A differential theory of radiative transfer
A differential theory of radiative transfer
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DOI：
10.1145/3355089.3356522
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发表时间：
2019-11
期刊：
影响因子：
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通讯作者：
Cheng Zhang;Lifan Wu;Changxi Zheng;Ioannis Gkioulekas;R. Ramamoorthi;Shuang Zhao
中科院分区：
文献类型：
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作者：
Cheng Zhang;Lifan Wu;Changxi Zheng;Ioannis Gkioulekas;R. Ramamoorthi;Shuang Zhao
基于物理的可微渲染是估计辐射测量相对于场景参数的导数的任务。计算这些导数的能力对于在各种应用中实现基于梯度的优化是必要的：从解决合成分析问题到训练包含前向渲染过程的机器学习管道。不幸的是，由于像素强度和场景参数之间复杂且典型的非线性关系，基于物理的可微分渲染仍然具有挑战性。我们介绍了一种辐射传递的微分理论，它显示了辐射传递方程（RTE）的各个分量如何可以相对于场景的任意可微分变化进行微分。我们的理论包含与标准RTE相同的通用性，允许区分，同时准确处理大范围的光传输现象，如体积吸收和散射，各向异性相函数和非均质性。为了对我们的理论给出的导数进行数值估计，我们引入了一个支持任意表面和体积构型的无偏蒙特卡罗估计。我们的技术象征性地区分路径贡献，并使用附加的边界积分来捕获几何不连续，如可见性变化。我们通过将我们的导数估计与使用有限差分方法生成的估计进行比较来验证我们的方法。此外，我们使用了一些合成的例子，这些例子的灵感来自于现实世界中反向渲染、非视距（NLOS）和生物医学成像和设计的应用，以展示我们技术的实际用途。
Physics-based differentiable rendering is the task of estimating the derivatives of radiometric measures with respect to scene parameters. The ability to compute these derivatives is necessary for enabling gradient-based optimization in a diverse array of applications: from solving analysis-by-synthesis problems to training machine learning pipelines incorporating forward rendering processes. Unfortunately, physics-based differentiable rendering remains challenging, due to the complex and typically nonlinear relation between pixel intensities and scene parameters. We introduce a differential theory of radiative transfer, which shows how individual components of the radiative transfer equation (RTE) can be differentiated with respect to arbitrary differentiable changes of a scene. Our theory encompasses the same generality as the standard RTE, allowing differentiation while accurately handling a large range of light transport phenomena such as volumetric absorption and scattering, anisotropic phase functions, and heterogeneity. To numerically estimate the derivatives given by our theory, we introduce an unbiased Monte Carlo estimator supporting arbitrary surface and volumetric configurations. Our technique differentiates path contributions symbolically and uses additional boundary integrals to capture geometric discontinuities such as visibility changes. We validate our method by comparing our derivative estimations to those generated using the finite-difference method. Furthermore, we use a few synthetic examples inspired by real-world applications in inverse rendering, non-line-of-sight (NLOS) and biomedical imaging, and design, to demonstrate the practical usefulness of our technique.