## Abstract

We propose a new method for rectifying a geometrical distortion in the elemental image set and extracting an accurate lens lattice lines by projective image transformation. The information of distortion in the acquired elemental image set is found by Hough transform algorithm. With this initial information of distortions, the acquired elemental image set is rectified automatically without the prior knowledge on the characteristics of pickup system by stratified image transformation procedure. Computer-generated elemental image sets with distortion on purpose are used for verifying the proposed rectification method. Experimentally-captured elemental image sets are optically reconstructed before and after the rectification by the proposed method. The experimental results support the validity of the proposed method with high accuracy of image rectification and lattice extraction.

© 2010 OSA

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### Equations (8)

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(1)
$$x={H}^{\prime}{x}^{\prime},$$
(2)
$${x}^{\prime}={\left({H}^{\prime}\right)}^{-1}x=Hx.$$
(3)
$$H={H}_{s}{H}_{a}{H}_{p},$$
(4)
$${H}_{s}=\left[\begin{array}{cc}sR& t\\ {0}^{T}& 1\end{array}\right],\text{\hspace{0.17em}}{H}_{a}=\left[\begin{array}{ccc}1/\beta & -\alpha /\beta & 0\\ 0& 1& 0\\ 0& 0& 1\end{array}\right],\text{\hspace{0.17em}}{H}_{p}=\left[\begin{array}{ccc}1& 0& 0\\ 0& 1& 0\\ {l}_{1}& {l}_{2}& {l}_{3}\end{array}\right],$$
(5)
$$({c}_{\alpha},{c}_{\beta})=\left(\frac{{d}_{1}+{d}_{2}}{2},0\right),$$
(6)
$$R=\left|\frac{{d}_{1}-{d}_{2}}{2}\right|,$$
(7)
$$({c}_{\alpha},{c}_{\beta})=\left(\frac{\mathrm{\Delta}{x}_{2}\mathrm{\Delta}{y}_{2}-{r}^{2}\mathrm{\Delta}{x}_{1}\mathrm{\Delta}{y}_{1}}{\mathrm{\Delta}{y}_{2}^{2}-{r}^{2}\mathrm{\Delta}{y}_{1}^{2}},0\right),$$
(8)
$$R=\left|\frac{r\left(\mathrm{\Delta}{x}_{1}\mathrm{\Delta}{y}_{2}-\mathrm{\Delta}{x}_{2}\mathrm{\Delta}{y}_{1}\right)}{\mathrm{\Delta}{y}_{2}^{2}-{r}^{2}\mathrm{\Delta}{y}_{1}^{2}}\right|.$$