Antibodies have the remarkable ability to recognise their cognate antigens with extraordinary affinity and specificity. Discerning the rules that define antibody-antigen recognition is a fundamental step in the rational design and engineering of functional antibodies with desired properties. In this study we apply the 3D Zernike formalism to the analysis of the surface properties of the antibody complementary determining regions (CDRs). Our results show that shape and electrostatic 3DZD descriptors of the surface of the CDRs are predictive of antigen specificity, with classification accuracy of 81% and area under the receiver operating characteristic curve (AUC) of 0.85. Additionally, while in terms of surface size, solvent accessibility and amino acid composition, antibody epitopes are typically not distinguishable from non-epitope, solvent-exposed regions of the antigen, the 3DZD descriptors detect significantly higher surface complementarity to the paratope, and are able to predict correct paratope-epitope interaction with an AUC = 0.75.