# Learning quadrangulated patches for 3D shape parameterization and completion

arXiv: https://arxiv.org/abs/1709.06868 · HTML: https://mlsanity.com/paper/1709.06868/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Sep 2017.

## Built on by (most cited first, 5 of 5)

- [ACL-SPC: Adaptive Closed-Loop system for Self-Supervised Point Cloud Completion](https://mlsanity.com/paper/2303.01979/) (2023)
- [Rethinking Multimodal Point Cloud Completion: A Completion-by-Correction Perspective](https://mlsanity.com/paper/2511.12170/) (2025)
- [Towards realistic symmetry-based completion of previously unseen point clouds](https://mlsanity.com/paper/2201.01858/) (2022)
- [TSCom-Net: Coarse-to-Fine 3D Textured Shape Completion Network](https://mlsanity.com/paper/2208.08768/) (2022)
- [PQDT: Pseudo-Query Dual Transformer for Robust Point Cloud Restoration](https://mlsanity.com/paper/2605.25127/) (2026)

## Abstract (arXiv)

We propose a novel 3D shape parameterization by surface patches, that are oriented by 3D mesh quadrangulation of the shape. By encoding 3D surface detail on local patches, we learn a patch dictionary that identifies principal surface features of the shape. Unlike previous methods, we are able to encode surface patches of variable size as determined by the user. We propose novel methods for dictionary learning and patch reconstruction based on the query of a noisy input patch with holes. We evaluate the patch dictionary towards various applications in 3D shape inpainting, denoising and compression. Our method is able to predict missing vertices and inpaint moderately sized holes. We demonstrate a complete pipeline for reconstructing the 3D mesh from the patch encoding. We validate our shape parameterization and reconstruction methods on both synthetic shapes and real world scans. We show that our patch dictionary performs successful shape completion of complicated surface textures.