In this work, we propose a new spatio-directional neural encoding that is compact and efficient, and supports all-frequency signals in both space and direction. Current learnable encodings focus on Cartesian orthonormal spaces, which have been shown to be useful for representing high-frequency signals in the spatial domain. However, directly applying these encodings in the directional domain results in distortions, singularities, and discontinuities. As a result, most related works have used more traditional encodings for the directional domain, which lack the expressivity of learnable neural encodings. We address this by proposing a new angular encoding that generalizes the hash-grid approach from proach from Müller et al. [2022] to the directional domain by encoding directions using a hierarchical geodesic grid. Each vertex in the geodesic grid stores a learnable latent parameter, which is used to feed a neural network. Armed with this directional encoding, we propose a five-dimensional encoding for spatio-directional signals. We demonstrate that both encodings significantly outperform other hash-based alternatives. We apply our five-dimensional encoding in the context of neural path guiding, outperforming the state of the art by up to a factor of 2 in terms of variance reduction for the same number of samples.

翻译：本文提出了一种新颖的紧凑高效空间-方向神经编码方法，能够同时支持空间域与方向域的全频信号。当前可学习的编码方法主要针对笛卡尔正交空间，这类方法已被证明在空间域中表征高频信号具有显著优势。然而，若直接将此类编码应用于方向域，则会产生畸变、奇点及不连续性等问题。因此，多数相关研究在方向域仍采用传统编码方案，但这些方案缺乏可学习神经编码的表达能力。为解决这一问题，我们提出了一种新型角度编码方法，该方法通过分层测地网格对方向进行编码，将Müller等人[2022]提出的哈希网格方法推广至方向域。测地网格中的每个顶点存储一个可学习的潜在参数，用于馈入神经网络。基于此方向编码，我们进一步构建了适用于空间-方向信号的五维编码框架。实验证明，两种编码方案均显著优于其他基于哈希的替代方法。我们将五维编码应用于神经路径引导任务，在相同采样数条件下，方差降低效果达到当前最优方法的2倍。