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  <doc>
    <id>6975</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
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    <completedDate>--</completedDate>
    <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>
  <doc>
    <id>7590</id>
    <completedYear/>
    <publishedYear>2020</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>549</pageFirst>
    <pageLast>559</pageLast>
    <pageNumber/>
    <edition/>
    <issue>4</issue>
    <volume>62</volume>
    <type>article</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
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    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Geodesic Analysis in Kendall's Shape Space with Epidemiological Applications</title>
    <abstract language="eng">We analytically determine Jacobi fields and parallel transports and compute geodesic regression in Kendall’s shape space. Using the derived expressions,&#13;
we can fully leverage the geometry via Riemannian optimization and thereby reduce the computational expense by several orders of magnitude over common,&#13;
nonlinear constrained approaches. The methodology is demonstrated by performing a longitudinal statistical analysis of epidemiological shape data. As an example&#13;
application we have chosen 3D shapes of knee bones, reconstructed from image&#13;
data of the Osteoarthritis Initiative (OAI). 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 alone.</abstract>
    <parentTitle language="eng">Journal of Mathematical Imaging and Vision</parentTitle>
    <identifier type="doi">10.1007/s10851-020-00945-w</identifier>
    <identifier type="arxiv">1906.11950</identifier>
    <enrichment key="PeerReviewed">yes</enrichment>
    <enrichment key="AcceptedDate">2020-01-28</enrichment>
    <author>Esfandiar Nava-Yazdani</author>
    <submitter>Christoph von Tycowicz</submitter>
    <author>Hans-Christian Hege</author>
    <author>T. J. Sullivan</author>
    <author>Christoph von Tycowicz</author>
    <collection role="institutes" number="vis">Visual Data Analysis</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="projects" number="MathPlus-EF2-3">MathPlus-EF2-3</collection>
    <collection role="institutes" number="VDcC">Visual and Data-centric Computing</collection>
    <collection role="institutes" number="GDAP">Geometric Data Analysis and Processing</collection>
  </doc>
  <doc>
    <id>7595</id>
    <completedYear/>
    <publishedYear>2019</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>209</pageFirst>
    <pageLast>218</pageLast>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume>11846</volume>
    <type>conferenceobject</type>
    <publisherName/>
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    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
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    <title language="eng">A Geodesic Mixed Effects Model in Kendall's Shape Space</title>
    <abstract language="eng">In many applications, geodesic hierarchical models are adequate for the study of temporal observations. We employ such a model derived for manifold-valued data to Kendall's shape space. In particular, instead of the Sasaki metric, we adapt a functional-based metric, which increases the computational efficiency and does not require the implementation of the curvature tensor. We propose the corresponding variational time discretization of geodesics and apply the approach for the estimation of group trends and statistical testing of 3D shapes derived from an open access longitudinal imaging study on osteoarthritis.</abstract>
    <parentTitle language="eng">Proc. 7th MICCAI workshop on Mathematical Foundations of Computational Anatomy (MFCA)</parentTitle>
    <identifier type="doi">10.1007/978-3-030-33226-6_22</identifier>
    <enrichment key="Series">Lecture Notes in Computer Science</enrichment>
    <enrichment key="PeerReviewed">yes</enrichment>
    <enrichment key="PreprintUrn">urn:nbn:de:0297-zib-74621</enrichment>
    <author>Esfandiar Nava-Yazdani</author>
    <submitter>Christoph von Tycowicz</submitter>
    <author>Hans-Christian Hege</author>
    <author>Christoph von Tycowicz</author>
    <collection role="institutes" number="vis">Visual Data Analysis</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>
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  </doc>
  <doc>
    <id>7462</id>
    <completedYear/>
    <publishedYear>2019</publishedYear>
    <thesisYearAccepted>2019</thesisYearAccepted>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">A Geodesic Mixed Effects Model in Kendall's Shape Space</title>
    <abstract language="eng">In many applications, geodesic hierarchical models are adequate for the study of temporal observations. We employ such a model derived for manifold-valued data to Kendall's shape space. In particular, instead of the Sasaki metric, we adapt a functional-based metric, which increases the computational efficiency and does not require the implementation of the curvature tensor. We propose the corresponding variational time discretization of geodesics and apply the approach for the estimation of group trends and statistical testing of 3D shapes derived from an open access longitudinal imaging study on osteoarthritis.</abstract>
    <parentTitle language="eng">Proc. 7th MICCAI workshop on Mathematical Foundations of Computational Anatomy (MFCA)</parentTitle>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-74621</identifier>
    <author>Esfandiar Nava-Yazdani</author>
    <submitter>Esfandiar Nava-Yazdani</submitter>
    <author>Hans-Christian Hege</author>
    <author>Christoph von Tycowicz</author>
    <series>
      <title>ZIB-Report</title>
      <number>19-49</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Shape Space</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Kendall</value>
    </subject>
    <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="65-XX">NUMERICAL ANALYSIS</collection>
    <collection role="institutes" number="vis">Visual Data Analysis</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>
    <file>https://opus4.kobv.de/opus4-zib/files/7462/geomixed_preprint.pdf</file>
  </doc>
  <doc>
    <id>9688</id>
    <completedYear/>
    <publishedYear>2024</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>104012</pageFirst>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume>123</volume>
    <type>article</type>
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    <title language="eng">SHREC 2024: Recognition Of Dynamic Hand Motions Molding Clay</title>
    <abstract language="eng">Gesture recognition is a tool to enable novel interactions with different techniques and&#13;
applications, like Mixed Reality and Virtual Reality environments. With all the recent&#13;
advancements in gesture recognition from skeletal data, it is still unclear how well state-of-&#13;
the-art techniques perform in a scenario using precise motions with two hands. This&#13;
paper presents the results of the SHREC 2024 contest organized to evaluate methods&#13;
for their recognition of highly similar hand motions using the skeletal spatial coordinate&#13;
data of both hands. The task is the recognition of 7 motion classes given their spatial&#13;
coordinates in a frame-by-frame motion. The skeletal data has been captured using&#13;
a Vicon system and pre-processed into a coordinate system using Blender and Vicon&#13;
Shogun Post. We created a small, novel dataset with a high variety of durations in&#13;
frames. This paper shows the results of the contest, showing the techniques created&#13;
by the 5 research groups on this challenging task and comparing them to our baseline&#13;
method.</abstract>
    <parentTitle language="eng">Computers &amp; Graphics</parentTitle>
    <identifier type="doi">10.1016/j.cag.2024.104012</identifier>
    <enrichment key="PeerReviewed">yes</enrichment>
    <enrichment key="opus.source">publish</enrichment>
    <enrichment key="AcceptedDate">2024-07-10</enrichment>
    <author>Ben Veldhuijzen</author>
    <submitter>Martin Hanik</submitter>
    <author>Remco C. Veltkamp</author>
    <author>Omar Ikne</author>
    <author>Benjamin Allaert</author>
    <author>Hazem Wannous</author>
    <author>Marco Emporio</author>
    <author>Andrea Giachetti</author>
    <author>Joseph J. LaViola Jr</author>
    <author>Ruiwen He</author>
    <author>Halim Benhabiles</author>
    <author>Adnane Cabani</author>
    <author>Anthony Fleury</author>
    <author>Karim Hammoudi</author>
    <author>Konstantinos Gavalas</author>
    <author>Christoforos Vlachos</author>
    <author>Athanasios Papanikolaou</author>
    <author>Ioannis Romanelis</author>
    <author>Vlassis Fotis</author>
    <author>Gerasimos Arvanitis</author>
    <author>Konstantinos Moustakas</author>
    <author>Martin Hanik</author>
    <author>Esfandiar Nava-Yazdani</author>
    <author>Christoph von Tycowicz</author>
    <collection role="persons" number="vontycowicz">Tycowicz, Christoph von</collection>
    <collection role="persons" number="navayazdani">Navayazdani, Esfandiar</collection>
    <collection role="persons" number="hanik">Hanik, Martin</collection>
    <collection role="institutes" number="VDcC">Visual and Data-centric Computing</collection>
    <collection role="institutes" number="GDAP">Geometric Data Analysis and Processing</collection>
    <collection role="projects" number="DDESAMT">DDESAMT</collection>
    <collection role="projects" number="Math+EF1-18">Math+EF1-18</collection>
  </doc>
  <doc>
    <id>8518</id>
    <completedYear/>
    <publishedYear/>
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    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>2021-12-07</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">A Hierarchical Geodesic Model for Longitudinal Analysis on Manifolds</title>
    <abstract language="eng">In many applications, geodesic hierarchical models are adequate for the study of temporal observations. We employ such a model derived for manifold-valued data to Kendall's shape space. In particular, instead of the Sasaki metric, we adapt a functional-based metric, which increases the computational efficiency and does not require the implementation of the curvature tensor. We propose the corresponding variational time discretization of geodesics and employ the approach for longitudinal analysis of 2D rat skulls shapes as well as 3D shapes derived from an imaging study on osteoarthritis. Particularly, we perform hypothesis test and estimate the mean trends.</abstract>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-85187</identifier>
    <note>sumbitted to: Journal of Mathematical Imaging and Vision</note>
    <author>Esfandiar Nava-Yazdani</author>
    <submitter>Esfandiar Nava-Yazdani</submitter>
    <author>Hans-Christian Hege</author>
    <author>Christoph von Tycowicz</author>
    <series>
      <title>ZIB-Report</title>
      <number>21-39</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Longitudinal</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Hierarchical</value>
    </subject>
    <collection role="msc" number="49-XX">CALCULUS OF VARIATIONS AND OPTIMAL CONTROL; OPTIMIZATION [See also 34H05, 34K35, 65Kxx, 90Cxx, 93-XX]</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="65-XX">NUMERICAL ANALYSIS</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>
    <file>https://opus4.kobv.de/opus4-zib/files/8518/geomixed_zib.pdf</file>
  </doc>
  <doc>
    <id>8606</id>
    <completedYear/>
    <publishedYear>2022</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>395</pageFirst>
    <pageLast>407</pageLast>
    <pageNumber/>
    <edition/>
    <issue>4</issue>
    <volume>64</volume>
    <type>article</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">A Hierarchical Geodesic Model for Longitudinal Analysis on Manifolds</title>
    <abstract language="eng">In many applications, geodesic hierarchical models are adequate for the study of temporal observations.&#13;
We employ such a model derived for manifold-valued data to Kendall's shape space.&#13;
In particular, instead of the Sasaki metric, we adapt a functional-based metric, which increases the computational efficiency and does not require the implementation of the curvature tensor. We propose the corresponding variational time discretization of geodesics &#13;
and employ the approach for longitudinal analysis of 2D rat skulls shapes as well as 3D shapes derived from an imaging study on osteoarthritis. Particularly, we perform hypothesis test and estimate the mean trends.</abstract>
    <parentTitle language="eng">Journal of Mathematical Imaging and Vision</parentTitle>
    <identifier type="doi">10.1007/s10851-022-01079-x</identifier>
    <enrichment key="PeerReviewed">yes</enrichment>
    <enrichment key="AcceptedDate">2022-02-24</enrichment>
    <enrichment key="opus.source">publish</enrichment>
    <enrichment key="PreprintUrn">urn:nbn:de:0297-zib-85187</enrichment>
    <author>Esfandiar Nava-Yazdani</author>
    <submitter>Christoph von Tycowicz</submitter>
    <author>Hans-Christian Hege</author>
    <author>Christoph von Tycowicz</author>
    <collection role="institutes" number="vis">Visual Data Analysis</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="projects" number="MathPlus-EF2-3">MathPlus-EF2-3</collection>
    <collection role="institutes" number="VDcC">Visual and Data-centric Computing</collection>
    <collection role="projects" number="DDESAMT">DDESAMT</collection>
  </doc>
  <doc>
    <id>8717</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>2022-06-24</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">On Gradient Formulas in an Algorithm for the Logarithm of the Sasaki Metric</title>
    <abstract language="eng">The Sasaki metric is the canonical metric on the tangent bundle TM of a Riemannian manifold M. It is highly useful for data analysis in TM (e.g., when one is interested in the statistics of a set of geodesics in M). To this end, computing the Riemannian logarithm is often necessary, and an iterative algorithm was proposed by Muralidharan and Fletcher. In this note, we derive approximation formulas of the energy gradients in their algorithm that we use with success.</abstract>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-87174</identifier>
    <enrichment key="opus.source">publish</enrichment>
    <author>Esfandiar Nava-Yazdani</author>
    <submitter>Martin Hanik</submitter>
    <author>Martin Hanik</author>
    <author>Felix Ambellan</author>
    <author>Christoph von Tycowicz</author>
    <series>
      <title>ZIB-Report</title>
      <number>22-12</number>
    </series>
    <collection role="ccs" number="I.">Computing Methodologies</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="persons" number="vontycowicz">Tycowicz, Christoph von</collection>
    <collection role="persons" number="ambellan">Ambellan, Felix</collection>
    <collection role="persons" number="navayazdani">Navayazdani, Esfandiar</collection>
    <collection role="persons" number="hanik">Hanik, Martin</collection>
    <collection role="projects" number="MathPlus-EF2-3">MathPlus-EF2-3</collection>
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    <file>https://opus4.kobv.de/opus4-zib/files/8717/Gradient_discrete_log_sasaki.pdf</file>
  </doc>
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