用极少参数精准表示2D/3D形状，支持精确建模与快速生成。
Patchwork: A compact representation for 3D polygonal shapes
- 基于数学框架的紧凑形状表示，可任意逼近任意维度形状。
- 参数量远低于现有方法，优化后冗余元素被逐步剔除。
- 适合几何学习、重建与3D生成任务，支持内外点判断。
我们提出Patchwork，一种新型通用形状表示方法，能以极少量参数建模二维和三维几何体。该方法建立在严谨的数学框架之上，提供可证明的复杂度边界，并可在任意维度中以任意精度逼近任意形状。我们设计了一种高效的基于梯度的优化方案，用于拟合2D和3D数据，并引入一种新颖的正则化损失函数，可逐步剪枝冗余成分，收敛后实现高度紧凑。本方法具备快速拟合性能，所需参数数量仅为现有方法的极小部分，且原生支持内外点分类，适用于几何学习与重建任务，未来在3D生成方面具有潜力。代码已开源：https://github.com/Ankbzpx/patchwork-experiment。
原文摘要 · Abstract (English)
We introduce Patchwork, a new general-purpose shape representation capable of modeling 2D and 3D geometry with a small number of parameters. Patchwork is grounded in a rigorous mathematical framework, providing provable complexity bounds and the ability to approximate arbitrary shapes with arbitrary precision in any dimension. We propose an efficient gradient-based optimization scheme to fit Patchwork representations to 2D and 3D data, along with a novel regularization loss that progressively prunes redundant elements, yielding high compactness after convergence. Our approach offers fast fitting performance, a fraction of the required parameters compared to existing alternatives, and native support for inside-outside classification, making it a versatile and compact representation for geometric learning and reconstruction tasks, with future potential for 3D generation. Our implementation is available at: https://github.com/Ankbzpx/patchwork-experiment.
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