Synthesizing 3-D images with voxels

Abstract

3-D images provide viewers with more accurate and realistic information than 2-D images. They also bring immersive feeling to the viewers with depth sense, on the other hand, often causing dizziness and serious eye fatigue. The main demands of 3-D images occur in themovies, broadcasting, medical applications, advertisement, telepresence, education and entertainment, and so on. Generally 3-D images adopt voxel representation, which is analogous to the concept of pixel in 2-D images. The voxels, basic elements of 3-D images, are used to describe virtual points. Any desired 3-D image can be displayed by synthesizing it with voxels of pre-defined coordinate values because 3-D images are formed by voxels. Voxels can be visible if a group of pixels in the display panel, which is responsible for making each voxel visible at the viewing zone, is defined because voxels are virtual points in a pre-defined space. The viewing zone is a spatial location where viewers can see entire images displayed on the screen. The multi-view (MV) [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14] and IP (Integral Photography) [15, 16, 17, 18, 19, 20, 21, 22, 23] are the typical methods of displaying a full parallax 3-D image on a flat panel display. As autostereoscopic image displays these methods have been a matter of great concern since 1990. MV and IP have the same optical structure composed of a viewing zone forming optics and a display panel located at the focal plane of the optics. The images projected to viewers' eyes in MV and IP have a conjugate relationship between them [16]. In this chapter, synthesizing 3-D images with voxels in a contact-type imaging system for these methods will be discussed. MV images for generating full parallax images can be easily obtained by using a two-dimensional (2-D) camera array. The images can also be synthesized with a computer by considering the relative viewing direction of each camera in the array for a given object [5, 6, 7, 12, 13, 14]. In order to configure these MV images, the display panels of MV 3-D imaging systems must be divided into a number of segments, called pixel cells. A 3-D imaging system can provide full parallax 3-D images. Pixel cells (the number of segments divided) corresponds either to (1) the number of pixels in the image from each camera in the array [8, 9] or (2) to the number of cameras in the array [10, 11, 15, 16]. The number of pixels in each pixel cell is equal to the number of cameras in the array. Each pixel in the cell represents a pixel from each camera for (1). For (2), each pixel cell in the display panel presents the whole image of each camera. The each camera position in the array corresponds to that of the cell in the panel. The typical shape of a pixel cell is either rectangular or square. Since these shapes are vulnerable to the Moire effect, rhomb shaped pixel cells can also be used [24]. In these configuration methods, we typically scale the proper resolution of each camera image to fit into the resolution of the display panels available. This scaling process is somewhat cumbersome and time consuming. 3-D images are formed by voxels, so we can synthesize the 3-D image with voxels of pre-defined coordinate values [16, 25]. Finally, we can display any desired 3-D image. The voxels are used to describe virtual points. Any desired 3-D image can be displayed by synthesizing it with voxels of predefined coordinate values because 3-D images are formed by voxels. Voxels can be visible if a group of pixels in the display panel, which is responsible for making each voxel visible at the viewing zone, is defined because voxels are virtual points in a pre-defined space. The scaling step can be eliminated and the computational time for preparing MV images can be minimized. To obtain these effects a set of voxels is defined in the optical configuration of a full parallax MV 3-D imaging system based on a 2-D PLS (Point Light Source), and the set is used to display 3-D images. In this configuration, the group of pixels provides passage for rays from PLSs such that the voxel is visible at the viewing zones cross section, where the viewing zone is centered. The pixel pattern formed by the group of pixels has a unique pattern to represent a voxel in a certain location. Finding pixel patterns in the display panel is required so that it will be able to display 3-D images. The configuration provides two voxel types; one is seen at the entire viewing zones cross section (complete voxel) and the other is only partially seen (incomplete voxel). The spatial volume is where 3-D images appear, and it depends on the spatial distribution of voxels. Similarly, the resolution of the images depends on their available number. As the number of complete voxels is limited and the voxels occupy only a small space, the image space and the voxel resolution of the displayable images will be extremely limited as well. Using incomplete voxels will effectively increase the volume and the resolution of the images. The incomplete voxels will successfully increase the image volume in the MV 3-D imaging systems, since most of these systems [9, 10, 11] are based on the optical configuration [26]. The pixel patterns for these voxels strongly depend on the shape of the pixel cells. The pixel pattern for the complete voxel has the same pixel arrangement in both vertical and horizontal directions. For this reason, we are easily able to determine the 2-D pixel pattern from the vertical or horizontal direction pattern for a rectangular or square pixel cell. However, for the rhomb shaped pixel cell, the difference in pixel numbers in both directions changes the arrangements of directions from each other. This chapter outlines synthesizing 3-D images with voxels in a contact-type imaging systembydescribingvoxels inthePLSarrayanddefining the incomplete voxels and their corresponding pixel patterns to increase the volume. Also, we mathematically identify their positions. In addition,we extend the pixel pattern to pixel cells with a rhombus shape for aMoire-free image display. ？ 2009 Springer-Verlag New York.