Mollifying Realistic Image Synthesis for Time Constrained Rendering

真实感图像合成或渲染是计算机图形学中的一个关键问题，从数字娱乐到建筑和工业设计，有着众多的应用领域。大多数以前的渲染算法的目标是随着计算时间的增加而尽可能快地收敛到地面真实解。计算通常会继续，直到满足所需的质量标准，但所需的计算时间不是渲染器的输入。与此相反，在这个项目中，我们考虑的是在给定的时间约束下获得最佳可能近似解的问题。一个关键的想法是通过修改手头的渲染问题来实现这一点，即包括图像重建在内的场景和光线传输模拟，以获得更容易的问题。这通常被称为“安抚”。软化使我们能够在给定的时间预算内实现对所需图像更好的近似。解决缓和的问题通常可能不会收敛到基本事实，但与解决原始问题相比，在有限的时间内它将提供更好的近似。我们认为，在用户不能简单地等待任意时间量直到模拟提供可接受的结果的应用场景中，该问题陈述是高度相关的。例如，在交互式建模或设计期间，用户指定他们愿意等待的给定时间量要有用得多。我们提出的技术试图在这个时间框架内提供可能的最佳近似解。在这个项目中，我们将开发一个安抚的理论框架，并使用实用的算法来演示它的好处。

Realistic image synthesis, or rendering, is a key problem in computer graphics with numerous application areas, from digital entertainment to architecture and industrial design. The goal of most previous rendering algorithms is to converge to the ground truth solution as quickly as possible with increasing computation time. Computation typically continues until desired quality criteria are met, but the desired computation time is not an input to the renderer. In contrast to this, in this project we consider the problem to obtain the best possible approximate solution under a given time constraint. A key idea is to achieve this by modifying the rendering problem at hand, that is the scene and the light transport simulation including image reconstruction, to obtain easier problems. This is often called "mollification". Mollification allows us to achieve better approximations of the desired image within a given time budget. Solving the mollified problem may in general not converge to the ground truth, but it will provide a better approximation given a limited time compared to solving the original problem. We believe this problem statement is highly relevant in application scenarios where the user cannot be expected to simply wait for an arbitrary amount of time until a simulation provides acceptable results. For example during interactive modeling or design, it is much more useful for users to specify a given amount of time they are willing to wait. Our proposed techniques attempt to deliver the best possible approximate solution in this time frame. In this project we will develop a theoretical framework for mollification, and practical algorithms to demonstrate its benefits.