LAUSR

Feature detection on smooth free-form surfaces is much more difficult than that on shapes with sharp features. In this paper, we extract the curved reflection axes (CRAs) of an arbitrary free-form surface as features if they exist. The extraction result is robust to boundary noises and strongly sensitive to extrinsic properties of the surface such as projected normals and curvatures. Compared with the general reflection symmetry, curved reflection symmetry is defined to be a reflection symmetry along a smooth 3D embedded curve instead of a plane, where any point on the curve is a local reflection center for some surface points. The properties of the curved reflection symmetric axis are analyzed, and a novel computational model for detecting and extracting CRAs on free-form surfaces is presented. The experimental results are then compared with both the medial axis and the intrinsic symmetric axis, which are two popular feature representations of 3D shapes, and the advantages and uniqueness of the proposed method are convincingly demonstrated. An application of the proposed method in sweep scanning is also presented. Other applications of the proposed method include feature extraction, shape symmetrization, segmentation, and registration.Note to Practitioners—This paper was originally motivated by the stylus path planning problem in sweep scanning on curved surfaces (which is a new surface inspection technology), though it is also applicable to shape registration and matching. Traditional coordinate measuring machine inspection of curved surfaces depends heavily on manual intervention, resulting in a very slow and tedious process and the acquired data are prone to inconsistency due to the discontinuous nature of the operation. In contrast, sweep scanning adopts a configuration of a deflectable stylus mounted on a motorized articulating head with two rotary axes inside, which enables the stylus tip to follow a continuous path without having to leave the surface. The head itself is mounted on an xyz table. During a sweep scanning, the head slowly moves on the xyz table (which is heavy and has stringent dynamic constraints due to its large mass) along a nominal path, while the stylus (which is extremely light) quickly oscillates in a direction transverse to the path of the head. The proposed curved reflection axis offers to be a powerful algebraic model for generating a nominal head path for sweep scanning. The reported work is preliminary though, especially in terms of covering the entire surface and also considering the specific length of the stylus, which will be our future work.