  Despite being vastly ignored in the literature, coping with topological noise
is an issue of increasing importance, especially as a consequence of the
increasing number and diversity of 3D polygonal models that are captured by
devices of different qualities or synthesized by algorithms of different
stabilities. One approach for matching 3D shapes under topological noise is to
replace the topology-sensitive geodesic distance with distances that are less
sensitive to topological changes. We propose an alternative approach utilising
gradual deflation (or inflation) of the shape volume, of which purpose is to
bring the pair of shapes to be matched to a \emph{comparable} topology before
the search for correspondences. Illustrative experiments using different
datasets demonstrate that as the level of topological noise increases, our
approach outperforms the other methods in the literature.
