# Fast Regularity-Constrained Plane Reconstruction

## TL;DR

This paper presents a fast, robust, and simple method for reconstructing planes in man-made environments by leveraging geometric relationships and energy minimization, outperforming existing methods in speed and noise resilience.

## Contribution

Introduces a novel energy minimization approach for plane reconstruction that uses minimal prior knowledge to enforce geometric regularities.

## Key findings

- Successfully reconstructs planes with high noise and outliers
- Outperforms state-of-the-art methods in speed and robustness
- Efficient and easy-to-implement algorithm

## Abstract

Man-made environments typically comprise planar structures that exhibit numerous geometric relationships, such as parallelism, coplanarity, and orthogonality. Making full use of these relationships can considerably improve the robustness of algorithmic plane reconstruction of complex scenes. This research leverages a constraint model requiring minimal prior knowledge to implicitly establish relationships among planes. We introduce a method based on energy minimization to reconstruct the planes consistent with our constraint model. The proposed algorithm is efficient, easily to understand, and simple to implement. The experimental results show that our algorithm successfully reconstructs planes under high percentages of noise and outliers. This is superior to other state-of-the-art regularity-constrained plane reconstruction methods in terms of speed and robustness.