Measurement of curved surface by stereo vision and error analysis

Using the advantage of reconstructing the surface of a body, the stereo vision is used to study the measurement of a curved surface, and the error of the measurement is analyzed. Under the world coordinate X-Y-Z erected by the stereo vision, the surface of the cylinder is measured, and the position coordinate of each point on the cylindrical surface is determined. By the use of the nonlinear optimization technique, the equation of cylindrical surface is solved to obtain a set of parameters: the direction cosine of the centerline of the cylinder, the point of intersection of the centerline of the cylinder with the XZ-plane, and the radius of the cylinder. The computed radius of the cylinder is compared to the measured value to evaluate the measurement error. Through coordinate transformation, the measured position coordinate of each point on the cylindrical surface, which is in the rectangular coordinate, is transformed into the cylindrical coordinate. The radial coordinate of each point is compared to the computed radius and the mean error and standard deviation are estimated. Results indicate that the stereo vision may accurately measure the curved surface in various curvatures, and a cylindrical coordinate system may be erected for the measured cylinder. Hence, the analysis method proposed in the paper may be further applied to study the deformation problems such as piping under pressure, and fracture problems such as piping with cracks. (C) 1999 Elsevier Science Ltd. All rights reserved.