Imperial College London
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ProfessorMichaelBronstein

Faculty of Engineering, Department of Computing

Visiting Professor
 
 
 
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Contact

 

m.bronstein Website

 
 
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Location

 

569Huxley BuildingSouth Kensington Campus

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Summary

 

Publications

Citation

BibTex format

@inproceedings{Wang:2018:10.1111/cgf.13488,
author = {Wang, L and Gehre, A and Bronstein, MM and Solomon, J},
doi = {10.1111/cgf.13488},
pages = {27--36},
publisher = {Wiley},
title = {Kernel functional maps},
url = {http://dx.doi.org/10.1111/cgf.13488},
year = {2018}
}
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RIS format (EndNote, RefMan)

TY  - CPAPER
AB  - Functional maps provide a means of extracting correspondences between surfaces using linearalgebraic machinery. While the functional framework suggests efficient algorithms for map computation, the basic technique does not incorporate the intuition that pointwise modifications of a descriptor function (e.g. composition of a descriptor and a nonlinearity) should be preserved under the mapping; the end result is that the basic functional maps problem can be underdetermined without regularization or additional assumptions on the map. In this paper, we show how this problem can be addressed through kernelization , in which descriptors are lifted to higherdimensional vectors or even infinitelength sequences of values. The key observation is that optimization problems for functional maps only depend on inner products between descriptors rather than descriptor values themselves. These inner products can be evaluated efficiently through use of kernel functions. In addition to deriving a kernelized version of functional maps including a recent extension in terms of pointwise multiplication operators, we provide an efficient conjugate gradient algorithm for optimizing our generalized problem as well as a strategy for lowrank estimation of kernel matrices through the Nyström approximation.
AU  - Wang,L
AU  - Gehre,A
AU  - Bronstein,MM
AU  - Solomon,J
DO  - 10.1111/cgf.13488
EP  - 36
PB  - Wiley
PY  - 2018///
SN  - 0167-7055
SP  - 27
TI  - Kernel functional maps
UR  - http://dx.doi.org/10.1111/cgf.13488
UR  - http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000440989100003&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=1ba7043ffcc86c417c072aa74d649202
UR  - http://hdl.handle.net/10044/1/80607
ER  -
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