NSF Young Investigator: Simulating Global Illumination

合成真实感图像是计算机图形学的一个基本挑战。 这项任务最困难的方面之一是模拟全局照明：表面之间的光的相互反射。 本研究将有限元素法应用于整体照明的模拟。 该工作分为三个子项目：（1）全局照明的误差度量，（2）辐射度的自适应网格化，和（3）具有任意反射率的场景的泛化。与其试图测量“现实主义”，这是一个相当模糊的感知质量，更简单的，定量的准确性措施正在开发中。 使用这些误差测量，现有的和未来的图像合成算法可以进行评估和定量排名。 在许多光能传递系统中，光能传递网格生成的自适应网格只是部分自动化的，并且对各种网格引入的误差知之甚少。 最近的实验简化，二维场景表明，使用自适应网格和更高程度的近似可以导致更快和/或更准确的解决方案比现有的算法。 当光能传递网格遵循解函数中的不连续性（如阴影边界处的不连续性）时，会产生更准确、更美观的图片。 这些“不连续网格”技术已经被研究人员所接受。 在这项研究中，网格辐射度进行了比较和评估使用误差度量作为一个客观的标准。 这种严格的辐射度函数分析表明，新的网格生成技术，允许更准确的模拟。 推广到具有任意反射率的场景（最后的子项目）是将这些方法推广到具有真实光散射的场景。 真实的表面的反射率不是纯粹的漫反射或镜面反射，而是由复杂的双向反射分布函数（BRDF）描述的。 最近的工作表明，球谐函数或其他适当的基函数的使用大大促进了方向依赖的光函数的近似。 这种位置和方向函数的表示法正在被分析和发展。 最终目标是开发精确、高效的算法来模拟具有任意反射率和透射率的复杂场景的全局照明。

Synthesizing realistic images is a fundamental challenge for computer graphics. One of the most difficult aspects of this task is the simulation of global illumination: the interreflection of light between surfaces. This research applies finite element methods to the simulation of global illumination. The work is divided into three subprojects: (1) error metrics for global illumination, (2) adaptive meshing for radiosity, and (3) generalization to scenes with arbitrary reflectance. Rather than attempting to measure ``realism'', which is a rather nebulous perceptual quality, simpler, quantitative accuracy measures are being developed. Using these error measures, existing and future image synthesis algorithms can be evaluated and quantitatively ranked. Adaptive meshes for radiosity mesh generation is only partially automated in many radiosity systems, and little is known about the errors introduced by various meshes. Recent experiments on simplified, two-dimensional scenes show that the use of adaptive meshes and higher degree approximations can lead to much faster and/or more accurate solutions than those of existing algorithms. More accurate, better looking pictures result when the radiosity mesh follows discontinuities in the solution function such as those at shadow boundaries. These ``discontinuity meshing'' techniques have been embraced by researchers. In this research, meshes for radiosity are compared and evaluated using error metrics as an objective criterion. This rigorous analysis of radiosity functions suggests new mesh generation techniques allowing more accurate simulations. Generalization to scenes with arbitrary reflectance, the final sub-project, is the generalization of these methods to scenes with realistic light scattering. The reflectance of real surfaces is not purely diffuse or specular, but is described by a complex bidirectional reflectance distribution function (BRDF). Recent work suggests that the use of spherical harmonics or other appropriate basis functions greatly facilitates the approximation of direction-dependent light functions. Such representations for functions of both position and direction are being analyzed and developed. The ultimate goal is the development of accurate, efficient algorithms for simulating global illumination on complex scenes with arbitrary reflectance and transmittance.