用球面距离构建3D形状新表示，支持重建与生成
MASH: Masked Anchored SpHerical Distances for 3D Shape Representation and Generation
- 以锚点为源的球面距离函数表征局部表面，结合球谐函数压缩
- 可将点云精准转换为逼近真实表面的MASH表示，适配任意几何拓扑
- 适用于重建、生成、补全等任务，兼具隐式与显式特征优势
我们提出一种新型多视角参数化3D形状表示方法——掩码锚点球面距离（MASH）。受多视角几何启发，并基于感知形状理解在3D学习中的重要性，MASH将3D形状表示为一系列可观测的局部表面块，每个块由从锚点出发的球面距离函数定义。我们利用球谐函数的紧凑性对MASH函数进行编码，并引入带参数基底的广义视锥，通过掩码控制球面函数的空间范围以实现局部性。我们开发了一种可微优化算法，能够将任意点云准确转换为逼近真实表面的MASH表示，支持任意几何与拓扑结构。大量实验表明，MASH在表面重建、形状生成、补全与融合等任务中表现优异，得益于其融合隐式与显式特性的独特表示。
原文摘要 · Abstract (English)
We introduce Masked Anchored SpHerical Distances (MASH), a novel multi-view and parametrized representation of 3D shapes. Inspired by multi-view geometry and motivated by the importance of perceptual shape understanding for learning 3D shapes, MASH represents a 3D shape as a collection of observable local surface patches, each defined by a spherical distance function emanating from an anchor point. We further leverage the compactness of spherical harmonics to encode the MASH functions, combined with a generalized view cone with a parameterized base that masks the spatial extent of the spherical function to attain locality. We develop a differentiable optimization algorithm capable of converting any point cloud into a MASH representation accurately approximating ground-truth surfaces with arbitrary geometry and topology. Extensive experiments demonstrate that MASH is versatile for multiple applications including surface reconstruction, shape generation, completion, and blending, achieving superior performance thanks to its unique representation encompassing both implicit and explicit features.
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