Shape Matching using Gromov-Hausdorff distances
Speaker: Facundo Memoli , Stanford University
Date: October 9 2009
Time: 1:00PM to 2:00PM
Location: 32-D507
Host: Martin Reuter, MIT
Contact: Martin Reuter, reuter@MIT.EDU
Relevant URL: Matching shapes under invariances is an important problem in pattern
recognition. One example is considering two 3D shapes to be the same
when there exists a rigid isometry that maps one shape into the
other. A more general notion consists of deeming two shapes to be the
same when there exists an intrinsic isometry, or bend, mapping one
shape into the other. This leads to the idea of regarding shapes as
metric spaces, and then, to comparing these shapes using a notion of
distance between metric spaces.
Based on the notion of Gromov-Hausdorff distance, we present a set of
ideas for achieving this goal. We show how this distance needs to be
modified in order to obtain more computationally tractable
alternatives. These alternative notions of distance between metric
spaces rely on Mass Transportation-like distances such as the Earth
Mover's distance (aka Wasserstein distance). These new distances
admit as lower bounds certain comparison of metric invariants
considered in the literature, for example, those known as Shape
Distributions and Shape Contexts.
We will discuss the underlying theoretical concepts, the numerical
framework and present computational examples.
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