平面分割与平面拟合之间的差异

本文介绍了平面分割与平面拟合之间的差异的处理方法，对大家解决问题具有一定的参考价值，需要的朋友们下面随着小编来一起学习吧！ 问题描述

我最近一直在进行一个项目，目的是检测3D网格中的墙壁，地板和天花板。经过研究，我已经能够使用RANSAC算法检测地板和墙壁的某些部分。我只是想知道是否有人能够解释平面拟合和平面分割之间的区别，因为它们似乎都导致包含地板的点云？

I've recently been working on a project in wich I'd have to detect walls, floor and ceiling in a 3D mesh. After doing some research I've been able to detect the floor and some part of the walls using RANSAC algorithms. I was just wondering if anybody could be able to explain the difference between plane-fitting and plane segmentation as they both seem to result into a point cloud containing the floor?

推荐答案

平面拟合通常被理解为基于最小二乘法的纯拟合技术，其中从点集到平面方程的距离最小。可以以多种方式制定这种优化方法，但最实用的方法是对协方差矩阵进行简单的SVD分析。

Plane fitting is generally understood as a pure least-squares based fitting technique where distance from a point set to the equation of a plane is minimized. One could formulate such optimization in many ways, but the most practical one is a simple SVD analysis of the covariance matrix.

平面细分可以看作是细分的一个实例数据中存在许多异常值的拟合问题。实际上，要分割的平面可能只是点集的一小部分。此外，可能存在多个方向不同的平面。最后，分割问题可能不一定要搜索平面方程，而是要关注找出共同位于一个平面上的点或位于多个平面上的多组点的问题。但是，许多旨在做到这一点的算法都隐含地使用具有某种几何或代数异常值处理的拟合技术，例如RANSAC，霍夫变换，鲁棒范数等。

Plane segmentation can be thought more as an instance of the fitting problem where a lot of outliers exist in the data. In fact, the plane to segment could be a tiny fraction of the point set. Moreover, there could be multiple planes in different orientations. Finally, the segmentation problem might not necessarily search for the plane equations but rather concerns finding out the points, which are jointly lying on a plane or multiple sets of points lying on multiple planes. Though, many algorithms which aim to do that implicitly use a fitting technique with some geometric or algebraic outlier handling such as RANSAC, Hough Transform, robust norms etc.

了解平面检测只能达到一定的精度非常重要。找出在特定平面上的哪些点是一个不同的问题，有时要比仅仅获取一堆足够接近该平面的点更为复杂。

It is also important to understand that plane detection can be done only up to a certain accuracy. Figuring out which points lie on a particular plane is a different problem and sometimes is more complex than just taking out a bunch of points which are close enough to the plane.

确定墙壁，天花板等的情况。安装和分割技术都是必要的。

For the case of identifying walls, ceilings and etc. both fitting and segmentation techniques will be necessary.