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    <publishedDate>2019-03-05</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Statistical Shape Models - Understanding and Mastering Variation in Anatomy</title>
    <abstract language="eng">In our chapter we are describing how to reconstruct three-dimensional anatomy from medical image data and how to build Statistical 3D Shape Models out of many such reconstructions yielding a new kind of anatomy that not only allows quantitative analysis of anatomical variation but also a visual exploration and educational visualization. Future digital anatomy atlases will not only show a static (average) anatomy but also its normal or pathological variation in three or even four dimensions, hence, illustrating growth and/or disease progression. Statistical Shape Models (SSMs) are geometric models that describe a collection of semantically similar objects in a very compact way. SSMs represent an average shape of many three-dimensional objects as well as their variation in shape. The creation of SSMs requires a correspondence mapping, which can be achieved e.g. by parameterization with a respective sampling. If a corresponding parameterization over all shapes can be established, variation between individual shape characteristics can be mathematically investigated. We will explain what Statistical Shape Models are and how they are constructed. Extensions of Statistical Shape Models will be motivated for articulated coupled structures. In addition to shape also the appearance of objects will be integrated into the concept. Appearance is a visual feature independent of shape that depends on observers or imaging techniques. Typical appearances are for instance the color and intensity of a visual surface of an object under particular lighting conditions, or measurements of material properties with computed tomography (CT) or magnetic resonance imaging (MRI). A combination of (articulated) statistical shape models with statistical models of appearance lead to articulated Statistical Shape and Appearance Models (a-SSAMs).After giving various examples of SSMs for human organs, skeletal structures, faces, and bodies, we will shortly describe clinical applications where such models have been successfully employed. Statistical Shape Models are the foundation for the analysis of anatomical cohort data, where characteristic shapes are correlated to demographic or epidemiologic data. SSMs consisting of several thousands of objects offer, in combination with statistical methods ormachine learning techniques, the possibility to identify characteristic clusters, thus being the foundation for advanced diagnostic disease scoring.</abstract>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-72699</identifier>
    <identifier type="doi">10.1007/978-3-030-19385-0_5</identifier>
    <author>Felix Ambellan</author>
    <submitter>Felix Ambellan</submitter>
    <author>Hans Lamecker</author>
    <author>Christoph von Tycowicz</author>
    <author>Stefan Zachow</author>
    <series>
      <title>ZIB-Report</title>
      <number>19-13</number>
    </series>
    <collection role="institutes" number="vis">Visual Data Analysis</collection>
    <collection role="institutes" number="medplan">Therapy Planning</collection>
    <collection role="persons" number="lamecker">Lamecker, Hans</collection>
    <collection role="persons" number="zachow">Zachow, Stefan</collection>
    <collection role="projects" number="BMBF-TOKMIS">BMBF-TOKMIS</collection>
    <collection role="projects" number="MODAL-MedLab">MODAL-MedLab</collection>
    <collection role="projects" number="Overload-PrevOP-SP4">Overload-PrevOP-SP4</collection>
    <collection role="persons" number="vontycowicz">Tycowicz, Christoph von</collection>
    <collection role="persons" number="ambellan">Ambellan, Felix</collection>
    <collection role="projects" number="MODAL-Gesamt">MODAL-Gesamt</collection>
    <collection role="projects" number="ECMath-CH15">ECMath-CH15</collection>
    <collection role="projects" number="MathPlus-TrU-1">MathPlus-TrU-1</collection>
    <collection role="projects" number="MathPlus-EF2-3">MathPlus-EF2-3</collection>
    <collection role="institutes" number="VDcC">Visual and Data-centric Computing</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/7269/ZIB-Report.pdf</file>
  </doc>
  <doc>
    <id>7321</id>
    <completedYear/>
    <publishedYear>2019</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>67</pageFirst>
    <pageLast>84</pageLast>
    <pageNumber/>
    <edition>1</edition>
    <issue>1156</issue>
    <volume>3</volume>
    <type>bookpart</type>
    <publisherName>Springer Nature Switzerland AG</publisherName>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2019-07-24</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Statistical Shape Models - Understanding and Mastering Variation in Anatomy</title>
    <abstract language="eng">In our chapter we are describing how to reconstruct three-dimensional anatomy from medical image data and how to build Statistical 3D Shape Models out of many such reconstructions yielding a new kind of anatomy that not only allows quantitative analysis of anatomical variation but also a visual exploration and educational visualization. Future digital anatomy atlases will not only show a static (average) anatomy but also its normal or pathological variation in three or even four dimensions, hence, illustrating growth and/or disease progression. Statistical Shape Models (SSMs) are geometric models that describe a collection of semantically similar objects in a very compact way. SSMs represent an average shape of many three-dimensional objects as well as their variation in shape. The creation of SSMs requires a correspondence mapping, which can be achieved e.g. by parameterization with a respective sampling. If a corresponding parameterization over all shapes can be established, variation between individual shape characteristics can be mathematically investigated. We will explain what Statistical Shape Models are and how they are constructed. Extensions of Statistical Shape Models will be motivated for articulated coupled structures. In addition to shape also the appearance of objects will be integrated into the concept. Appearance is a visual feature independent of shape that depends on observers or imaging techniques. Typical appearances are for instance the color and intensity of a visual surface of an object under particular lighting conditions, or measurements of material properties with computed tomography (CT) or magnetic resonance imaging (MRI). A combination of (articulated) statistical shape models with statistical models of appearance lead to articulated Statistical Shape and Appearance Models (a-SSAMs).After giving various examples of SSMs for human organs, skeletal structures, faces, and bodies, we will shortly describe clinical applications where such models have been successfully employed. Statistical Shape Models are the foundation for the analysis of anatomical cohort data, where characteristic shapes are correlated to demographic or epidemiologic data. SSMs consisting of several thousands of objects offer, in combination with statistical methods ormachine learning techniques, the possibility to identify characteristic clusters, thus being the foundation for advanced diagnostic disease scoring.</abstract>
    <parentTitle language="eng">Biomedical Visualisation</parentTitle>
    <identifier type="isbn">978-3-030-19384-3</identifier>
    <identifier type="doi">10.1007/978-3-030-19385-0_5</identifier>
    <identifier type="isbn">978-3-030-19385-0</identifier>
    <enrichment key="Series">Advances in Experimental Medicine and Biology</enrichment>
    <enrichment key="PeerReviewed">yes</enrichment>
    <enrichment key="PreprintUrn">urn:nbn:de:0297-zib-72699</enrichment>
    <author>Felix Ambellan</author>
    <submitter>Stefan Zachow</submitter>
    <editor>Paul M. Rea</editor>
    <author>Hans Lamecker</author>
    <author>Christoph von Tycowicz</author>
    <author>Stefan Zachow</author>
    <collection role="institutes" number="vis">Visual Data Analysis</collection>
    <collection role="institutes" number="medplan">Therapy Planning</collection>
    <collection role="persons" number="lamecker">Lamecker, Hans</collection>
    <collection role="persons" number="zachow">Zachow, Stefan</collection>
    <collection role="projects" number="BMBF-TOKMIS">BMBF-TOKMIS</collection>
    <collection role="projects" number="MODAL-MedLab">MODAL-MedLab</collection>
    <collection role="projects" number="Overload-PrevOP-SP4">Overload-PrevOP-SP4</collection>
    <collection role="persons" number="vontycowicz">Tycowicz, Christoph von</collection>
    <collection role="persons" number="ambellan">Ambellan, Felix</collection>
    <collection role="projects" number="MODAL-Gesamt">MODAL-Gesamt</collection>
    <collection role="projects" number="ECMath-CH15">ECMath-CH15</collection>
    <collection role="projects" number="MathPlus-TrU-1">MathPlus-TrU-1</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>4269</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
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    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2013-10-11</completedDate>
    <publishedDate>2013-10-11</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Reducing Memory Requirements in Scientific Computing and Optimal Control</title>
    <abstract language="eng">In high accuracy numerical simulations and optimal control of time-dependent processes, often both many time steps and fine spatial discretizations are needed. Adjoint gradient computation, or post-processing of simulation results, requires the storage of the solution trajectories over the whole time, if necessary together with the adaptively refined spatial grids. In this paper we discuss various techniques to reduce the memory requirements, focusing first on the storage of the solution data, which typically are double precision floating point values. We highlight advantages and disadvantages of the different approaches. Moreover, we present an algorithm for the efficient storage of adaptively refined, hierarchic grids, and the integration with the compressed storage of solution data.</abstract>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-42695</identifier>
    <enrichment key="SourceTitle">submitted to "Multiple Shooting and Time Domain Decomposition Methods", Springer Series "Contributions in Mathematical and Computational Sciences"</enrichment>
    <author>Sebastian Götschel</author>
    <submitter>Sebastian Götschel</submitter>
    <author>Christoph von Tycowicz</author>
    <author>Konrad Polthier</author>
    <author>Martin Weiser</author>
    <series>
      <title>ZIB-Report</title>
      <number>13-64</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>optimal control</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>trajectory storage</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>mesh compression</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>compression</value>
    </subject>
    <collection role="msc" number="65M60">Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods</collection>
    <collection role="msc" number="68P05">Data structures</collection>
    <collection role="msc" number="68P30">Coding and information theory (compaction, compression, models of communication, encoding schemes, etc.) [See also 94Axx]</collection>
    <collection role="msc" number="94A29">Source coding [See also 68P30]</collection>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="institutes" number="compmed">Computational Medicine</collection>
    <collection role="persons" number="weiser">Weiser, Martin</collection>
    <collection role="projects" number="MATHEON-F9">MATHEON-F9</collection>
    <collection role="projects" number="ZIB-Kaskade7">ZIB-Kaskade7</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/4269/ZR13-64.pdf</file>
  </doc>
  <doc>
    <id>6975</id>
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    <language>eng</language>
    <pageFirst/>
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    <issue/>
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    <type>reportzib</type>
    <publisherName/>
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    <belongsToBibliography>0</belongsToBibliography>
    <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>7551</id>
    <completedYear/>
    <publishedYear>2020</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
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    <completedDate>--</completedDate>
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    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Towards Shape-based Knee Osteoarthritis Classification using Graph Convolutional Networks</title>
    <abstract language="eng">We present a transductive learning approach for morphometric osteophyte grading based on geometric deep learning. We formulate the grading task as semi-supervised node classification problem on a graph embedded in shape space. To account for the high-dimensionality and non-Euclidean structure of shape space we employ a combination of an intrinsic dimension reduction together with a graph convolutional neural network. We demonstrate the performance of our derived classifier in comparisons to an alternative extrinsic approach.</abstract>
    <parentTitle language="eng">2020 IEEE 17th International Symposium on Biomedical Imaging (ISBI 2020)</parentTitle>
    <identifier type="arxiv">1910.06119</identifier>
    <identifier type="doi">10.1109/ISBI45749.2020.9098687</identifier>
    <enrichment key="PeerReviewed">yes</enrichment>
    <enrichment key="AcceptedDate">2020-01-06</enrichment>
    <author>Christoph von Tycowicz</author>
    <submitter>Christoph von Tycowicz</submitter>
    <collection role="institutes" number="vis">Visual Data Analysis</collection>
    <collection role="persons" number="vontycowicz">Tycowicz, Christoph von</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>
    <collection role="projects" number="Math+EF1-18">Math+EF1-18</collection>
  </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/>
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    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <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/>
    <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="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>
    <collection role="institutes" number="GDAP">Geometric Data Analysis and Processing</collection>
  </doc>
  <doc>
    <id>7834</id>
    <completedYear/>
    <publishedYear>2020</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>617</pageFirst>
    <pageLast>626</pageLast>
    <pageNumber>10</pageNumber>
    <edition/>
    <issue/>
    <volume/>
    <type>conferenceobject</type>
    <publisherName>Springer International Publishing</publisherName>
    <publisherPlace>Cham</publisherPlace>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2020-09-29</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Nonlinear Regression on Manifolds for Shape Analysis using Intrinsic Bézier Splines</title>
    <abstract language="eng">Intrinsic and parametric regression models are of high interest for the statistical analysis of manifold-valued data such as images and shapes. The standard linear ansatz has been generalized to geodesic regression on manifolds making it possible to analyze dependencies of random variables that spread along generalized straight lines. Nevertheless, in some scenarios, the evolution of the data cannot be modeled adequately by a geodesic.&#13;
We present a framework for nonlinear regression on manifolds by considering Riemannian splines, whose segments are Bézier curves, as trajectories.&#13;
Unlike variational formulations that require time-discretization, we take a constructive approach that provides efficient and exact evaluation by virtue of the generalized de Casteljau algorithm.&#13;
We validate our method in experiments on the reconstruction of periodic motion of the mitral valve as well as the analysis of femoral shape changes during the course of osteoarthritis, endorsing Bézier spline regression as an effective and flexible tool for manifold-valued regression.</abstract>
    <parentTitle language="eng">Proc. Medical Image Computing and Computer Assisted Intervention (MICCAI)</parentTitle>
    <identifier type="arxiv">2007.05275</identifier>
    <identifier type="doi">10.1007/978-3-030-59719-1_60</identifier>
    <enrichment key="PeerReviewed">yes</enrichment>
    <enrichment key="AcceptedDate">2020-05-18</enrichment>
    <author>Martin Hanik</author>
    <submitter>Christoph von Tycowicz</submitter>
    <author>Hans-Christian Hege</author>
    <author>Anja Hennemuth</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>
  <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>
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    <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>
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    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>2019-08-28</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">An as-invariant-as-possible GL+(3)-based Statistical Shape Model</title>
    <abstract language="eng">We describe a novel nonlinear statistical shape model basedon differential coordinates viewed as elements of GL+(3). We adopt an as-invariant-as possible framework comprising a bi-invariant Lie group mean and a tangent principal component analysis based on a unique GL+(3)-left-invariant, O(3)-right-invariant metric. Contrary to earlier work that equips the coordinates with a specifically constructed group structure, our method employs the inherent geometric structure of the group-valued data and therefore features an improved statistical power in identifying shape differences. We demonstrate this in experiments on two anatomical datasets including comparison to the standard Euclidean as well as recent state-of-the-art nonlinear approaches to statistical shape modeling.</abstract>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-74566</identifier>
    <author>Felix Ambellan</author>
    <submitter>Felix Ambellan</submitter>
    <author>Stefan Zachow</author>
    <author>Christoph von Tycowicz</author>
    <series>
      <title>ZIB-Report</title>
      <number>19-46</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Statistical shape analysis</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Tangent principal component analysis</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Lie groups</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Classification</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Manifold valued statistics</value>
    </subject>
    <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="persons" number="vontycowicz">Tycowicz, Christoph von</collection>
    <collection role="persons" number="ambellan">Ambellan, Felix</collection>
    <collection role="projects" number="MathPlus-TrU-1">MathPlus-TrU-1</collection>
    <collection role="projects" number="MathPlus-EF2-3">MathPlus-EF2-3</collection>
    <collection role="institutes" number="VDcC">Visual and Data-centric Computing</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/7456/ZIBReport_19-46.pdf</file>
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