A robust cylindrical fitting to point cloud data

ABSTRACT

Environmental, engineering and industrial modelling of natural features (e.g. trees) and man-made features (e.g. pipelines) requires some form of fitting of geometrical objects such as cylinders, which is commonly undertaken using a least-squares method that—in order to get optimal estimation—assumes normal Gaussian distribution. In the presence of outliers, however, this assumption is violated leading to a Gaussian mixture distribution. This study proposes a robust parameter estimation method, which is an improved and extended form of vector algebraic modelling. The proposed method employs expectation maximisation and maximum likelihood estimation (MLE) to find cylindrical parameters in case of Gaussian mixture distribution. MLE computes the model parameters assuming that the distribution of model errors is a Gaussian mixture corresponding to inlier and outlier points. The parameters of the Gaussian mixture distribution and the membership functions of the inliers and outliers are computed using an expectation maximisation algorithm from the histogram of the model error distribution, and the initial guess values for the model parameters are obtained using total least squares. The method, illustrated by a practical example from a terrestrial laser scanning point cloud, is novel in that it is algebraic (i.e. provides a non-iterative solution to the global maximisation problem of the likelihood function), is practically useful for any type of error distribution model and is capable of separating points of interest and outliers.

KEYWORDS:

• Robust parameter estimation
• cylindrical fitting
• point cloud
• maximum likelihood
• Gaussian mixture
• expectation maximisation
• tree modelling
• terrestrial laser scanning

Acknowledgements

The authors thank the useful comments and suggestions for Daniel Lichtblau and the second reviewer. B. Paláncz is grateful to the visiting grant provided by TIGeR and The Department of Spatial Science, Curtin University (Australia). J. Awange is grateful to the Japan Society of Promotion of Science for supporting his stay at Kyoto University (Japan) and the conducive working atmosphere provided by his host Prof Yoichi Fukuda (Department of Geophysics, Kyoto University, Japan). He further thanks the Brazilian Science Without Borders Program/CAPES Grant No. 88881.068057/2014-01, which supported his stay in UFPE Federal University of Pernambuco, Brazi.

Disclosure statement

No potential conflict of interest was reported by the authors.