Robust statistical approaches for circle fitting in laser scanning three-dimensional point cloud data

This paper explores the problem of circle fitting for incomplete (partial arc) laser scanning point cloud data in the presence of outliers. In mobile laser scanning, data are commonly incomplete because of the orientation of the scanning unit to the surveying objects and the limited street-based positions. Also, multiple structures in the built environment often produce clustered outliers. To address these problems, this paper combines robust Principal Component Analysis (PCA) and robust regression with an efficient algebraic circle fitting method to develop two algorithms for circle fitting. Experimental efforts show that the proposed algorithms are statistically robust and can tolerate a high-percentage (exceeding 44%) of clustered outliers with insignificant error levels, while still achieving better shape recognition compared to existing competitive methods. For example, for a simulation of 1000 quarter circle datasets including 20% clustered outliers, RANSAC estimated the circle radius with a Mean Squared Error (MSE) of 172.10, whereas the proposed algorithms fit circles with an MSE of less than 0.42. The algorithms have potential in many areas including building information modeling, particle tracking, product quality control, arboreal assessment, and road asset monitoring.