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2-D image coordinate measurement precision of theintersection point of cross-cutting lines, and depthmeasurementprecision of binocular stereo vision.To verify the final measurement precision of the total mea-suring system, the verification experiment is done on theOPTON UMM500 CMM, and the experimental procedures aredescribed in the list that follows.1) The linear equation of the driving locus of the precisionX–Y stage can be calibrated by the 3-D coordinates ofthe angular point of the precision measuring block that isput on the precision X–Y stage.2) The measured workpiece is fixed on the precision X–Ystage, and the same intersection point of cross-cuttinglines will be used. The workpiece is moved along the lo-cus of an oblique line. According to the calibrated drivinglinear equation and the moving distance of each step ofthe workpiece, the moving distances LXi and LZi of eachstep of the workpiece along the X and Z directions inthe CMM coordinate system can be calculated. Note thatthere is no movement in the Y direction of the workpiece.3) When the workpiece is moved each step in the afore-mentioned procedures, 3-D coordinates of the intersec-tion point of cross-cutting lines on the correspondingmeasured position in the CMM coordinate system canbe calculated by the proposed monocular and binocularstereo vision methods.The moving distances L Xi and L Zi in the X and Z di-rections in the CMM coordinate system can be calculatedby subtracting the corresponding X and Z coordinatesof the intersection point of cross-cutting lines of back-measured positions from fore-measured positions.4) The final measurement errors can be obtained by subtract-ing LXi with L Xi and LZi with L Zi.The experimental results of the final experiment are givenin Table III. The moving distance of each nominal step of theworkpiece in the X direction is 2 mm, and the total movingrange is 10 mm. The moving distance of each nominal step ofthe workpiece in the Z direction is 6 mm, and the total movingrange is 30 mm. There is no movement in the Y direction.The experimental results indicate that the maximum absoluteerrors are 0.0193 and 0.0721 mm in the X and Z directions,respectively, and the corresponding maximum relative errorsare 0.192% and 0.239%, respectively. The experimental resultsindicate the correctness and reliability of the proposed visionmeasuring system and show that they can be used in thehigh-precision fast noncontact 3-D coordinate measurementof cross-cutting feature points on the surface of a large-scaleworkpiece.
VII. CONCLUSIONAn accurate, simple, and novel vision measuring system hasbeen set up for the noncontact 3-D coordinate measurementof cross-cutting feature points on the surface of a large-scaleworkpiece in this paper. Based on the principle and compositionof the proposed vision measuring system, the following algo-rithms are implemented according to the proposed measure-ment procedures: 1) a monocular vision algorithm combiningthe position-from-defocus and position-from-focus methods forcamera locating; 2) the calibration algorithm of the CCD cam-era; 3) the image processing algorithm of cross-cutting featurepoints and the calculation of their 2-D image coordinates; and4) the binocular stereo vision algorithm for depth acquisitionbased on the large-scale CMM.The experiment was performed, and all the proposed al-gorithms were evaluated and verified. 3-D coordinates of thecross-cutting feature point were measured, and the experimen-tal results indicate that the maximum absolute errors are 0.0193and 0.0721 mm in the X and Z directions, respectively, andthe corresponding maximum relative errors are 0.192% and0.239%, respectively. With regard to measurement accuracy,it indicates the correctness and reliability of the proposed measuring system, which will be a reliable and flexible tech-nique for the high-precision fast noncontact 3-D coordinatemeasurement of cross-cutting feature points on the surface ofa large-scale workpiece.Further efforts will be investigated into the noncontact 3-Dcoordinate measurement of different kinds of feature points onthe surface of a large-scale workpiece, including the active pro-jecting light pattern. We believe that the proposed vision-basedmeasuring algorithms and system will lay a solid foundation forthe successful extension of the proposed technique.ACKNOWLEDGMENTS. Zhu would like to thank Professor Emeritus X. Qiangfor his supervision, the Department of Automatic Testing andControl, School of Electrical Engineering and Automation,Harbin Institute of Technology, Harbin, China, for supplyingthe experimental equipment and instruments, and the facultiesand Ph.D. students who previously provided technical supportand help. The authors would also like to thank the anonymousreviewers for their insightful comments, which help improvedthis paper.REFERENCES[1] G. Sansoni, M. Carocci, and R. Rodella,