Fitting Geometric Shapes to Fuzzy Point Cloud Data

This article describes procedures and thoughts regarding the reconstruction of geometry-given data and its uncertainty. The data are considered as a continuous fuzzy point cloud, instead of a discrete point cloud. Shape fitting is commonly performed by minimizing the discrete Euclidean distance; however, we propose the novel approach of using the expected Mahalanobis distance. The primary benefit is that it takes both the different magnitude and orientation of uncertainty for each data point into account. We illustrate the approach with laser scanning data of a cylinder and compare its performance with that of the conventional least squares method with and without random sample consensus (RANSAC). Our proposed method fits the geometry more accurately, albeit generally with greater uncertainty, and shows promise for geometry reconstruction with laser-scanned data.