## 3 Proposed Method of Extracting Elemental Image Array
### Re-Calibration  
The proposed re-calibration algorithm is shown in Figure 3. First, the reference lattice lines are sorted in the order of the largest projection profile value. This is because the greater the value obtained from the projection profile, the higher the probability that an accurate line is detected. Let the reference lines be \(R_{i}\) and the number of reference lines be \(N\). Then, the possible distances between two chosen reference lines \(D_{k}\) are defined as  
\[D_{k}=R_{m}-R_{n}\ \left(k=1,2,\ldots,\frac{N(N-1)}{2},=\backslash r\right) \tag{3}\]  
where the maximum of \(k\) is calculated by N-choose-2 and \(R_{m}>R_{n}\).  
The locations of reference lattice lines obtained from larger projection profiles are relatively robust, and there should be an integer number of lenses between the lattice lines. The number of lenses between the reference lines can be easily estimated. The distance \(D_{k}\) is divided by the initial value of the elemental image size, \(w_{0}\), obtained by the existing method. By rounding this value, the number of lenses is estimated. The estimated number of lenses is very accurate since some errors in \(w_{0}\) can be eliminated by the rounding or quantizing process. Thus, a new size of the elemental image can be calculated by dividing  
Figure 3: Proposed enhancement method of EIA extraction.  
the distance \(D_{k}\) by the number of lenses. An updated size of the elemental image \(w_{k}\) can be written as  
\[w_{k}\ =\frac{D_{k}}{Round\left(\frac{D_{k}}{w_{0}}\right)} \tag{3}\]  
Here, it can be said that \(w_{k}\) is more accurate than \(w_{0}\) since the number is more accurate and the distances \(D_{k}\) are more accurately chosen than the existing method. Note that the ideal distance of \(D_{k}\) is a multiple of the ideal size of \(w_{k}\). Moreover, \(w_{k}\) can still have an error due to an inaccurate \(D_{k}\). Thus, we introduce a method to extract the robust size from a set of \(w_{k}\).  
To determine the final version of the elemental image size \(w_{f}\), we employ a continuous probability density function along the size space. The data \(w_{k}\) in the size space are discrete and sparse, thus a continuous window is required to prepare a continuous probability density function [32]. Here, we use a Gaussian window which can be written by  
\[G(w_{k},\sigma)=\frac{1}{\sqrt{2\pi\sigma^{2}}}e^{\frac{-(w-w_{k})^{2}}{2 \sigma^{2}}} \tag{4}\]  
where the sigma \(\sigma\) is a parameter of the Gaussian function and we fixed the sigma to be 2 in our method. Now, a linear combination of the Gaussian function for all \(w_{k}\) provide us with the continuous probability function or likelihood function for \(w_{k}\). Taking the argument of maximizing the probability yields the final version of elemental image size, which is written by  
\[w_{f}\ =\arg\max\sum_{k=1}^{M}G(w_{k},\sigma) \tag{5}\]  
For example, a set of Gaussian density functions for \(w_{k}\) = {216, 216.5, 217.625, 219.875, 228.25, 240} using Equation (4) and their linear combination are depicted in Figure 4. Moreover, the argument of maximizing the likelihood function is calculated as \(w_{f}\) =217.03 by using Equation (5). It is seen that a group of \(w_{k}\) which is the set of candidates of the accurate size provides the final version of \(w_{f}\) whereas some of \(w_{k}\) which is considered to be an inaccurate size are discarded. Therefore, our re-calibration technique is an effective method to suppress the noise due to inaccuracy in the size of the elemental image.