Volumetric rendering has become central to modern novel view synthesis methods, which use differentiable rendering to optimize 3D scene representations directly from observed views. While many recent works build on NeRF or 3D Gaussians, we explore an alternative volumetric scene representation. More specifically, we introduce two new scene representations based on linear primitives - octahedra and tetrahedra - both of which define homogeneous volumes bounded by triangular faces. To optimize these primitives, we present a differentiable rasterizer that runs efficiently on GPUs, allowing end-to-end gradient-based optimization while maintaining real-time rendering capabilities. Through experiments on real-world datasets, we demonstrate comparable performance to state-of-the-art volumetric methods while requiring fewer primitives to achieve similar reconstruction fidelity. Our findings deepen the understanding of 3D representations by providing insights into the fidelity and performance characteristics of transparent polyhedra and suggest that adopting novel primitives can expand the available design space.

翻译：体渲染已成为现代新视角合成方法的核心技术，该方法通过可微分渲染直接从观测视角优化三维场景表示。尽管近期许多研究基于NeRF或三维高斯模型，我们探索了一种替代性的体场景表示方法。具体而言，我们引入了两种基于线性基元的新场景表示——八面体与四面体，这两种基元均定义了由三角面片围成的均匀体积区域。为优化这些基元，我们提出了一种在GPU上高效运行的可微分光栅化器，在保持实时渲染能力的同时实现端到端的基于梯度的优化。通过在真实数据集上的实验，我们证明了该方法在达到相近重建保真度时所需基元数量更少的情况下，仍能取得与最先进体渲染方法相当的性能。我们的研究通过揭示透明多面体的保真度与性能特征，深化了对三维表示的理解，并表明采用新型基元能够拓展可用的设计空间。