Error Analysis and Robust Position Measurement for Vertex of a Small Polyhedron

A robust measurement method for vertex position of a small polyhedron using 3D image procession is proposed. Shape from focus method is applied for getting 3D positions on surfaces of the polyhedron. Averaging of in-focus function is usually applied for reducing noises, but it lacks sharp edge information of the target. The position of the vertex is indirectory calculated from the 3D data using geometrical model of the polyhedron. In this paper, relations between measurement noise and appropriate number of data for averaging of focal measurement, and area of data for fitting of the Gaussian function were investigated. Then, error propagation analysis is applied to the equations of the indirect measurement of the vertex position. By using the geometrical characteristics of the polyhedron, measurement of the vertex position became robust against the measurement errors. Effectiveness of the proposed method was confirmed by numerical simulation and experimental result for measurement of a vertex of a small polyhedron.