Error reduction in three-dimensional metrology combining optical and touch probe data

Abstract

Analysis of footwear under the Harmonized Tariff Schedule of the United States (HTSUS) is partly based on identifying the boundary (parting line) between the external surface area upper (ESAU) and the sample's sole. Often, that boundary is obscured. We establish the parting line as the curved intersection between the sample outer surface and its insole surface. The outer surface is determined by discrete point cloud coordinates obtained using a laser scanner. The insole surface is defined by point cloud data, obtained using a touch probe device-a coordinate measuring machine (CMM). Because these point cloud data sets do not overlap spatially, a polynomial surface is fitted to the insole data and extended to intersect a mesh fitted to the outer surface point cloud. This line of intersection defines the ESAU boundary, permitting further fractional area calculations to proceed. The defined parting line location is sensitive to the polynomial used to fit experimental data. Extrapolation to the intersection with the ESAU can heighten this sensitivity. We discuss a methodology for transforming these data into a common reference frame. Three scenarios are considered: measurement error in point cloud coordinates, from fitting a polynomial surface to a point cloud then extrapolating beyond the data set, and error from reference frame transformation. These error sources can influence calculated surface areas. We describe experiments to assess error magnitude, the sensitivity of calculated results on these errors, and minimizing error impact on calculated quantities. Ultimately, we must ensure that statistical error from these procedures is minimized and within acceptance criteria.