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Three-dimensional (3-D) point cloud data are increasingly being used to describe a wide range of physical objects in detail, corresponding to customized and flexible shape designs. The advent of a new generation of optical sensors has simplified and reduced the costs of acquiring 3-D data in near-real-time. However, the variation of the acquired point clouds, and methods to describe them, create bottlenecks in manufacturing practices such as Reverse Engineering (RE) and metrology in additive manufacturing. We address this issue by developing an automated variance modeling algorithm that utilizes a physical object's local geometric descriptors and Bayesian Extreme Learning Machines (BELMs). Our proposed ensemble and residual BELM-variants are trained by a scanning history that is composed of multiple scans of other, distinct objects. The specific scanning history is selected by a new empirical Kullback–Leibler divergence we developed to identify objects that are geometrically similar to an object of interest. A case study of our algorithm on additively manufactured products demonstrates its capability to model the variance of point cloud data for arbitrary freeform shapes based on a scanning history involving simpler, and distinct, shapes. Our algorithm has utility for measuring the process capability of 3-D scanning for RE processes. [ABSTRACT FROM AUTHOR]

Reverse Engineering (RE) has been widely used to extract geometric design information from a physical product for reproduction or redesign purposes. A scan of an object is often implemented to (re-)construct the computer-aided design model. However, this model is most likely an inaccurate representation of the original design, due to the existing uncertainties in each part and the scanning process. This randomness can result in shrinking the original tolerance region or even yielding asymmetric tolerance regions, which can call for unnecessarily high precision reproduction. In this article, we first propose an algorithm to generate the mean configuration based on the data clouds collected from several scans and multiple parts (if applicable). A Bayesian model with prior knowledge of production processes and scanners is specified to model the statistical properties of the mean configuration. Its marginal posterior outperforms single-scan models with lower variances, concentrating around the physical object or initial design. Furthermore, we propose a bi-objective optimization model to address RE process planning questions regarding the required number of scans and parts to achieve target accuracy requirements. Simulations and industrial case studies, including both unique freeform objects and mechanical parts, are conducted to illustrate and evaluate the performances of proposed methods. [ABSTRACT FROM AUTHOR]