用高斯过程混合模型实现轻量级3D形状表示，高效建模复杂几何。
Shape Representation using Gaussian Process mixture models
- 基于高斯过程混合模型，从稀疏点云学习连续方向距离场。
- 在ShapeNetCore和IndustryShapes数据集上实现高精度几何表示。
- 无需神经网络，适合需要紧凑、连续表示的场景。
传统显式3D表示如点云和网格需大量存储以捕捉精细几何细节，并需复杂索引系统进行表面查询，而功能表示则提供了高效、紧凑且连续的替代方案。本文提出一种新型、对象特定的功能形状表示方法，利用高斯过程（GP）混合模型建模表面几何。与依赖计算密集型神经架构的方法不同，本方法轻量且有效，通过高斯过程从稀疏采样点云中学习连续方向距离场。通过在关键参考点处锚定局部GP先验，结合任意结构分解方法（如骨架化、基于距离的聚类）灵活提取参考点，从而捕捉复杂拓扑结构。在ShapeNetCore和IndustryShapes数据集上的广泛评估表明，该方法能高效且准确地表示复杂几何形态。
原文摘要 · Abstract (English)
Traditional explicit 3D representations, such as point clouds and meshes, demand significant storage to capture fine geometric details and require complex indexing systems for surface lookups, making functional representations an efficient, compact, and continuous alternative. In this work, we propose a novel, object-specific functional shape representation that models surface geometry with Gaussian Process (GP) mixture models. Rather than relying on computationally heavy neural architectures, our method is lightweight, leveraging GPs to learn continuous directional distance fields from sparsely sampled point clouds. We capture complex topologies by anchoring local GP priors at strategic reference points, which can be flexibly extracted using any structural decomposition method (e.g. skeletonization, distance-based clustering). Extensive evaluations on the ShapeNetCore and IndustryShapes datasets demonstrate that our method can efficiently and accurately represent complex geometries.
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