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 fitting 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 fits planes under high percentages of noise and outliers. This is superior to other state-of-the-art regularity-constrained plane fitting methods in terms of speed and robustness.

人造环境通常包含呈现出许多几何关系（例如平行度，共面性和正交性）的平面结构。充分利用这些关系可以大大提高复杂场景的算法平面拟合的鲁棒性。这项研究利用了一个约束模型，该模型需要最少的先验知识来隐式地建立平面之间的关系。我们引入了一种基于能量最小化的方法来重构与我们的约束模型一致的平面。所提出的算法高效，易于理解并且易于实现。实验结果表明，我们的算法成功地拟合了高百分比噪声和离群值的平面。就速度和鲁棒性而言，这优于其他最新的受规律性约束的平面拟合方法。