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  <doc>
    <id>7456</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>2019-08-28</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">An as-invariant-as-possible GL+(3)-based Statistical Shape Model</title>
    <abstract language="eng">We describe a novel nonlinear statistical shape model basedon differential coordinates viewed as elements of GL+(3). We adopt an as-invariant-as possible framework comprising a bi-invariant Lie group mean and a tangent principal component analysis based on a unique GL+(3)-left-invariant, O(3)-right-invariant metric. Contrary to earlier work that equips the coordinates with a specifically constructed group structure, our method employs the inherent geometric structure of the group-valued data and therefore features an improved statistical power in identifying shape differences. We demonstrate this in experiments on two anatomical datasets including comparison to the standard Euclidean as well as recent state-of-the-art nonlinear approaches to statistical shape modeling.</abstract>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-74566</identifier>
    <author>Felix Ambellan</author>
    <submitter>Felix Ambellan</submitter>
    <author>Stefan Zachow</author>
    <author>Christoph von Tycowicz</author>
    <series>
      <title>ZIB-Report</title>
      <number>19-46</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Statistical shape analysis</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Tangent principal component analysis</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Lie groups</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Classification</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Manifold valued statistics</value>
    </subject>
    <collection role="institutes" number="vis">Visual Data Analysis</collection>
    <collection role="institutes" number="medplan">Therapy Planning</collection>
    <collection role="persons" number="zachow">Zachow, Stefan</collection>
    <collection role="persons" number="vontycowicz">Tycowicz, Christoph von</collection>
    <collection role="persons" number="ambellan">Ambellan, Felix</collection>
    <collection role="projects" number="MathPlus-TrU-1">MathPlus-TrU-1</collection>
    <collection role="projects" number="MathPlus-EF2-3">MathPlus-EF2-3</collection>
    <collection role="institutes" number="VDcC">Visual and Data-centric Computing</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/7456/ZIBReport_19-46.pdf</file>
  </doc>
</export-example>
