Verhoeven Vincent B, Raumonen Pasi, Åkerblom Markku
Faculty of Information Technology and Communication Sciences, Mathematics Research Centre, Tampere University, Korkeakoulunkatu 1, 33720 Tampere, Finland.
J Imaging. 2025 Jan 3;11(1):7. doi: 10.3390/jimaging11010007.
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.
本文描述了关于给定几何数据及其不确定性重建的过程和思路。数据被视为连续模糊点云，而非离散点云。形状拟合通常通过最小化离散欧几里得距离来进行；然而，我们提出了使用期望马氏距离的新方法。主要优点是它考虑了每个数据点不确定性的不同大小和方向。我们用圆柱体的激光扫描数据说明了该方法，并将其性能与带和不带随机抽样一致性（RANSAC）的传统最小二乘法进行了比较。我们提出的方法能更精确地拟合几何形状，尽管通常不确定性更大，并且在利用激光扫描数据进行几何重建方面显示出前景。
