New Approach for Measured Surface Localization Based on Umbilical Points

Measured surface localization （MSL） is one of the key essentials for the assessment of form error in pre- cision manufacturing. Currently, the researches on MSL have focused on the corresponding relation search between two surfaces, the performance improvement of localization algorithms and the uncertainty analysis of localization. However, low efficiency, limitation of localization algo- rithms and mismatch of multiple similarities of feature points with no prior are the common disadvantages for MSL. In order to match feature points quickly and fulfill MSL efficiently, this paper presents a new localization approach for measured surfaces by extracting the generic umbilics and estimating their single complex variables, describing the match methods of ambiguous relation at umbilics, presenting the initial localization process of one pair matched points, refining MSL on the basis of obtained closet points for some measured points by the improvement directed projection method. In addition, the proposed algorithm is simulated in two different types of surfaces,two different localization types and multiple similar sur- faces, also tested with the part of B-spline surface machined and bottle mould with no knowledge, finally the initial and accurate rigid body transformation matrix, localization errors between two surfaces and execution time are got. The experimental results show that the pro- posed method is feasible, more accurate in localization and high in efficiency. The proposed research can not only improve the accuracy and performance of form error assessment, but also provide an effective guideline for the integration of different types of measured surfaces.