Robust image estimation and progressive rendering techniques are introduced, and these novel methods are used to simulate the appearance of teeth and dental restorations. The realistic visualization of these translucent objects is essential for computer-aided processes in the field of dentistry, because a successful dental treatment is dependent on the recovery not only of the tooth's function, but also its appearance. However, due to the heterogeneity of the tooth structure and the coupled subsurface scatterings that this causes, simulating the translucency of these objects presents a difficult computational challenge. A Monte-Carlo ray tracing system is employed to model the complex interactions of light within the material and to develop the robust image estimation and progressive rendering techniques. Because low probability samples are infrequently encountered in an image, for standard Monte-Carlo estimation these samples can become noise. Robust image estimation techniques are suggested as a way to suppress these low probability samples, and it is demonstrated that for a given sample size robust estimation techniques can produce less noisy renderings. In other words, the sample size necessary to satisfy a certain user requirement will decrease, and an improvement in rendering speed can be obtained. The robust estimation techniques are discussed in both pixel and image space, and their statistical analysis is provided. This analysis determines the inclusion rate for sample probabilities and is thus able to specify the sample probability thresholds necessary to discard or include samples. The statistical analysis also makes it possible to determine the performance boundaries in terms of the number of disclosed low probability samples in an image; as a result, a sample size for a given user requirement can be identified. A progressive approach for rendering translucent objects based on volume photon mapping is also presented. Because conventional volume photon mapping requires long preprocessing to build up a complete volume photon map, it is not able to support progressive rendering. Even worse, due to the limited memory space in a given computer system, the rendering results suffer from a potentially incorrect volume photon map. Progressive volume photon mapping uses a subset of volume photons for rendering, so it provides a high frame rate for preview rendering. In addition, by recycling the volume photons used for previous image estimation, progressive volume photon mapping does not suffer from memory restriction. It is therefore able to use a virtually unlimited number of volume photons and this makes exact rendering plausible. Although these methods were developed to realistically visualize teeth and dental restorations, they are effective in any rendering situation that suffers from noise, restricted computational performance, and limited memory space; as a consequence, these procedures are expected to be useful for many other types of realistic image synthesis including motion picture special effects and video games. The statistical interpretation developed for robust estimation is based on the pixel radiance sample probability. This allows the image synthesis sampling problem to be studied in a manner similar to how it would be treated in other established fields of science and engineering: in terms of the statistical properties of the signal to be sampled. This approach can provide the groundwork for further stochastic analyses in the context of computer graphic rendering.
University of Minnesota Ph.D. dissertation. February 2016. Major: Computer Science. Advisor: Gary Meyer. 1 computer file (PDF); viii, 115 pages.
Jung, Jin Woo.
Rendering of Teeth and Dental Restorations using Robust Statistical Estimation Techniques.
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