In tribological functions high peaks (summits) in the surface topography play a dominant role in that they determine the position of first contact and how the contact will occur. Both statistic-based methods and feature-based methods address the characterization of a single surface, while neglecting the interacting surface. A morphological method is proposed to simulate the contact of two mating surfaces. The surface under evaluation is rolled by a ball with radius meant to simulate the largest reasonable peak curvature at a contact. In such a situation the contact points of the rolling ball may serve as an identification of those surface portions that are in real contact. The morphological closing operation could then be applied to detect the contact points of the rolling ball, however, the traditional computation method does not lead to an accurate result. To overcome this deficiency, a geometrical computation approach has been developed to capture the contact points based on four searching procedures. The resulting method has been verified through experimentation and then applied to a case study in which the underlying form of the surface of a hip replacement taper junction is analyzed to remove the effect of the dominant threaded structure.