Much of human perception is driven by the visual appearance of the world. People are captivated by the effects of natural lighting and shading patterns, such as the soft shadows from the leaves of a tree in skylight, the glints of sunlight in ocean waves, or the shiny reflections from a velvet cushion. In computer graphics, it is important to be able to accurately reproduce these appearance effects, to create realistic images for applications like video games, vehicle and flight simulators, or architectural design of interior spaces. However, it is still very difficult to accurately model complex illumination and reflection effects in interactive applications like games, in image-based rendering applications like e-commerce, or in computer vision applications like face recognition. In the past, the above applications have been addressed separately, by devising particular algorithms for specific problems. In this project, the research focuses on the mathematical and computational fundamentals of visual appearance, seeking to understand the intrinsic computational structure of illumination, reflection and shadowing, and develop a unified approach to many problems in graphics and vision.
The main thrust of the research will be to develop appropriate mathematical representations for appearance, along with computational algorithms and signal-processing techniques such as Clebsch-Gordan expansions, wavelet methods with triple product expansions, and radial basis functions. A major advantage of this approach is that the same representations, analysis and computation tools can then be applied to many application domains, such as real-time and image-based rendering, Monte Carlo sampling and lighting-insensitive recognition. This research philosophy builds on the investigator's dissertation, where he developed a signal-processing framework for reflection, leading to new frequency domain algorithms for both forward and inverse rendering.
