Path-space Exploration for Light Transport and Appearance Modelling

我的研究模拟和模拟了视觉现象背后的物理现象，这些现象塑造了我们对世界的理解，无论是夕阳天空令人敬畏的颜色，拉丝金属盘的闪闪发光，阳光充足的游泳池地板上的聚光灯，还是从你客厅的迪斯科舞会上从墙上反射过来的光线。 通过建立牢牢植根于这些现象和其他现象的物理基础上的数学公式，我的实验室能够开发出新颖的计算机算法，用于求解光传输方程，并生成与真实照片难以区分的合成图像。这需要开发软件工具来帮助数字艺术家更轻松地为我们的模拟器创作引人注目的3D内容，以及提高这些模拟器处理更复杂和逼真的照明效果的能力。 我提出的研究计划将在三个方面取得进展：对真实世界场景中的光传输进行新的、更准确的数学分析；在这些模型上构建更高效的照明模拟器；以及使用这些模拟器设计更逼真的3D内容的艺术家友好的数字内容创作工具。 具体来说，对于这个拟议的研究计划，我们将对路径空间进行独特的第一原理分析：路径空间是一种抽象的数学空间，包含有助于图像形成的携带能量的路径(无论是在现实世界还是在虚拟世界中)。在这样做的过程中，我们将建立关于这个空间的形式和结构的新的理论见解，这些见解将驱使我们设计新的强大的数值算法，以更高效、更准确地求解照明方程。最后，为了更好地了解照明在这个空间中的动态是如何运作的，我们将设计出独特的内容创作工具，能够向数字艺术家展示这些直觉，并促进他们的艺术设计。 在学术上，这项工作是计算机图形和渲染社区最感兴趣的，在那里，高效的照明模拟和数字内容创建仍然是最重要的两个挑战。更广泛地说，我的实验室将在这项研究过程中开发的数学模型和数值技术将有助于解决计算物理、统计学、应用数学和高性能计算领域的问题。 由于数字媒体行业是加拿大最大的经济驱动力之一，这项研究将首先解决在视频游戏、视觉效果、建筑设计、虚拟和增强现实以及产品设计行业立即应用的重要开放挑战。

My research models and simulates the physics behind visual phenomena that shape our understanding of the world whether it's the awe-inspiring colours of a sunset sky, the glistening of brushed metallic plates, the focussed light on a sunny pool floor, or the rays of light bouncing off your wall from that disco ball in your living room. By building mathematical formulations rooted firmly in the physics of these and other phenomena, my lab is able to develop novel computer algorithms for solving the equations of light transport and generating synthetic images that are indistinguishable from real photos. This requires developing software tools to help digital artists more easily author compelling 3D content for our simulators, as well as improving the capabilities of these simulators to handle more complex and realistic lighting effects. My proposed research program will make progress on three fronts: new, more accurate mathematical analyses of light transport in real-world scenes; more efficient lighting simulators built atop these models; and, artist-friendly digital content creation tools that use these simulators to design more realistic 3D content. Specifically for this proposed research program, we will perform a unique, first-principles analysis of path-space: an abstract mathematical space of energy-carrying paths that contribute to an image's formation (whether in the real or virtual world). In doing so, we will build new theoretical insights about the form and structure of this space, and these insights will drive us to design new powerful numerical algorithms to solve lighting equations more efficiently and more accurately. Lastly, in gaining a better sense of how the dynamics of lighting operates in this space, we will devise unique content creation tools capable of exposing these intuitions to digital artists and facilitating their artistic designs. Academically, this work is of interest most immediately to the computer graphics and rendering communities, where efficient lighting simulation and digital content creation remain two of the most important challenges. More broadly, the mathematical models and numerical techniques my lab will develop during the course of this research will contribute to problems in the areas of computational physics, statistics, applied mathematics, and high-performance computing. As the digital media industry is one of the largest economic drivers in Canada, this research will be the first to solve important open challenges that have immediate applications in video gaming, visual effects, architectural design, virtual and augmented reality, and product design industries.