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A robust measurement method for measuring the vertex position of a small polyhedron using 3D image processing is proposed. The shape from focus method is applied for obtaining 3D positions of surfaces of the polyhedron. The in-focus function is usually averaged for reducing noise, but the resultant function lacks sharp edge information of the target. The position of the vertex is indirectly calculated from 3D data using the geometrical model of the polyhedron. In this study, relationships between measurement noise and (a) the appropriate number of data values required for averaging of focal measurement and (b) the area of data fitted by the Gaussian function are 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, the vertex position measurement is made robust against measurement errors. The effectiveness of the proposed method is confirmed by numerical simulations and experiments.

Robust Method for Position Measurement of Vertex of Polyhedron Using Shape from Focus