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  <doc>
    <id>6117</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>2016-11-29</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">A Riemannian Statistical Shape Model using Differential Coordinates</title>
    <abstract language="eng">We propose a novel Riemannian framework for statistical analysis of shapes that is able to account for the nonlinearity in shape variation. By adopting a physical perspective, we introduce a differential representation that puts the local geometric variability into focus. We model these differential coordinates as elements of a Lie group thereby endowing our shape space with a non-Euclidian structure. A key advantage of our framework is that statistics in a manifold shape space become numerically tractable improving performance by several orders of magnitude over state-of-the-art. We show that our Riemannian model is well suited for the identification of intra-population variability as well as inter-population differences. In particular, we demonstrate the superiority of the proposed model in experiments on specificity and generalization ability. We further derive a statistical shape descriptor that outperforms the standard Euclidian approach in terms of shape-based classification of morphological disorders.</abstract>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-61175</identifier>
    <identifier type="url">https://opus4.kobv.de/opus4-zib/frontdoor/index/index/docId/6485</identifier>
    <author>Christoph von Tycowicz</author>
    <submitter>Felix Ambellan</submitter>
    <author>Felix Ambellan</author>
    <author>Anirban Mukhopadhyay</author>
    <author>Stefan Zachow</author>
    <series>
      <title>ZIB-Report</title>
      <number>16-69</number>
    </series>
    <collection role="ccs" number="">Statistical computing</collection>
    <collection role="ccs" number="I.3.5">Computational Geometry and Object Modeling</collection>
    <collection role="msc" number="53-04">Explicit machine computation and programs (not the theory of computation or programming)</collection>
    <collection role="msc" number="62-04">Explicit machine computation and programs (not the theory of computation or programming)</collection>
    <collection role="msc" number="68U05">Computer graphics; computational geometry [See also 65D18]</collection>
    <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="projects" number="BMBF-TOKMIS">BMBF-TOKMIS</collection>
    <collection role="projects" number="DFG-Knee-Laxity">DFG-Knee-Laxity</collection>
    <collection role="persons" number="vontycowicz">Tycowicz, Christoph von</collection>
    <collection role="persons" number="ambellan">Ambellan, Felix</collection>
    <collection role="projects" number="ECMath-CH15">ECMath-CH15</collection>
    <collection role="institutes" number="VDcC">Visual and Data-centric Computing</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/6117/ZIBReport_16-69.pdf</file>
  </doc>
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