# From Planes to Corners: Multi-Purpose Primitive Detection in Unorganized 3D Point Clouds

arXiv: https://arxiv.org/abs/2001.07360 · HTML: https://mlsanity.com/paper/2001.07360/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Jan 2020.

## Built on by (most cited first, 7 of 7)

- [Point2Cyl: Reverse Engineering 3D Objects from Point Clouds to Extrusion Cylinders](https://mlsanity.com/paper/2112.09329/) (2021)
- [PlanarSplatting: Accurate Planar Surface Reconstruction in 3 Minutes](https://mlsanity.com/paper/2412.03451/) (2024)
- [AlphaTablets: A Generic Plane Representation for 3D Planar Reconstruction from Monocular Videos](https://mlsanity.com/paper/2411.19950/) (2024)
- [QuadricsNet: Learning Concise Representation for Geometric Primitives in Point Clouds](https://mlsanity.com/paper/2309.14211/) (2023)
- [SPPSFormer: High-quality Superpoint-based Transformer for Roof Plane Instance Segmentation from Point Clouds](https://mlsanity.com/paper/2505.24475/) (2025)
- [GSPlane: Concise and Accurate Planar Reconstruction via Structured Representation](https://mlsanity.com/paper/2510.17095/) (2025)
- [PlanaReLoc: Camera Relocalization in 3D Planar Primitives via Region-Based Structure Matching](https://mlsanity.com/paper/2603.20818/) (2026)

## Abstract (arXiv)

We propose a new method for segmentation-free joint estimation of orthogonal planes, their intersection lines, relationship graph and corners lying at the intersection of three orthogonal planes. Such unified scene exploration under orthogonality allows for multitudes of applications such as semantic plane detection or local and global scan alignment, which in turn can aid robot localization or grasping tasks. Our two-stage pipeline involves a rough yet joint estimation of orthogonal planes followed by a subsequent joint refinement of plane parameters respecting their orthogonality relations. We form a graph of these primitives, paving the way to the extraction of further reliable features: lines and corners. Our experiments demonstrate the validity of our approach in numerous scenarios from wall detection to 6D tracking, both on synthetic and real data.