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

人类的大部分感知都是由世界的视觉外观驱动的。 人们被自然光线和阴影图案的效果所吸引，例如天窗中树叶的柔和阴影，海浪中阳光的闪烁，或者天鹅绒垫子上闪闪发光的反射。 在计算机图形学中，能够准确地再现这些外观效果，为视频游戏、车辆和飞行模拟器或内部空间的建筑设计等应用创建逼真的图像是非常重要的。然而，在诸如游戏的交互式应用中，在诸如电子商务的基于图像的渲染应用中，or in computer计算机vision视觉applications应用like face面对recognition识别. 在过去，上述应用程序已被单独解决，通过designingparticular算法的具体问题。 在这个项目中，研究的重点是视觉外观的数学和计算基础，寻求理解照明，反射和阴影的内在计算结构，并开发一个统一的方法来解决图形和视觉中的许多问题。研究的主要目标是开发适当的数学表示，沿着计算算法和信号处理技术，如Clebsch-Gordan展开，小波方法与三重积展开，和radialbasis函数。 这种方法的一个主要优点是，相同的表示，分析和计算工具，然后可以应用到任何应用领域，如实时和基于图像的渲染，蒙特卡罗采样和光照不敏感的识别。 这一研究理念建立在研究者的论文之上，他在论文中开发了一个反射信号处理框架，为正向和反向渲染引入了一种新的频域算法。

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.