## Abstract

We propose a depth extraction method by using the correlation between an elemental image and a periodic function in computational integral imaging. Because each elemental image corresponds to a different perspective of the three-dimensional (3-D) object, an elemental image is regarded as the sum of the periodic spatial frequencies depending on the depth of a 3-D object. In this regard, we analyze the property of correlation between the same periodic functions and vice versa. To show the feasibility of the proposed method, we carried out our experiment and presented the results.

© 2012 Optical Society of America

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### Equations (9)

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(1)
$${x}_{Ek}={x}_{O}+\frac{{z}_{\mathrm{On}}}{{z}_{\mathrm{On}}+f}[(k-\frac{1}{2})P-{x}_{O}].$$
(2)
$$\{\begin{array}{l}{x}_{O}>\frac{P(K-1)}{2fK}{z}_{\mathrm{On}}+(K-\frac{1}{2})P,\\ {x}_{O}<-\frac{P(K-1)}{fK}{z}_{\mathrm{On}}+\frac{P}{2},\\ {z}_{\mathrm{On}}<0,\end{array}$$
(3)
$${g({x}_{E})|}_{{z}_{\mathrm{On}}}={f({x}_{E})|}_{{z}_{\mathrm{On}}}*{h({x}_{E})|}_{{z}_{\mathrm{On}}}.$$
(4)
$${f({x}_{E})|}_{{z}_{\mathrm{On}}}=\left|\frac{{z}_{En}}{{z}_{\mathrm{On}}}\right|{{f}_{O}(-{x}_{E})|}_{{z}_{\mathrm{On}}}.$$
(5)
$$h({x}_{E}){|}_{{z}_{\mathrm{On}}}=\sum _{k=1}^{K}\delta ({x}_{E}-{x}_{Ek}{|}_{{z}_{\mathrm{On}}}),$$
(6)
$${g({x}_{E})|}_{{z}_{\mathrm{On}}}=\left|\frac{{z}_{En}}{{z}_{\mathrm{On}}}\right|{{f}_{O}(-{x}_{E})|}_{{z}_{\mathrm{On}}}*\sum _{k=1}^{K}\delta ({x}_{E}-{{x}_{Ek}|}_{{z}_{\mathrm{On}}}).$$
(7)
$${X}_{{Z}_{\mathrm{On}}}=\mathrm{ceil}[|{x}_{Es}-{x}_{E(s-1)}|\times \frac{\text{number of pixel}}{P\times \text{number of lens}}],$$
(8)
$${h({x}_{E})|}_{{z}_{\mathrm{On}}}\otimes {h({x}_{E})|}_{{z}_{\mathrm{Om}}}=\sum _{k=1}^{K}\delta ({x}_{E}-{{x}_{Ek}|}_{{z}_{\mathrm{On}}})*\sum _{k=1}^{K}\delta ({x}_{E}-{{x}_{Ek}|}_{{z}_{\mathrm{Om}}}).$$
(9)
$$\mathrm{\Delta}{z}_{O}=\frac{Nf}{({X}_{Zon}-N)({X}_{Zon}+1-N)},$$