CAREER: Mathematical and Computational Fundamentals of Visual Appearance for Computer Graphics

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Much of human perception is driven by the visual appearance of theworld. People are captivated by the effects of natural lighting andshading patterns, such as the soft shadows from the leaves of a treein skylight, the glints of sunlight in ocean waves, or the shinyreflections from a velvet cushion. In computer graphics, it isimportant to be able to accurately reproduce these appearance effects,to create realistic images for applications like video games, vehicleand flight simulators, or architectural design of interior spaces.However, it is still very difficult to accurately model complexillumination and reflection effects in interactive applications likegames, in image-based rendering applications like e-commerce, or incomputer vision applications like face recognition. In the past, theabove applications have been addressed separately, by devisingparticular algorithms for specific problems. In this project, theresearch focuses on the mathematical and computational fundamentals ofvisual appearance, seeking to understand the intrinsic computationalstructure of illumination, reflection and shadowing, and develop aunified approach to many problems in graphics and vision.The main thrust of the research will be to develop appropriatemathematical representations for appearance, along with computationalalgorithms and signal-processing techniques such as Clebsch-Gordanexpansions, wavelet methods with triple product expansions, and radialbasis functions. A major advantage of this approach is that the samerepresentations, analysis and computation tools can then be applied tomany application domains, such as real-time and image-based rendering,Monte Carlo sampling and lighting-insensitive recognition. Thisresearch philosophy builds on the investigator's dissertation, wherehe developed a signal-processing framework for reflection, leading tonew frequency domain algorithms for both forward and inverse rendering.