2,971 research outputs found
Efficient Deformable Shape Correspondence via Kernel Matching
We present a method to match three dimensional shapes under non-isometric
deformations, topology changes and partiality. We formulate the problem as
matching between a set of pair-wise and point-wise descriptors, imposing a
continuity prior on the mapping, and propose a projected descent optimization
procedure inspired by difference of convex functions (DC) programming.
Surprisingly, in spite of the highly non-convex nature of the resulting
quadratic assignment problem, our method converges to a semantically meaningful
and continuous mapping in most of our experiments, and scales well. We provide
preliminary theoretical analysis and several interpretations of the method.Comment: Accepted for oral presentation at 3DV 2017, including supplementary
materia
Representation theory for subfactors, -lattices and C*-tensor categories
We develop a representation theory for -lattices, arising as
standard invariants of subfactors, and for rigid C*-tensor categories,
including a definition of their universal C*-algebra. We use this to give a
systematic account of approximation and rigidity properties for subfactors and
tensor categories, like (weak) amenability, the Haagerup property and property
(T). We determine all unitary representations of the Temperley-Lieb-Jones
-lattices and prove that they have the Haagerup property and the
complete metric approximation property. We also present the first subfactors
with property (T) standard invariant and that are not constructed from property
(T) groups.Comment: v3: minor changes, final version to appear in Communications in
Mathematical Physics. v2: improved exposition; permanence of property (T)
under quotients adde
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