Study of the morphology of proteins, and their 3D structure, supports investigations of their functions and represents an initial step towards protein-based drug design. The goal of this paper is to define techniques, based on the geometrical and topological structure of protein surfaces, for the detection and analysis of sites of potential protein-protein and protein-ligand interactions. Two protein representation modalities based on the Concavity Tree (CT) and the Enriched Complex Extended Gaussian Image (EC-EGI) are considered. In particular, the concavity tree, in which the interface is usually extended and roughly planar, is considered to be better suited to protein-protein interaction studies. Instead, the EGI is more suited to protein-ligand interactions, in which the small ligand molecule usually has to fit into the protein cavity. In fact, the histogram of the orientations is better suited to representing a mainly convex object and its dual matching region (the cavity). Both these data structures are open, and can be easily integrated with biochemical features.