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

人类的大部分感知是由世界的视觉外观驱动的。人们被自然光线和阴影模式的效果所吸引，比如树的树叶在天窗上的柔和阴影，海浪中闪烁的阳光，或者天鹅绒靠垫的反光。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室内空间的建筑设计等应用创建逼真的图像是很重要的。然而，在像游戏这样的交互式应用中，在像电子商务这样的基于图像的渲染应用中，或者在像人脸识别这样的计算机视觉应用中，精确地建模复杂的照明和反射效果仍然是非常困难的。在过去，上述应用都是通过设计特定问题的特定算法来单独解决的。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。该研究的主要目的是为外观开发适当的数学表示，以及计算算法和信号处理技术，如clebsch - gordan展开、具有三重积展开的小波方法和径向基函数。这种方法的一个主要优点是，相同的表示、分析和计算工具可以应用于许多应用领域，如实时和基于图像的渲染、蒙特卡罗采样和光照不敏感识别。该研究理念建立在研究者的论文基础上，他在论文中开发了一个用于反射的信号处理框架，领导了用于正向和反向渲染的新频域算法。

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.