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No abstract

Given a collection of sets of 2-D views of 3-D objects and

Abstract. In this paper we will consider tight upper-and lower-bounds on the weight of the optimal matching for random point sets distributed among the leaves of a tree, as a function of its cardinality. Specifically, given two n sets of points R = {r1, ..., rn} and B = {b1, ..., bn} distributed uniformly and randomly on the m leaves of λ-Hierarchically Separated Trees with branching factor b such that each one of its leaves are of depth δ, we will prove that the expected weight of optimal matching between R and B is Θ(Using a simple embedding algorithm from R d to HSTs, we are able to reproduce the results concerning the expected optimal transportation cost in [0,1] d , except for d = 2. We also show that giving random weights to the points does not affect the expected matching weight by more than a constant factor. Finally, we prove upper bounds on several sets for which showing reasonable matching results would previously have been intractable, e.g., the Cantor set, and various fractals.