Conventional rendering techniques are primarily designed and optimized for single-frame rendering. In practical applications, such as scene editing and animation rendering, users frequently encounter scenes where only a small portion is modified between consecutive frames. In this paper, we develop a novel approach to incremental re-rendering of scenes with dynamic objects, where only a small part of a scene moves from one frame to the next. We formulate the difference (or residual) in the image between two frames as a (correlated) light-transport integral which we call the residual path integral. Efficient numerical solution of this integral then involves (1)~devising importance sampling strategies to focus on paths with non-zero residual-transport contributions and (2)~choosing appropriate mappings between the native path spaces of the two frames. We introduce a set of path importance sampling strategies that trace from the moving object(s) which are the sources of residual energy. We explore path mapping strategies that generalize those from gradient-domain path tracing to our importance sampling techniques specially for dynamic scenes. Additionally, our formulation can be applied to material editing as a simpler special case. We demonstrate speed-ups over previous correlated sampling of path differences and over rendering the new frame independently. Our formulation brings new insights into the re-rendering problem and paves the way for devising new types of sampling techniques and path mappings with different trade-offs.

翻译：传统渲染技术主要针对单帧渲染进行设计和优化。在实际应用中，如场景编辑和动画渲染，用户常遇到连续帧间仅小部分场景被修改的情况。本文提出了一种针对动态场景增量式重渲染的新方法，其中场景中仅小部分物体在帧间发生移动。我们将两帧图像间的差异（即残差）表述为一个（相关的）光传输积分，称之为残差路径积分。该积分的高效数值求解涉及：（1）设计重要性采样策略以聚焦于具有非零残差传输贡献的路径；（2）选择两帧原生路径空间之间的适当映射关系。我们引入了一套从作为残差能量源的移动物体出发进行追踪的路径重要性采样策略。我们探索了将梯度域路径追踪中的路径映射策略推广至动态场景专用重要性采样技术的方法。此外，我们的公式可将材质编辑作为更简单的特例进行处理。实验证明，相较于先前的路径差异相关采样方法及独立渲染新帧的方式，本方法实现了加速效果。该理论框架为重渲染问题提供了新的见解，并为设计具有不同权衡特性的新型采样技术与路径映射方法奠定了基础。