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Direct comparison of three-dimensional (3D) objects is computationallyexpensive due to the need for translation, rotation, and scaling of the objectsto evaluate their similarity. In applications of 3D object comparison, oftenidentifying specific local regions of objects is of particular interest. Wehave recently developed a set of 2D moment invariants based on discreteorthogonal Krawtchouk polynomials for comparison of local image patches. Inthis work, we extend them to 3D and construct 3D Krawtchouk descriptors (3DKD)that are invariant under translation, rotation, and scaling. The newdescriptors have the ability to extract local features of a 3D surface from anyregion-of-interest. This property enables comparison of two arbitrary localsurface regions from different 3D objects. We present the new formulation of3DKD and apply it to the local shape comparison of protein surfaces in order topredict ligand molecules that bind to query proteins.

Three-Dimensional Krawtchouk Descriptors for Protein Local Surface Shape Comparison