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  <doc>
    <id>5483</id>
    <completedYear/>
    <publishedYear>2010</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>296</pageFirst>
    <pageLast>314</pageLast>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume>6130</volume>
    <type>incollection</type>
    <publisherName>Springer Berlin / Heidelberg</publisherName>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Eigenmodes of Surface Energies for Shape Analysis</title>
    <abstract language="eng">In this work, we study the spectra and eigenmodes of the Hessian of various discrete surface energies and discuss applications to shape analysis. In particular, we consider a physical model that describes the vibration modes and frequencies of a surface through the eigenfunctions and eigenvalues of the Hessian of a deformation energy, and we derive a closed form representation for the Hessian (at the rest state of the energy) for a general class of deformation energies. Furthermore, we design a quadratic energy, such that the eigenmodes of the Hessian of this energy are sensitive to the extrinsic curvature of the surface. &#13;
Based on these spectra and eigenmodes, we derive two shape signatures. One that measures the similarity of points on a surface, and another that can be used to identify features of the surface. In addition, we discuss a spectral quadrangulation scheme for surfaces.</abstract>
    <parentTitle language="eng">Advances in Geometric Modeling and Processing (Proceedings of Geometric Modeling and Processing 2010)</parentTitle>
    <identifier type="doi">10.1007/978-3-642-13411-1_20</identifier>
    <enrichment key="Series">Lecture Notes in Computer Science</enrichment>
    <enrichment key="PeerReviewed">yes</enrichment>
    <enrichment key="FulltextUrl">https://nbn-resolving.org/urn:nbn:de:0296-matheon-7325</enrichment>
    <author>Klaus Hildebrandt</author>
    <editor>Bernard Mourrain</editor>
    <submitter>Christoph von Tycowicz</submitter>
    <author>Christian Schulz</author>
    <editor>Scott Schaefer</editor>
    <author>Christoph von Tycowicz</author>
    <editor>Guoliang Xu</editor>
    <author>Konrad Polthier</author>
    <collection role="institutes" number="vis">Visual Data Analysis</collection>
    <collection role="persons" number="vontycowicz">Tycowicz, Christoph von</collection>
    <collection role="institutes" number="VDcC">Visual and Data-centric Computing</collection>
  </doc>
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