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

人类的感知在很大程度上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迷住了，比如天窗树叶的柔和阴影，海浪中的阳光闪烁，或者天鹅绒靠垫的闪闪发光。在计算机图形学中，能够准确地再现这些外观效果非常重要，能够为视频游戏、飞行器和飞行模拟器或室内空间的建筑设计等应用程序创建逼真的图像。然而，在交互式应用程序(如游戏)、基于图像的渲染应用程序(如电子商务)或计算机视觉应用程序(如人脸识别)中，精确建模复杂的照明和反射效果仍然是非常困难的。在过去，通过为特定的问题设计特定的算法，上述应用是分开处理的。在这个项目中，研究重点放在视觉外观的数学和计算基础上，试图了解照明、反射和阴影的内在计算结构，并开发一种统一的方法来解决图形和视觉中的许多问题。研究的主要重点将是开发适合外观的数学表示法，以及计算算法和信号处理技术，如Clebsch-Gordan展开、三重乘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绘制、蒙特卡罗采样和光照不敏感的识别。这一研究哲学建立在研究人员的论文基础上，他开发了一个反射信号处理框架，导致了用于正反向渲染的新的频域算法。

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.