGGRAPH) 25, 924–934 (2006).

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