The three-dimensional morphology of frictional sub-surfaces holds significant importance for studying tribological issues. However, the uniformity of horizontal datum in 3D scanning is limited for curved surfaces, resulting in the inability to obtain accurate contour characterization parameters from the scanning results. This study aims to address this issue by constructing regular surface equations and normalizing the 3D profiler scanning results. By fitting the data, a "plane" surface representative of the surface features is obtained, and the paper demonstrates this approach on the surface morphology of different worn parts in the frictional area of spherical bearings located in the specific environment of the Three Gorges gate. The results indicate that the obtained "plane" effectively reconstructs the three-dimensional morphology map of the regular surface. Moreover, this reconstructed plane not only clearly illustrates the surface characteristics but also provides the foundation for analyzing the wear mechanism.