In the wake of many new ML-inspired approaches for reconstructing and representing high-quality 3D content, recent hybrid and explicitly learned representations exhibit promising performance and quality characteristics. However, their scaling to higher dimensions is challenging, e.g. when accounting for dynamic content with respect to additional parameters such as material properties, illumination, or time. In this paper, we tackle these challenges for an explicit representations based on Gaussian mixture models. With our solutions, we arrive at efficient fitting of compact N-dimensional Gaussian mixtures and enable efficient evaluation at render time: For fast fitting and evaluation, we introduce a high-dimensional culling scheme that efficiently bounds N-D Gaussians, inspired by Locality Sensitive Hashing. For adaptive refinement yet compact representation, we introduce a loss-adaptive density control scheme that incrementally guides the use of additional capacity towards missing details. With these tools we can for the first time represent complex appearance that depends on many input dimensions beyond position or viewing angle within a compact, explicit representation optimized in minutes and rendered in milliseconds.

翻译：随着许多受机器学习启发的新方法被用于重建和表示高质量三维内容，近期的混合与显式学习表示展现出优异的性能和品质特征。然而，这些方法向更高维度的扩展面临挑战，例如在考虑动态内容时需兼顾材质属性、光照或时间等附加参数。本文针对基于高斯混合模型的显式表示解决了这些挑战。通过我们的解决方案，我们实现了紧凑N维高斯混合模型的高效拟合，并能在渲染时进行高效评估：为实现快速拟合与评估，我们受局部敏感哈希启发，提出了一种高效界定N维高斯函数的高维剔除方案；为实现自适应细化与紧凑表示，我们提出了一种损失自适应密度控制方案，该方案能增量引导额外容量向缺失细节分配。借助这些工具，我们首次能够在紧凑的显式表示中呈现超越位置或视角的、依赖多输入维度的复杂外观表现，该表示可在数分钟内完成优化并在毫秒级时间内完成渲染。