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  <doc>
    <id>6975</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
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    <publishedDate>2018-08-01</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">A Shape Trajectories Approach to Longitudinal Statistical Analysis</title>
    <abstract language="eng">For Kendall’s shape space we determine analytically Jacobi fields and parallel transport, and compute geodesic regression. Using the derived expressions, we can fully leverage the geometry via Riemannian optimization and reduce the computational expense by several orders of magnitude. The methodology is demonstrated by performing a longitudinal statistical analysis of epidemiological shape data.&#13;
&#13;
As application example we have chosen 3D shapes of knee bones, reconstructed from image data of the Osteoarthritis Initiative. Comparing subject groups with incident and developing osteoarthritis versus normal controls, we find clear differences in the temporal development of femur shapes. This paves the way for early prediction of incident knee osteoarthritis, using geometry data only.</abstract>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-69759</identifier>
    <author>Esfandiar Nava-Yazdani</author>
    <submitter>Hans-Christian Hege</submitter>
    <author>Hans-Christian Hege</author>
    <author>Christoph von Tycowicz</author>
    <author>T. J. Sullivan</author>
    <series>
      <title>ZIB-Report</title>
      <number>18-42</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>shape space, shape trajectories, geodesic regression, longitudinal analysis, osteoarthritis</value>
    </subject>
    <collection role="ccs" number="G.3">PROBABILITY AND STATISTICS</collection>
    <collection role="msc" number="53-XX">DIFFERENTIAL GEOMETRY (For differential topology, see 57Rxx. For foundational questions of differentiable manifolds, see 58Axx)</collection>
    <collection role="msc" number="62-XX">STATISTICS</collection>
    <collection role="institutes" number="vis">Visual Data Analysis</collection>
    <collection role="institutes" number="visalgo">Visual Data Analysis in Science and Engineering</collection>
    <collection role="institutes" number="medplan">Therapy Planning</collection>
    <collection role="persons" number="hege">Hege, Hans-Christian</collection>
    <collection role="persons" number="vontycowicz">Tycowicz, Christoph von</collection>
    <collection role="persons" number="navayazdani">Navayazdani, Esfandiar</collection>
    <collection role="projects" number="ECMath-CH15">ECMath-CH15</collection>
    <collection role="institutes" number="VDcC">Visual and Data-centric Computing</collection>
    <collection role="institutes" number="GDAP">Geometric Data Analysis and Processing</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/6975/shape_trj.pdf</file>
  </doc>
</export-example>
