Patchwork: A compact representation for 3D polygonal shapes
This work provides a new general-purpose shape representation for geometric learning and reconstruction, offering theoretical guarantees and practical efficiency.
Patchwork introduces a compact representation for 2D and 3D shapes with provable complexity bounds, achieving high compactness and fast fitting with fewer parameters than existing methods.
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.