Fast Matching of Volumetric Functions Using Multi-resolution Dual Contour Trees

We present an algorithm of matching 3D volumetric functions based on affine-invariant multi-resolution dual contour trees. A dual contour tree structure is constructed from the contour tree of a volume by dividing its functional range into segments such that the connected contour tree edges within a segment become a node in the dual tree. Each node of the dual contour tree corresponds to a connected sub-volume bounded by contours within a certain range segment. Attributes such as functional range, volume, and Betti number of bounding contours are further computed for each node of the dual contour tree. A similarity metric between two volumes is computed by matching the multi-resolution dual contour trees and corresponding attributes. When applied to biomolecular structures and associated properties such as electrostatic potentials, this algorithm shows good performance separating proteins into different classes.