Systematically Differentiating Parametric Discontinuities
Systematically Differentiating Parametric Discontinuities
复制标题
系统地区分参数不连续性
DOI：
10.1145/3450626.3459775
复制
发表时间：
2021
影响因子：
6.2
通讯作者：
Ragan-Kelley, Jonathan
中科院分区：
文献类型：
--
作者：
Bangaru, Sai Praveen;Michel, Jesse;Mu, Kevin;Bernstein, Gilbert;Li, Tzu-Mao;Ragan-Kelley, Jonathan
计算机图形学、反问题和机器学习方面的新兴研究要求我们区分和优化参数间断。这些不连续出现在对象边界、遮挡、接触和随时间变化的突然变化中。在许多领域，如绘制和物理模拟，我们区分表示为不连续函数上的积分的模型参数。忽略微分过程中的不连续性往往会对优化过程产生重大影响。通过开发一种新的可微程序设计语言，提出了一种系统的方法来区分具有间断被积分项的积分。我们引入积分作为一种语言基元，并解释了狄拉克增量的贡献与被积函数中参数不连续的区分。我们形式化地定义了语言语义，并证明了它在微分下的正确性和封闭性，允许生成梯度和高阶导数。我们还构建了一个实现这些语义的系统Teg。我们的方法广泛适用于各种任务，包括图像样式化、匹配着色器参数、轨迹优化和优化物理设计。
Emerging research in computer graphics, inverse problems, and machine learning requires us to differentiate and optimize parametric discontinuities. These discontinuities appear in object boundaries, occlusion, contact, and sudden change over time. In many domains, such as rendering and physics simulation, we differentiate the parameters of models that are expressed as integrals over discontinuous functions. Ignoring the discontinuities during differentiation often has a significant impact on the optimization process. Previous approaches either apply specialized hand-derived solutions, smooth out the discontinuities, or rely on incorrect automatic differentiation.We propose a systematic approach to differentiating integrals with discontinuous integrands, by developing a new differentiable programming language. We introduce integration as a language primitive and account for the Dirac delta contribution from differentiating parametric discontinuities in the integrand. We formally define the language semantics and prove the correctness and closure under the differentiation, allowing the generation of gradients and higher-order derivatives. We also build a system, Teg, implementing these semantics. Our approach is widely applicable to a variety of tasks, including image stylization, fitting shader parameters, trajectory optimization, and optimizing physical designs.