<?xml version="1.0" encoding="utf-8"?>
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  <doc>
    <id>7912</id>
    <completedYear/>
    <publishedYear>2020</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>44</pageFirst>
    <pageLast>54</pageLast>
    <pageNumber>11</pageNumber>
    <edition/>
    <issue/>
    <volume/>
    <type>conferenceobject</type>
    <publisherName>Springer International Publishing</publisherName>
    <publisherPlace>Cham</publisherPlace>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2020-10-03</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Bi-invariant Two-Sample Tests in Lie Groups for Shape Analysis</title>
    <abstract language="eng">We propose generalizations of the T²-statistics of Hotelling and the Bhattacharayya distance for data taking values in Lie groups.&#13;
A key feature of the derived measures is that they are compatible with the group structure even for manifolds that do not admit any bi-invariant metric.&#13;
This property, e.g., assures analysis that does not depend on the reference shape, thus, preventing bias due to arbitrary choices thereof. &#13;
Furthermore, the generalizations agree with the common definitions for the special case of flat vector spaces guaranteeing consistency.&#13;
Employing a permutation test setup, we further obtain nonparametric, two-sample testing procedures that themselves are bi-invariant and consistent. &#13;
We validate our method in group tests revealing significant differences in hippocampal shape between individuals with mild cognitive impairment and normal controls.</abstract>
    <parentTitle language="eng">Shape in Medical Imaging</parentTitle>
    <identifier type="arxiv">2008.12195</identifier>
    <identifier type="doi">10.1007/978-3-030-61056-2_4</identifier>
    <enrichment key="PeerReviewed">yes</enrichment>
    <enrichment key="AcceptedDate">13.08.2020</enrichment>
    <author>Martin Hanik</author>
    <submitter>Martin Hanik</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>
    <collection role="institutes" number="GDAP">Geometric Data Analysis and Processing</collection>
  </doc>
</export-example>
