Path-space Exploration for Light Transport and Appearance Modelling

我的研究模型和模拟了视觉现象背后的物理学，这些现象塑造了我们对世界的理解——无论是日落天空中令人敬畏的色彩，拉丝金属板的闪闪发光，阳光明媚的游泳池地板上的聚焦光，还是客厅里迪斯科球从墙上反射回来的光线。******通过建立牢牢扎根于这些和其他现象的物理学的数学公式，我的实验室能够开发新的计算机算法来解决光传输方程，并生成与真实照片无法区分的合成图像。这需要开发软件工具来帮助数字艺术家更容易地为我们的模拟器编写引人注目的3D内容，以及提高这些模拟器处理更复杂和逼真的灯光效果的能力。******我提出的研究计划将在三个方面取得进展：在现实场景中对光输运进行新的、更精确的数学分析；更高效的照明模拟器建立在这些模型之上；以及艺术家友好的数字内容创建工具，使用这些模拟器来设计更逼真的3D内容。******特别对于这个提议的研究计划，我们将执行一个独特的，第一性原理的路径空间分析：一个抽象的数学空间的能量携带路径，有助于图像的形成（无论是在现实世界还是虚拟世界）。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，这些见解将推动我们设计新的强大的数值算法，以更有效、更准确地解决照明方程。最后，为了更好地了解照明在这个空间中的动态运作方式，我们将设计出独特的内容创作工具，能够将这些直觉暴露给数字艺术家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，其中有效的照明模拟和数字内容创建仍然是两个最重要的挑战。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，这项研究将率先解决在视频游戏、视觉效果、建筑设计、虚拟和增强现实以及产品设计行业中具有直接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.