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    <id>8540</id>
    <completedYear/>
    <publishedYear>2022</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>1</pageFirst>
    <pageLast>5</pageLast>
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    <issue/>
    <volume/>
    <type>conferenceobject</type>
    <publisherName/>
    <publisherPlace/>
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    <belongsToBibliography>1</belongsToBibliography>
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    <title language="eng">A Nonlinear Hierarchical Model for Longitudinal Data on Manifolds</title>
    <abstract language="eng">Large longitudinal studies provide lots of valuable information, especially in medical applications. A problem which must be taken care of in order to utilize their full potential is that of correlation between intra-subject measurements taken at different times. For data in Euclidean space this can be done with hierarchical models, that is, models that consider intra-subject and between-subject variability in two different stages. Nevertheless, data from medical studies often takes values in nonlinear manifolds. Here, as a first step, geodesic hierarchical models have been developed that generalize the linear ansatz by assuming that time-induced intra-subject variations occur along a generalized straight line in the manifold. However, this is often not the case (e.g., periodic motion or processes with saturation). We propose a hierarchical model for manifold-valued data that extends this to include trends along higher-order curves, namely Bézier splines in the manifold.&#13;
To this end, we present a principled way of comparing shape trends in terms of a functional-based Riemannian metric.&#13;
Remarkably, this metric allows efficient, yet simple computations by virtue of a variational time discretization requiring only the solution of regression problems. &#13;
We validate our model on longitudinal data from the osteoarthritis initiative, including classification of disease progression.</abstract>
    <parentTitle language="eng">2022 IEEE 19th International Symposium on Biomedical Imaging (ISBI)</parentTitle>
    <identifier type="arxiv">2202.01180</identifier>
    <identifier type="doi">10.1109/ISBI52829.2022.9761465</identifier>
    <enrichment key="PeerReviewed">yes</enrichment>
    <enrichment key="AcceptedDate">2022-01-07</enrichment>
    <enrichment key="opus.source">publish</enrichment>
    <author>Martin Hanik</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="hanik">Hanik, Martin</collection>
    <collection role="projects" number="MathPlus-EF2-3">MathPlus-EF2-3</collection>
    <collection role="institutes" number="VDcC">Visual and Data-centric Computing</collection>
  </doc>
</export-example>
