平面分割和平面拟合的区别 [英] difference between plane segmentation and plane fitting

问题描述

我最近一直在做一个项目，我必须在 3D 网格中检测墙壁、地板和天花板.在做了一些研究之后，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，因为它们似乎都会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一种基于纯最小二乘法的拟合技术，其中从点集到平面方程的距离被最小化.可以通过多种方式来制定这种优化，但最实用的一种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.

平面分割可以更多地被认为是拟合问题的一个实例，其中数据中存在大量异常值.事实上，要分割的平面可能只是点集的一小部分.此外，可能存在不同方向的多个平面.最后，分割问题可能不一定要搜索平面方程，而是要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.尽管如此，许多旨在做到这一点的算法都隐含地使用了具有一些几何或代数异常值处理的拟合技术，例如 RANSAC、霍夫变换、鲁棒规范等.

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也很重要.找出哪些点位于特定平面上是一个不同的问题，有时比仅仅取出一堆离平面足够近的点更复杂.

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.

对于识别墙壁、天花板等，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.

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