# Systematic Approach for Alignment of Light Field Mirage
## 5 Image Stitching Technique for Multiple Skewed LFDs  
The light field Mirage approximates the parabolic mirror surfaces of the original Mirage as multiple LFDs to provide a continuous 360-degree viewing zone. As shown in Figure 6, because the LFDs have flat rectangular screens, there exists overlapping regions among the screens of the LFDs. The overlapping regions become visible because their intensities become higher than those of the surroundings. When slanted 2D displays are circularly aligned, image discontinuity occurs in the images along the crossing lines of the screens. The image discontinuity should not necessarily be considered for the light field Mirage because the ray directions are controlled by all LFDs. Therefore, a technique to smoothly connect images generated by the multiple LFDs should be developed.  
The image blending technique has been usually used to diminish the appearance of overlapping regions by adjusting the intensities of the two overlapping images. The image blending technique is effective only when the overlapping screens are parallel. However, for the light field Mirage, the screens of the LFDs that overlap each other are skewed to each other, and the directions of the rays emitted from the overlapping screens are not partially identical. Therefore, we used the image stitching technique, in which either display shows images in the overlapping region and the other display does not show images there. Figure 6 depicts the stitching scheme, in which the reflected images of the upper LFDs by the half mirror were drawn with those of the lower LFDs. In each LFD, a trapezoid area in the rectangular screen was used to display the 3D images. When the number of the LFDs is eight, the angle between the side lines and the bottom line of the trapezoid is 22.5\({}^{\circ}\). When the LFD height is denoted by \(a\) and the LFD is inclined at an angle of 45.0\({}^{\circ}\), the trapezoid's height is given by a \(\cos\) 45.0\({}^{\circ}\). Since the distance from the center axis to the trapezoid's center is denoted by \(r\), the trapezoid's center width is 2 \(r\) tan 22.5\({}^{\circ}\), the long side of the  
Figure 6: Stitching of screens of LFDs (top view and drawn in an orthographic projection).  
trapezoid is 2 tan22.5\({}^{\circ}\) (\(r+a/2\) cos 45.0\({}^{\circ}\)), and the short side of trapezoid is 2 tan22.5\({}^{\circ}\) (\(r-a/2\) cos 45.0\({}^{\circ}\)).  
As shown in Figure 7a, when the image stitching technique was not used, the overlapping region of the two images became brighter when images were displayed on the adjacent LFDs. Figure 7b,c show the images when the image stitching technique was applied. When 3D images were displayed using the lenses that were completely included in the trapezoids, a black line was observed along the connecting lines, as shown in Figure 7b. When 3D images were displayed using the lenses that were completely or partly included in the trapezoids, a bright line was observed along the connecting lines, as shown in Figure 7c. Thus, 3D images were displayed using trapezoids expanded by five lenses, and we used the bilinear interpolation technique to connect the two trapezoid regions. The resultant image is shown in Figure 7d. The two images were smoothly stitched.  
In the case of stitching skewed 2D displays, any image correction technique can provide continuous images only for a specified viewing direction. However, when skewed LFDs are stitched, the images are continuously connected along the connecting lines because the directions of the rays are properly controlled by all displays. Since the ray directions of all LFDs were calibrated by the technique described in Section 4, no additional image correction technique was required to stitch the skewed LFDs.