Abstract

In this paper, we propose a computational integral imaging reconstruction (CIIR) method by use of image interpolation algorithms to improve the visual quality of 3D reconstructed images. We investigate the characteristics of the conventional CIIR method along the distance between lenslet and objects. What we observe is that the visual quality of reconstructed images is periodically degraded. The experimentally observed period is half size of the elemental image. To remedy this problem, we focus on the interpolation methods in computational integral imaging. Several interpolation methods are applied to the conventional CIIR method and their performances are analyzed. To objectively evaluate the proposed CIIR method, we introduce an experimental framework for the computational pickup process and the CIIR process using a Gaussian function. We also carry out experiments on real objects to subjectively evaluate the proposed method. Experimental results indicate that our method outperforms the conventional CIIR method. In addition, our method reduces the grid noise that the conventional CIIR method suffers from.

© 2007 Optical Society of America

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References

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    [CrossRef] [PubMed]
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2007 (1)

H. Yoo, "Closed-form least-squares technique for adaptive linear image interpolation," Elect. Lett. 43, pp. 210-212 (2007).
[CrossRef]

2006 (3)

2005 (3)

2004 (4)

2003 (2)

J.-S. Jang and B. Javidi, "Formation of orthoscopic three-dimensional real images in direct pickup one-stepintegral imaging," Opt. Eng. 42, 1869-1870 (2003).
[CrossRef]

A. Stern and B. Javidi, "Three-dimensional image sensing and reconstruction with time-division multiplexed computational integral imaging," Appl. Opt. 42, 7036-7042 (2003).
[CrossRef] [PubMed]

2002 (3)

2001 (1)

1997 (1)

1981 (1)

Keys, R.G , "Cubic convolution interpolation for digital image processing," IEEE Trans. Acoust. Speech Signal Process. 29, 1153-1160 (1981).
[CrossRef]

1908 (1)

G. Lippmann, "La photographic intergrale," Comptes-Rendus, Acad. Sci. 146, 446-451 (1908).

Acad. Sci. (1)

G. Lippmann, "La photographic intergrale," Comptes-Rendus, Acad. Sci. 146, 446-451 (1908).

Appl. Opt. (5)

Elect. Lett. (1)

H. Yoo, "Closed-form least-squares technique for adaptive linear image interpolation," Elect. Lett. 43, pp. 210-212 (2007).
[CrossRef]

ETRI Journal (1)

D.-H. Shin, M. Cho and E.-S. Kim, "Computational implementation of asymmetric integral imaging by use of two crossed lenticular sheets," ETRI Journal 27, 289-293 (2005).
[CrossRef]

IEEE Trans. Acoust. Speech Signal Process. (1)

Keys, R.G , "Cubic convolution interpolation for digital image processing," IEEE Trans. Acoust. Speech Signal Process. 29, 1153-1160 (1981).
[CrossRef]

IEEE Trans. Image Proc. (1)

T. Blu, P. Thevenaz, and M. Unser, "Linear interpolation revitalized," IEEE Trans. Image Proc. 13, pp.710-719 (2004).
[CrossRef]

J. Display Technol. (1)

Opt. Eng. (2)

J.-S. Park, D.-C. Hwang, D.-H. Shin, and E.-S. Kim, "Resolution-enhanced computational integral imaging reconstruction using intermediate-view reconstruction technique," Opt. Eng. 45, 117004 (2006).
[CrossRef]

J.-S. Jang and B. Javidi, "Formation of orthoscopic three-dimensional real images in direct pickup one-stepintegral imaging," Opt. Eng. 42, 1869-1870 (2003).
[CrossRef]

Opt. Express (3)

Opt. Lett. (3)

Proc. IEEE (1)

E. Meijering, "A Chronology of interpolation: From ancient astronomy to modern signal and image processing," Proc. IEEE 90, 319-342 (2002).
[CrossRef]

Other (1)

W. K. Pratt, Digital Image Processing, (New York: Wiley, 1991).

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Figures (11)

Fig. 1.
Fig. 1.

Principle of conventional CIIR method (a) Pickup (b) Display.

Fig. 2.
Fig. 2.

(a). Simple magnification in the conventional CIIR (b). Example of reconstructed image with the grid noise

Fig. 3.
Fig. 3.

Process of proposed method

Fig. 4.
Fig. 4.

Experimental structure for performance evaluation of Gaussian function.

Fig. 5.
Fig. 5.

Comparison of MSE according to three types of interpolation algorithm. Round mark (blue line): zero-order interpolation. Diamond mark (red line): linear interpolation. Star mark (black line): CCI (a) p=30 (b) p=40 (c) p=50 (d) p=60.

Fig. 6.
Fig. 6.

Examples of reconstructed images when p=30. (a) z/g=14 (b) z/g=15. Dot blue line: original Gaussian function. Dash red line : reconstructed image.

Fig. 7.
Fig. 7.

Experimental Structure

Fig. 8.
Fig. 8.

Images reconstructed at z=45 mm (z/g=15) by using three interpolation algorithms. (a) Zero-order interpolation (b) Linear interpolation (c) CCI

Fig. 9.
Fig. 9.

MSE results for 3D objects

Fig. 10.
Fig. 10.

(a). Structure of optical pickup (b). Pickuped elemental images

Fig. 11.
Fig. 11.

Experiments by optical pickup. (a) Conventional CIIR method. (b) Proposed CIIR method.

Equations (6)

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f ( x ) = k = 0 N 1 f ( x k ) β ( x k ) ,
β 0 ( x ) = { 1 , 0 x < 0.5 0 , elsewhere .
β 1 ( x ) = { 1 x , 0 x ∣< 1 0 , elsewhere .
β 3 ( x ) = { 3 2 x 3 5 2 x 2 + 1 , 0 x < 1 1 2 x 3 + 5 2 x 2 4 x 2 , 1 x < 2 0 , elsewhere .
G ( x ) = e x 2 2
MSE = 1 N k = 1 N G ( x k ) R ( x k ) 2

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