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