基于 SuperFrusta 的三维形状残差基元拟合
Residual Primitive Fitting of 3D Shapes with SuperFrusta
SuperFrustum 用 8 个参数即可表达圆柱、球、锥及其锥化与弯曲变体，且其 SDF 对参数几乎处处可微，可直接作为可微基元嵌入任何基元拟合或形状程序学习流程；ResFit 的「全局分析 + 残差迭代拟合」范式也可迁移到点云/网格的紧凑结构化重建。
原文依据 ResFit is an unsupervised procedure that interleaves global shape analysis with local optimization
摘要译文
由模型翻译 · 术语统一 · 请对照原文核对关键结论我们提出一个将三维形状转换为紧凑且可编辑的解析基元装配体的框架，直接应对重建保真度与简洁性之间长期存在的权衡。我们的方法包含两项关键贡献：一种称为 SuperFrustum 的新型基元，以及一种迭代推理算法——残差基元拟合（Residual Primitive Fitting，ResFit）。SuperFrustum 是一种解析基元，它同时具备以下性质：(1) 表达力强，能够表达圆柱、球、锥及其锥化与弯曲形式等多种常见实体；(2) 可编辑，以 8 个参数进行紧凑参数化；(3) 可优化，其符号距离场对其参数几乎处处可微。ResFit 是一种无监督流程，将全局形状分析与局部优化交替进行，迭代地把基元拟合到形状中尚未被解释的残差上，从而为每个输入形状发现既简洁又准确的分解。在多个三维基准上，我们的方法取得了最优结果，IoU 提升超过 9 个点，同时所用基元数量仅为先前工作的一半左右。所得的装配体弥合了稠密三维数据与人类可控设计之间的差距，生成高保真且可编辑的形状程序。
英文原文摘要 1271 字符
We introduce a framework for converting 3D shapes into compact and editable assemblies of analytic primitives, directly addressing the persistent trade-off between reconstruction fidelity and parsimony. Our approach combines two key contributions: a novel primitive, termed SuperFrustum, and an iterative inference algorithm, Residual Primitive Fitting (ResFit). SuperFrustum is a analytical primitive that is simultaneously (1) expressive, being able to express various common solids such as cylinders, spheres, cones & their tapered and bent forms, (2) editable, being compactly parameterized with 8 parameters, and (3) optimizable, with a sign distance field differentiable w.r.t. its parameters almost everywhere. ResFit is an unsupervised procedure that interleaves global shape analysis with local optimization, iteratively fitting primitives to the unexplained residual of a shape to discover a parsimonious yet accurate decompositions for each input shape. On diverse 3D benchmarks, our method achieves state-of-the-art results, improving IoU by over 9 points while using nearly half as many primitives as prior work. The resulting assemblies bridge the gap between dense 3D data and human-controllable design, producing high-fidelity and editable shape programs.