In order to understand the correlation between the connection of surface microstructures and lubrication and seal performances, a novel method to characterize the connectivity of the three-dimensional (3D) surface topography, based on mathematical morphology, is presented. A new concept of surface connectivity index is proposed. Quantitative description of the connectivity of 3D topography in digital space is made by recursive operation of multiscale erosion. The variations of the surface connectivity index with the surface height are approached. The reliability of the surface connectivity measure method is analysed. As a practical application, the connectivity of the 3D topography of a cylinder liner of an engine is evaluated. The results of calculation and analysis indicate that this approach has an explicit signification and reliable arithmetic, and it can effectively describe the connection characteristics of surface structures.