Complementary Shape Comparison with Additional Properties

We present an algorithm for comparing 3D shapes by considering their pockets in the complementary space. The pockets of a closed compact surface can be represented by a 3D volumetric function. Multi-resolution dual contour trees are constructed from the pocket functions to efficiently match them in an affine-invariant way. DCTs are simplified data structures computed from contour trees (CT) of 3D functions. The DCTs capture the important features of the volumetric functions and are not sensitive to noises. Each node of a DCT corresponds to an interval volume and is tagged with geometrical, topological, and functional attributes. Similarities among shapes are compared by matching nodes from multi-resolution DCTs and calculating the score based on the attributes of the matched nodes. This method is particularly useful for comparing complicated molecular shapes, for which other properties such as electrostatic potentials can be added as additional attributes to improve performance.