标题： 结构化字段：统一结构化几何与辐射场 显示英文标题

标题： StructuredField: Unifying Structured Geometry and Radiance Field

摘要： 基于点的可微渲染技术最近在高保真重建和快速渲染方面取得了显著成功。 然而，由于基于点的表示具有非结构化的特性，它们难以应用于为结构化网格设计的现代图形流水线，以及各种与结构化网格表示配合良好的模拟和编辑算法。 为此，我们提出了一种新的表示方法StructuredField，该方法既能实现重建物体的结构化几何表示，又能实现物体的高保真渲染重建。 我们采用结构化四面体网格来表示重建的物体。 我们将四面体网格的几何参数重新参数化为3D高斯的几何形状参数，从而实现了四面体网格的可微高保真渲染。 我们提出了一种新颖的无反演同胚，以约束四面体网格的优化，这严格保证了在优化过程和最终结果中四面体网格始终保持无反演和无自相交。 基于我们提出的StructuredField，我们实现了高质量的结构化网格和高保真重建。 我们还展示了该表示方法在物理模拟和变形等多种应用中的适用性。 显示英文摘要

摘要： Recent point-based differentiable rendering techniques have achieved significant success in high-fidelity reconstruction and fast rendering. However, due to the unstructured nature of point-based representations, they are difficult to apply to modern graphics pipelines designed for structured meshes, as well as to a variety of simulation and editing algorithms that work well with structured mesh representations. To this end, we propose StructuredField, a novel representation that achieves both a structured geometric representation of the reconstructed object and a high-fidelity rendering reconstruction of the object. We employ structured tetrahedral meshes to represent the reconstructed object. We reparameterize the geometric parameters of the tetrahedral mesh into the geometric shape parameters of a 3D Gaussians, thereby achieving differentiable high-fidelity rendering of the tetrahedral mesh. We propose a novel inversion-free homeomorphism to constrain the optimization of the tetrahedral mesh, which strictly guarantees that the tetrahedral mesh is remains both inversion-free and self-intersection-free during the optimization process and the final result. Based on our proposed StructuredField, we achieve high-quality structured meshes and high-fidelity reconstruction. We also demonstrate the applicability of our representation to various applications such as physical simulation and deformation.