The mapping of physicochemical characteristics onto the surface of a protein provides crucial insights into its function and evolution. This information can be further used in the characterization and identification of similarities within protein surface regions. We propose a novel method which quantitatively compares global and local properties on the protein surface. We have tested the method on comparison of electrostatic potentials and hydrophobicity. The method is based on 3D Zernike descriptors, which provides a compact representation of a given property defined on a protein surface. Compactness and rotational invariance of this descriptor enable fast comparison suitable for database searches. The usefulness of this method is exemplified by studying several protein families including globins, thermophilic and mesophilic proteins, and active sites of TIM beta/alpha barrel proteins. In all the cases studied, the descriptor is able to cluster proteins into functionally relevant groups. The proposed approach can also be easily extended to other surface properties. This protein surface-based approach will add a new way of viewing and comparing proteins to conventional methods, which compare proteins in terms of their primary sequence or tertiary structure.