# Fast Numerical Reconstruction of Integral Imaging Based on a Determined Interval Mapping
## 3 Results
### Quality Comparison of the Reconstructed Image  
The structural similarity index measure (SSIM) is a useful method to predict image quality based on features of the human visual system [40; 41; 42]. Therefore, the SSIM was employed to quantitatively evaluate the quality of each refocused image by the conventional method and the proposed methods. To calculate the SSIM value, three kinds of single letters of \"W\", \"K\", and \"U\" located at 150 mm, 350 mm, and 550 mm are modeled by the 3 ds max software. Then, each EIA from each letter is acquired by the computational capturing method. Figure 8 shows the individual EIA acquired from a single letter of \"W\", \"K\", and \"U\" and the corresponding EIAs. Figure 8: Three kinds of letters of ‘W’, ‘K’, and ‘U’ and their EIAs located at (**a**) 150 mm, (**b**) 350 mm, and (**c**) 550 mm. Figure 7: Comparison of the total computation time of the conventional and proposed method. All specifications relating to the acquired EIAs are the same as the previous experiment. Figure 9 shows each refocused image by the conventional and proposed methods for the calculation of the SSIM value. Three reference images are on the left of Figure 9. Three reconstructed letters 'W', 'K', and 'U' by the conventional method at the corresponding reconstruction plane are positioned in the two columns of Figure 9. In 3\(\sim\)5 columns and 1 to 3 rows, each reconstructed letter 'W', 'K', and 'U' by the use of the three different interpolation methods in the proposed method is visualized, depending on the corresponding reconstruction plane. To ensure consistency in the calculation of the SSIM, the resolution of each refocused image has been set to 3840 \(\times\) 2160 pixels because the number of pixels of each refocused image is different. Each SSIM value between each reference image and its corresponding refocused image is measured, and the calculated SSIM value is shown in Figure 10.  
In Figure 10, the \(x\)-axis is three reconstruction planes with 150 mm, 350 mm, and 550 mm, and the \(y\)-axis corresponds to the SSIM value. The blue-colored bar indicates the SSIM value of each refocused image by the conventional method, and the orange-, gray-, and yellow-colored bars indicate the individual value of the SSIM between each reference image and refocused image by the proposed method with the nearest, linear, and bicubic interpolation. As shown in Figure 10, the SSIM values of refocused images by the  
Figure 10: Measured SSIM values of each reconstructed image. Figure 9: Reference and each refocused image by the conventional and proposed methods by use of the different interpolations. conventional method are 0.646, 0.648, and 0.582 at 150 mm, 350 mm, and 550 mm. However, the individual SSIM value of the refocused letters 'W', 'K', and 'U' in the proposed method with the use of the nearest interpolation represents 0.740, 0.881, and 0.813 at 150 mm, 350 mm, and 550 mm, respectively. When linear interpolation is used in the proposed method, the SSIM values between the reference and refocused images are 0.741, 0.865, and 0.789 at the same distances. Similarly, the proposed method using bicubic interpolation yields SSIM values of 0.733, 0.825, and 0.769 at distances of 150 mm, 350 mm, and 550 mm, respectively. In order to compare the qualitative quality of the refocused image, the numerical experiment was performed employing a 3D model of a dragon with continuous depth and fine texture, as shown in Figure 11.  
Figure 11a illustrates the rendered dragon featuring a rich texture on its surface. Additionally, the range of this 3D modeling spans from 120 mm to 550 mm in the \(z\)-direction. After the EIA was acquired from this rendered dragon, each refocused image reconstructed by the conventional and proposed method is shown in Figure 11b, and the four different reconstruction planes are 170 mm, 240 mm, 310 mm, and 380 mm, respectively.