Photon surfaces for robust, unbiased volumetric density estimation
Photon surfaces for robust, unbiased volumetric density estimation
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DOI：
10.1145/3306346.3323041
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发表时间：
2019-07
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影响因子：
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通讯作者：
Xi Deng;Shaojie Jiao;Benedikt Bitterli;Wojciech Jarosz
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作者：
Xi Deng;Shaojie Jiao;Benedikt Bitterli;Wojciech Jarosz
我们将光子平面推广到光子表面：一系列新的无偏体积密度估计器，我们使用多重重要性采样将其组合起来。为了导出我们的新估计器，我们从扩展路径积分开始，它复制相机末端的顶点和光子子路径，并使用模糊内核将它们耦合起来。然而，为了使我们的公式不偏不倚，我们使用 delta 内核来耦合这两个端点。不幸的是，使用蒙特卡罗对所得奇异积分进行采样是不可能的，因为通过独立采样两个子路径来生成贡献光路的概率为零。我们的主要见解是，我们可以通过分析集成任何三个维度并使用蒙特卡罗仅集成剩余维度来消除 delta 核并使蒙特卡罗估计变得实用。我们通过实例化一组估计器来证明这种方法的实用性，这些估计器对沿相机光线的距离和沿光子子路径的两个任意采样维度（例如距离、方向、表面积）进行分析积分。这将光子平面概括为弯曲的“光子表面”，包括新的“光子锥体”、“光子圆柱体”、“光子球体”和多个新的“光子平面”估计器。这些估计器使我们能够处理光子平面不支持的光路，包括单次散射和表面到介质传输。更重要的是，由于我们的估计器由于分析整合路径积分的不同维度而具有互补的优势，因此我们可以使用多重重要性采样将它们组合起来。这种组合减轻了个体估计量中存在的奇异性，大大减少了方差，同时保持完全无偏。我们在许多包含具有高度各向异性相函数的均匀介质的场景上展示了我们改进的估计器，与现有技术相比，加速了多重散射和单次散射。
We generalize photon planes to photon surfaces: a new family of unbiased volumetric density estimators which we combine using multiple importance sampling. To derive our new estimators, we start with the extended path integral which duplicates the vertex at the end of the camera and photon subpaths and couples them using a blurring kernel. To make our formulation unbiased, however, we use a delta kernel to couple these two end points. Unfortunately, sampling the resulting singular integral using Monte Carlo is impossible since the probability of generating a contributing light path by independently sampling the two subpaths is zero. Our key insight is that we can eliminate the delta kernel and make Monte Carlo estimation practical by integrating any three dimensions analytically, and integrating only the remaining dimensions using Monte Carlo. We demonstrate the practicality of this approach by instantiating a collection of estimators which analytically integrate the distance along the camera ray and two arbitrary sampling dimensions along the photon subpath (e.g., distance, direction, surface area). This generalizes photon planes to curved "photon surfaces", including new "photon cone", "photon cylinder", "photon sphere", and multiple new "photon plane" estimators. These estimators allow us to handle light paths not supported by photon planes, including single scattering, and surface-to-media transport. More importantly, since our estimators have complementary strengths due to analytically integrating different dimensions of the path integral, we can combine them using multiple importance sampling. This combination mitigates singularities present in individual estimators, substantially reducing variance while remaining fully unbiased. We demonstrate our improved estimators on a number of scenes containing homogeneous media with highly anisotropic phase functions, accelerating both multiple scattering and single scattering compared to prior techniques.