This paper initially develops the discrete-point sampling operator's concept, model, and parameters that we have previously proposed, and makes its belt-shaped regions in a discrete-point sampling map more salient and appropriate for centerline extraction. The cross-sectional features of these belt-shaped regions are then analyzed and seven types of feature points are defined to facilitate descriptions of such features. Based on these feature points, a three-level detection system is proposed, including feature points, line segments, and centerlines, to extract centerlines from the belt-shaped regions. Eight basic types of centerlines and five types of relationships among the centerlines are defined by computational geometry algorithms, and Gestalt laws are used to cluster them into groupings. If some prior information about a desired shape is available, retrieval grouping may be carried out by a discrete-point sampling map, the purpose of which is to find centerlines by best matching with prior information. Discrete-point sampling effectually overcomes the influences of interference from noise, textures, and uneven illumination, and greatly reduces the difficulty of centerline extraction. Centerline clustered groupings and retrieval grouping can offer a strong anti-interference ability with nonlinear deformations such as articulation and occlusion. This method can extract large-scale complex shapes combined of lines and planes from complex images. The wheel location results of noise test and other shape extraction experiments show that our method has a strong capability to persist with nonlinear deformations.