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  <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>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <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>9861</id>
    <completedYear/>
    <publishedYear>2024</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume>24</volume>
    <type>article</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Shape-based Disease Grading via Functional Maps and Graph Convolutional Networks with Application to Alzheimer’s Disease</title>
    <abstract language="eng">Shape analysis provides methods for understanding anatomical structures extracted from medical images. However, the underlying notions of shape spaces that are frequently employed come with strict assumptions prohibiting the analysis of incomplete and/or topologically varying shapes. This work aims to alleviate these limitations by adapting the concept of functional maps. Further, we present a graph-based learning approach for morphometric classification of disease states that uses novel shape descriptors based on this concept. We demonstrate the performance of the derived classifier on the open-access ADNI database differentiating normal controls and subjects with Alzheimer’s disease. Notably, the experiments show that our approach can improve over state-of-the-art from geometric deep learning.</abstract>
    <parentTitle language="eng">BMC Medical Imaging</parentTitle>
    <identifier type="doi">10.1186/s12880-024-01513-z</identifier>
    <enrichment key="PeerReviewed">yes</enrichment>
    <enrichment key="AcceptedDate">2024-11-21</enrichment>
    <enrichment key="opus.source">publish</enrichment>
    <author>Julius Mayer</author>
    <submitter>Christoph von Tycowicz</submitter>
    <author>Daniel Baum</author>
    <author>Felix Ambellan</author>
    <author>Christoph von Tycowicz</author>
    <author> for the Alzheimer’s Disease Neuroimaging Initiative</author>
    <collection role="persons" number="baum">Baum, Daniel</collection>
    <collection role="persons" number="vontycowicz">Tycowicz, Christoph von</collection>
    <collection role="persons" number="ambellan">Ambellan, Felix</collection>
    <collection role="institutes" number="VDcC">Visual and Data-centric Computing</collection>
    <collection role="persons" number="mayer">Mayer, Julius Marcus</collection>
    <collection role="projects" number="MathPlus-EF2-5">MathPlus-EF2-5</collection>
  </doc>
  <doc>
    <id>8518</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>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>9183</id>
    <completedYear/>
    <publishedYear>2023</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>211</pageFirst>
    <pageLast>222</pageLast>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>conferenceobject</type>
    <publisherName>Springer Nature</publisherName>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Predicting Shape Development: A Riemannian Method</title>
    <abstract language="eng">Predicting the future development of an anatomical shape from a single baseline observation is a challenging task. But it can be essential for clinical decision-making. Research has shown that it should be tackled in curved shape spaces, as (e.g., disease-related) shape changes frequently expose nonlinear characteristics. We thus propose a novel prediction method that encodes the whole shape in a Riemannian shape space. It then learns a simple prediction technique founded on hierarchical statistical modeling of longitudinal training data. When applied to predict the future development of the shape of the right hippocampus under Alzheimer's disease and to human body motion, it outperforms deep learning-supported variants as well as state-of-the-art.</abstract>
    <parentTitle language="eng">Shape in Medical Imaging</parentTitle>
    <identifier type="arxiv">2212.04740</identifier>
    <identifier type="doi">10.1007/978-3-031-46914-5_17</identifier>
    <enrichment key="PeerReviewed">yes</enrichment>
    <enrichment key="AcceptedDate">2023-08-07</enrichment>
    <enrichment key="opus.source">publish</enrichment>
    <author>Doğa Türkseven</author>
    <submitter>Martin Hanik</submitter>
    <author>Islem Rekik</author>
    <author>Christoph von Tycowicz</author>
    <author>Martin Hanik</author>
    <collection role="persons" number="vontycowicz">Tycowicz, Christoph von</collection>
    <collection role="persons" number="hanik">Hanik, Martin</collection>
    <collection role="institutes" number="VDcC">Visual and Data-centric Computing</collection>
    <collection role="projects" number="Math+EF1-18">Math+EF1-18</collection>
  </doc>
  <doc>
    <id>9094</id>
    <completedYear/>
    <publishedYear>2023</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>1</pageFirst>
    <pageLast>26</pageLast>
    <pageNumber/>
    <edition/>
    <issue>4</issue>
    <volume>16</volume>
    <type>article</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Intrinsic shape analysis in archaeology: A case study on ancient sundials</title>
    <abstract language="eng">The fact that the physical shapes of man-made objects are subject to overlapping influences—such as technological, economic, geographic, and stylistic progressions—holds great information potential. On the other hand, it is also a major analytical challenge to uncover these overlapping trends and to disentagle them in an unbiased way. This paper explores a novel mathematical approach to extract archaeological insights from ensembles of similar artifact shapes. We show that by considering all shape information in a find collection, it is possible to identify shape patterns that would be difficult to discern by considering the artifacts individually or by classifying shapes into predefined archaeological types and analyzing the associated distinguishing characteristics. Recently, series of high-resolution digital representations of artifacts have become available. Such data sets enable the application of extremely sensitive and flexible methods of shape analysis. We explore this potential on a set of 3D models of ancient Greek and Roman sundials, with the aim of providing alternatives to the traditional archaeological method of “trend extraction by ordination” (typology). In the proposed approach, each 3D shape is represented as a point in a shape space—a high-dimensional, curved, non-Euclidean space. Proper consideration of its mathematical properties reduces bias in data analysis and thus improves analytical power. By performing regression in shape space, we find that for Roman sundials, the bend of the shadow-receiving surface of the sundials changes with the latitude of the location. This suggests that, apart from the inscribed hour lines, also a sundial’s shape was adjusted to the place of installation. As an example of more advanced inference, we use the identified trend to infer the latitude at which a sundial, whose location of installation is unknown, was placed. We also derive a novel method for differentiated morphological trend assertion, building upon and extending the theory of geometric statistics and shape analysis. Specifically, we present a regression-based method for statistical normalization of shapes that serves as a means of disentangling parameter-dependent effects (trends) and unexplained variability. In addition, we show that this approach is robust to noise in the digital reconstructions of the artifact shapes.</abstract>
    <parentTitle language="eng">Journal on Computing and Cultural Heritage</parentTitle>
    <identifier type="arxiv">2305.18960</identifier>
    <identifier type="doi">10.1145/3606698</identifier>
    <enrichment key="PeerReviewed">yes</enrichment>
    <enrichment key="AcceptedDate">2023-05-23</enrichment>
    <enrichment key="opus.source">publish</enrichment>
    <author>Martin Hanik</author>
    <submitter>Martin Hanik</submitter>
    <author>Benjamin Ducke</author>
    <author>Hans-Christian Hege</author>
    <author>Friederike Fless</author>
    <author>Christoph von Tycowicz</author>
    <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>
  <doc>
    <id>10066</id>
    <completedYear/>
    <publishedYear>2025</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume>16034</volume>
    <type>conferenceobject</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2025-10-25</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Tree inference with varifold distances</title>
    <abstract language="eng">In this paper, we consider a tree inference problem motivated by the critical problem in single-cell genomics of reconstructing dynamic cellular processes from sequencing data. In particular, given a population of cells sampled from such a process, we are interested in the problem of ordering the cells according to their progression in the process. This is known as trajectory inference. If the process is differentiation, this amounts to reconstructing the corresponding differentiation tree. One way of doing this in practice is to estimate the shortest-path distance between nodes based on cell similarities observed in sequencing data. Recent sequencing techniques make it possible to measure two types of data: gene expression levels, and RNA velocity, a vector that predicts changes in gene expression. The data then consist of a discrete vector field on a (subset of a) Euclidean space of dimension equal to the number of genes under consideration. By integrating this velocity field, we trace the evolution of gene expression levels in each single cell from some initial stage to its current stage. Eventually, we assume that we have a faithful embedding of the differentiation tree in a Euclidean space, but which we only observe through the curves representing the paths from the root to the nodes. Using varifold distances between such curves, we define a similarity measure between nodes which we prove approximates the shortest-path distance in a tree that is isomorphic to the target tree.</abstract>
    <parentTitle language="eng">Geometric Science of Information. GSI 2025</parentTitle>
    <identifier type="arxiv">2507.11313</identifier>
    <identifier type="doi">10.1007/978-3-032-03921-7_30</identifier>
    <enrichment key="Series">Lecture Notes in Computer Science</enrichment>
    <enrichment key="PeerReviewed">yes</enrichment>
    <enrichment key="AcceptedDate">2025-06-27</enrichment>
    <enrichment key="opus.source">publish</enrichment>
    <author>Elodie Maignant</author>
    <submitter>Christoph von Tycowicz</submitter>
    <author>Tim Conrad</author>
    <author>Christoph von Tycowicz</author>
    <collection role="persons" number="conrad">Conrad, Tim</collection>
    <collection role="persons" number="vontycowicz">Tycowicz, Christoph von</collection>
    <collection role="institutes" number="VDcC">Visual and Data-centric Computing</collection>
    <collection role="persons" number="maignant">Maignant, Elodie</collection>
    <collection role="projects" number="MathPlus-AA1-20">MathPlus-AA1-20</collection>
  </doc>
  <doc>
    <id>8154</id>
    <completedYear/>
    <publishedYear>2021</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>177</pageFirst>
    <pageLast>188</pageLast>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>conferenceobject</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2021-06-14</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Geodesic B-Score for Improved Assessment of Knee Osteoarthritis</title>
    <abstract language="eng">Three-dimensional medical imaging enables detailed understanding of osteoarthritis structural status. However, there remains a vast need for automatic, thus, reader-independent measures that provide reliable assessment of subject-specific clinical outcomes. To this end, we derive a consistent generalization of the recently proposed B-score to Riemannian shape spaces. We further present an algorithmic treatment yielding simple, yet efficient computations allowing for analysis of large shape populations with several thousand samples. Our intrinsic formulation exhibits improved discrimination ability over its Euclidean counterpart, which we demonstrate for predictive validity on assessing risks of total knee replacement. This result highlights the potential of the geodesic B-score to enable improved personalized assessment and stratification for interventions.</abstract>
    <parentTitle language="eng">Proc. Information Processing in Medical Imaging (IPMI)</parentTitle>
    <identifier type="arxiv">2104.01107</identifier>
    <identifier type="doi">10.1007/978-3-030-78191-0_14</identifier>
    <enrichment key="Series">Lecture Notes in Computer Science</enrichment>
    <enrichment key="PeerReviewed">yes</enrichment>
    <enrichment key="AcceptedDate">2021-02-12</enrichment>
    <enrichment key="opus.source">publish</enrichment>
    <enrichment key="PreprintUrn">urn:nbn:de:0297-zib-81930</enrichment>
    <author>Felix Ambellan</author>
    <submitter>Felix Ambellan</submitter>
    <author>Stefan Zachow</author>
    <author>Christoph von Tycowicz</author>
    <collection role="institutes" number="vis">Visual Data Analysis</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="BIFOLD">BIFOLD</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>8346</id>
    <completedYear/>
    <publishedYear>2022</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>1</pageFirst>
    <pageLast>11</pageLast>
    <pageNumber/>
    <edition/>
    <issue>1</issue>
    <volume>12</volume>
    <type>article</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2022-08-02</completedDate>
    <publishedDate>2022-08-02</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">PCL insufficient patients with increased translational and rotational passive knee joint laxity have no increased range of anterior–posterior and rotational tibiofemoral motion during level walking</title>
    <parentTitle language="eng">Scientific Reports</parentTitle>
    <identifier type="doi">10.1038/s41598-022-17328-3</identifier>
    <enrichment key="PeerReviewed">yes</enrichment>
    <enrichment key="AcceptedDate">2022-07-25</enrichment>
    <enrichment key="FulltextUrl">https://doi.org/10.1038/s41598-022-17328-3</enrichment>
    <licence>Creative Commons - CC BY - Namensnennung 4.0 International</licence>
    <author>Stephan Oehme</author>
    <submitter>Rainald Ehrig</submitter>
    <author>Philippe Moewis</author>
    <author>Heide Boeth</author>
    <author>Benjamin Bartek</author>
    <author>Annika Lippert</author>
    <author>Christoph von Tycowicz</author>
    <author>Rainald Ehrig</author>
    <author>Georg Duda</author>
    <author>Tobias Jung</author>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="institutes" number="compsys">Computational Systems Biology</collection>
    <collection role="persons" number="ehrig">Ehrig, Rainald</collection>
    <collection role="projects" number="DFG-Knee-Laxity">DFG-Knee-Laxity</collection>
    <collection role="persons" number="vontycowicz">Tycowicz, Christoph von</collection>
    <collection role="institutes" number="MSoCP">Modeling and Simulation of Complex Processes</collection>
    <collection role="institutes" number="VDcC">Visual and Data-centric Computing</collection>
  </doc>
  <doc>
    <id>8284</id>
    <completedYear/>
    <publishedYear>2021</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>1</pageFirst>
    <pageLast>20</pageLast>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume>100</volume>
    <type>article</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">SHREC 2021: Retrieval of Cultural Heritage Objects</title>
    <abstract language="eng">This paper presents the methods and results of the SHREC’21 contest on a dataset of cultural heritage (CH) objects. We present a dataset of 938 scanned models that have varied geometry and artistic styles. For the competition, we propose two challenges: the retrieval-by-shape challenge and the retrieval-by-culture challenge. The former aims at evaluating the ability of retrieval methods to discriminate cultural heritage objects by overall shape. The latter focuses on assessing the effectiveness of retrieving objects from the same culture. Both challenges constitute a suitable scenario to evaluate modern shape retrieval methods in a CH domain. Ten groups participated in the contest: thirty runs were submitted for the retrieval-by-shape task, and twenty-six runs were submitted for the retrieval-by-culture challenge. The results show a predominance of learning methods on image-based multi-view representations to characterize 3D objects. Nevertheless, the problem presented in our challenges is far from being solved. We also identify the potential paths for further improvements and give insights into the future directions of research.</abstract>
    <parentTitle language="eng">Computers and Graphics</parentTitle>
    <identifier type="doi">10.1016/j.cag.2021.07.010</identifier>
    <enrichment key="PeerReviewed">yes</enrichment>
    <enrichment key="AcceptedDate">2021-07-12</enrichment>
    <enrichment key="opus.source">publish</enrichment>
    <author>Ivan Sipiran</author>
    <submitter>Christoph von Tycowicz</submitter>
    <author>Patrick Lazo</author>
    <author>Cristian Lopez</author>
    <author>Nihar Bagewadi</author>
    <author>Benjamin Bustos</author>
    <author>Hieu Dao</author>
    <author>Shankar Gangisetty</author>
    <author>Martin Hanik</author>
    <author>Ngoc-Phuong Ho-Thi</author>
    <author>Mike Holenderski</author>
    <author>Dmitri Jarnikov</author>
    <author>Arniel Labrada</author>
    <author>Stefan Lengauer</author>
    <author>Roxane Licandro</author>
    <author>Dinh-Huan Nguyen</author>
    <author>Thang-Long Nguyen-Ho</author>
    <author>Luis A. Pérez Rey</author>
    <author>Bang-Dang Pham</author>
    <author>Minh-Khoi Pham</author>
    <author>Reinhold Preiner</author>
    <author>Tobias Schreck</author>
    <author>Quoc-Huy Trinh</author>
    <author>Loek Tonnaer</author>
    <author>Christoph von Tycowicz</author>
    <author>The-Anh Vu-Le</author>
    <collection role="institutes" number="vis">Visual Data Analysis</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>
    <collection role="projects" number="Math+EF1-18">Math+EF1-18</collection>
  </doc>
  <doc>
    <id>8350</id>
    <completedYear/>
    <publishedYear>2021</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>article</type>
    <publisherName/>
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    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Patient specific resurfacing implant knee surgery in subjects with early osteoarthritis results in medial pivot and lateral femoral rollback during flexion: A retrospective pilot study</title>
    <abstract language="eng">Purpose. Metallic resurfacing implants have been developed for the treatment of early, focal, small, condylar and trochlear osteoarthritis (OA) lesions. They represent an option for patients who are either too young to fulfill the criteria for total knee arthroplasty (TKA) or too old for biological treatment. Although relevant clinical evidence has been collected for different resurfacing types, the in vivo post-operative knee kinematics remains unknown. The present study aims to measure and analyse the knee joint kinematics in subjects with patient-specific Episealer implants&#13;
Methods. Retrospective study design. Fluoroscopic analyses during high flexion activities (unloaded flexion-extension and loaded lunge) were conducted at &gt;12 months post-surgery in ten Episealer knees. The post-operative knee joint kinematics was compared to equally assessed kinematic from ten healthy knees, twenty G-Curve TKA knees and 10 J-Curve knees. Pre- and postoperative clinical data of the Episealer knees were collected using a visual analog scale (VAS), the EQ 5d Health Questionnaire and the Knee Injury and Osteoarthritis Outcome Score (KOOS).&#13;
Results. During unloaded flexion-extension and loaded lunge, the medial condyle in the Episealer knees remained relative stationary, indicating a medial pivot, while the lateral condyle translated consistently towards posterior. Similarly, reduced movement of the medial condyle and posterior translation of the lateral condyle was also observed in the healthy knees, although to a lesser extent. In contrast, the kinematics of both TKA cohorts during unloaded flexion-extension showed a tendency towards anterior displacement in the medial compartment, which led to significant differences in comparison with the Episealer knees. In the lateral compartment, a certain degree of femoral rollback was noted in the G-Curve TKA cohort. Improved scores were observed in the Episealer subjects between the preoperative and 1-year postoperative follow-up.&#13;
Conclusion. At 12 months postsurgery, a physiological-like knee kinematics was observed in the group of patient-specific reconstructed chondral/osteochondral lesions by means of a resurfacing Episealer implant strategy. Considering that these patients are physically active and do not fulfill the criteria for TKA, the group is hard to be compared to TKA patients which usually are less active and more challenging. Nevertheless, the comparison to either healthy knee kinematics as well as to TKA reconstructed knees with different implant designs showed a more physiological-like kinematics in the resurfacing implants that seems more appropriate for such a patient group. Despite positive results, careful clinical follow-up of treated patients is recommended for the long-term OA progression. Further investigations need to be encouraged not only in larger patient groups but also in a prospective manner to assess the pre- to postoperative kinematic changes.</abstract>
    <parentTitle language="eng">Knee Surgery, Sports Traumatology, Arthroscopy</parentTitle>
    <identifier type="doi">10.1007/s00167-021-06749-8</identifier>
    <enrichment key="PeerReviewed">yes</enrichment>
    <enrichment key="AcceptedDate">2021-09-09</enrichment>
    <enrichment key="opus.source">publish</enrichment>
    <author>Philippe Moewis</author>
    <submitter>Christoph von Tycowicz</submitter>
    <author>René Kaiser</author>
    <author>Adam Trepczynski</author>
    <author>Christoph von Tycowicz</author>
    <author>Leonie Krahl</author>
    <author>Ansgar Ilg</author>
    <author>Johannes Holz</author>
    <author>Georg Duda</author>
    <collection role="institutes" number="vis">Visual Data Analysis</collection>
    <collection role="projects" number="DFG-Knee-Laxity">DFG-Knee-Laxity</collection>
    <collection role="persons" number="vontycowicz">Tycowicz, Christoph von</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>8425</id>
    <completedYear/>
    <publishedYear>2022</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>researchdata</type>
    <publisherName/>
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    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Triangle meshes of shadow-recieving surfaces of ancient sundials</title>
    <abstract language="eng">This repository contains triangle meshes of the shadow-recieving surfaces of 13 ancient sundials; three of them are from Greece and 10 from Italy. The meshes are in correspondence.</abstract>
    <identifier type="doi">10.12752/8425</identifier>
    <enrichment key="ScientificResourceTypeGeneral">Dataset</enrichment>
    <enrichment key="ScientificGeolocation">Italy, Greece</enrichment>
    <enrichment key="ScientificDateCreated">October 2020</enrichment>
    <enrichment key="SoftwareDescription">MeshLab, Amira</enrichment>
    <enrichment key="opus.source">publish</enrichment>
    <enrichment key="zib_DownloadUrl">https://www.zib.de/ext-data/sundial_shadow_surfaces/meshes.zip</enrichment>
    <licence>Creative Commons - CC BY-NC-SA - Namensnennung - Nicht kommerziell -  Weitergabe unter gleichen Bedingungen 4.0 International</licence>
    <author>Martin Hanik</author>
    <submitter>Martin Hanik</submitter>
    <author>Christoph von Tycowicz</author>
    <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>
  <doc>
    <id>9026</id>
    <completedYear/>
    <publishedYear>2023</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>102220</pageFirst>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume>104</volume>
    <type>article</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Sasaki Metric for Spline Models of Manifold-Valued Trajectories</title>
    <abstract language="eng">We propose a generic spatiotemporal framework to analyze manifold-valued measurements, which allows for employing an intrinsic and computationally efficient Riemannian hierarchical model. Particularly, utilizing regression, we represent discrete trajectories in a Riemannian manifold by composite Bézier splines, propose a natural metric induced by the Sasaki metric to compare the trajectories, and estimate average trajectories as group-wise trends. We evaluate our framework in comparison to state-of-the-art methods within qualitative and quantitative experiments on hurricane tracks. Notably, our results demonstrate the superiority of spline-based approaches for an intensity classification of the tracks.</abstract>
    <parentTitle language="eng">Computer Aided Geometric Design</parentTitle>
    <identifier type="arxiv">arXiv:2303.17299</identifier>
    <identifier type="doi">10.1016/j.cagd.2023.102220</identifier>
    <enrichment key="PeerReviewed">yes</enrichment>
    <enrichment key="AcceptedDate">29.03.2023</enrichment>
    <enrichment key="opus.source">publish</enrichment>
    <author>Esfandiar Navayazdani</author>
    <submitter>Martin Hanik</submitter>
    <author>Felix Ambellan</author>
    <author>Martin Hanik</author>
    <author>Christoph von Tycowicz</author>
    <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="institutes" number="VDcC">Visual and Data-centric Computing</collection>
    <collection role="projects" number="DDESAMT">DDESAMT</collection>
  </doc>
  <doc>
    <id>8193</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>--</completedDate>
    <publishedDate>2021-03-29</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Geodesic B-Score for Improved Assessment of Knee Osteoarthritis</title>
    <abstract language="eng">Three-dimensional medical imaging enables detailed understanding of osteoarthritis structural status. However, there remains a vast need for automatic, thus, reader-independent measures that provide reliable assessment of subject-specific clinical outcomes. To this end, we derive a consistent generalization of the recently proposed B-score to Riemannian shape spaces. We further present an algorithmic treatment yielding simple, yet efficient computations allowing for analysis of large shape populations with several thousand samples. Our intrinsic formulation exhibits improved discrimination ability over its Euclidean counterpart, which we demonstrate for predictive validity on assessing risks of total knee replacement. This result highlights the potential of the geodesic B-score to enable improved personalized assessment and stratification for interventions.</abstract>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-81930</identifier>
    <enrichment key="opus.source">publish</enrichment>
    <author>Felix Ambellan</author>
    <submitter>Felix Ambellan</submitter>
    <author>Stefan Zachow</author>
    <author>Christoph von Tycowicz</author>
    <series>
      <title>ZIB-Report</title>
      <number>21-09</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Statistical shape analysis</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Osteoarthritis</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Geometric statistics</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Riemannian manifolds</value>
    </subject>
    <collection role="institutes" number="vis">Visual Data Analysis</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="BIFOLD">BIFOLD</collection>
    <collection role="institutes" number="VDcC">Visual and Data-centric Computing</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/8193/ZIBReport_21-09.pdf</file>
    <file>https://opus4.kobv.de/opus4-zib/files/8193/ZIBReport_21-09_suppl.zip</file>
  </doc>
  <doc>
    <id>8789</id>
    <completedYear/>
    <publishedYear>2022</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>85</pageFirst>
    <pageLast>95</pageLast>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume>194</volume>
    <type>conferenceobject</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">A Soft-Correspondence Approach to Shape-based Disease Grading with Graph Convolutional Networks</title>
    <abstract language="eng">Shape analysis provides principled means for understanding anatomical structures from medical images. The underlying notions of shape spaces, however, come with strict assumptions prohibiting the analysis of incomplete and/or topologically varying shapes. This work aims to alleviate these limitations by adapting the concept of soft correspondences. In particular, we present a graph-based learning approach for morphometric classification of disease states that is based on a generalized notion of shape correspondences in terms of functional maps. We demonstrate the performance of the derived classifier on the open-access ADNI database for differentiating normal controls and subjects with Alzheimer’s disease. Notably, our experiment shows that our approach can improve over state-of-the-art from geometric deep learning.</abstract>
    <parentTitle language="eng">Proceedings of Machine Learning Research</parentTitle>
    <enrichment key="PeerReviewed">yes</enrichment>
    <enrichment key="AcceptedDate">2022-10-06</enrichment>
    <enrichment key="opus.source">publish</enrichment>
    <enrichment key="FulltextUrl">https://openreview.net/pdf?id=Wa6mfpfr29o</enrichment>
    <author>Julius Mayer</author>
    <submitter>Julius Mayer</submitter>
    <author>Daniel Baum</author>
    <author>Felix Ambellan</author>
    <author>Christoph von Tycowicz</author>
    <collection role="persons" number="baum">Baum, Daniel</collection>
    <collection role="persons" number="vontycowicz">Tycowicz, Christoph von</collection>
    <collection role="persons" number="ambellan">Ambellan, Felix</collection>
    <collection role="institutes" number="VDcC">Visual and Data-centric Computing</collection>
    <collection role="persons" number="mayer">Mayer, Julius Marcus</collection>
    <collection role="projects" number="MathPlus-EF2-5">MathPlus-EF2-5</collection>
  </doc>
  <doc>
    <id>9557</id>
    <completedYear/>
    <publishedYear>2024</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue>9</issue>
    <volume>69</volume>
    <type>article</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Joint Reconstruction and Segmentation in Undersampled 3D Knee MRI combining Shape Knowledge and Deep Learning</title>
    <abstract language="eng">Task-adapted image reconstruction methods using end-to-end trainable neural networks (NNs) have been proposed to optimize reconstruction for subsequent processing tasks, such as segmentation. However, their training typically requires considerable hardware resources and thus, only relatively simple building blocks, e.g. U-Nets, are typically used, which, albeit powerful, do not integrate model-specific knowledge.&#13;
In this work, we extend an end-to-end trainable task-adapted image reconstruction method for a clinically realistic reconstruction and segmentation problem of bone and cartilage in 3D knee MRI by incorporating statistical shape models (SSMs). The SSMs model the prior information and help to regularize the segmentation maps as a final post-processing step.&#13;
We compare the proposed method to a state-of-the-art (SOTA) simultaneous multitask learning approach for image reconstruction and segmentation (MTL) and to a complex SSMs-informed segmentation pipeline (SIS). &#13;
Our experiments show that the combination of joint end-to-end training and SSMs to further regularize the segmentation maps obtained by MTL highly improves the results, especially in terms of mean and maximal surface errors.&#13;
In particular, we achieve the segmentation quality of SIS and, at the same time, a substantial model reduction that yields a five-fold decimation in model parameters and a computational speedup of an order of magnitude.&#13;
Remarkably, even for undersampling factors of up to R=8, the obtained segmentation maps are of comparable quality to those obtained by SIS from ground-truth images.</abstract>
    <parentTitle language="eng">Physics in Medicine and Biology</parentTitle>
    <identifier type="doi">10.1088/1361-6560/ad3797</identifier>
    <enrichment key="PeerReviewed">yes</enrichment>
    <enrichment key="AcceptedDate">2024-03-14</enrichment>
    <enrichment key="opus.source">publish</enrichment>
    <enrichment key="FulltextUrl">https://iopscience.iop.org/article/10.1088/1361-6560/ad3797/pdf</enrichment>
    <author>Andreas Kofler</author>
    <submitter>Christoph von Tycowicz</submitter>
    <author>Christian Wald</author>
    <author>Christoph Kolbitsch</author>
    <author>Christoph von Tycowicz</author>
    <author>Felix Ambellan</author>
    <collection role="persons" number="vontycowicz">Tycowicz, Christoph von</collection>
    <collection role="persons" number="ambellan">Ambellan, Felix</collection>
    <collection role="institutes" number="VDcC">Visual and Data-centric Computing</collection>
    <collection role="projects" number="Math+EF1-18">Math+EF1-18</collection>
  </doc>
  <doc>
    <id>9468</id>
    <completedYear/>
    <publishedYear>2024</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>102288</pageFirst>
    <pageLast/>
    <pageNumber>24</pageNumber>
    <edition/>
    <issue/>
    <volume>110</volume>
    <type>article</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">De Casteljau's Algorithm in Geometric Data Analysis: Theory and Application</title>
    <abstract language="eng">For decades, de Casteljau's algorithm has been used as a fundamental building block in curve and surface design and has found a wide range of applications in fields such as scientific computing, and discrete geometry to name but a few. With increasing interest in nonlinear data science, its constructive approach has been shown to provide a principled way to generalize parametric smooth curves to manifolds. These curves have found remarkable new applications in the analysis of parameter-dependent, geometric data. This article provides a survey of the recent theoretical developments in this exciting area as well as its applications in fields such as geometric morphometrics and longitudinal data analysis in medicine, archaeology, and meteorology.</abstract>
    <parentTitle language="eng">Computer Aided Geometric Design</parentTitle>
    <identifier type="arxiv">2402.07550</identifier>
    <identifier type="doi">10.1016/j.cagd.2024.102288</identifier>
    <enrichment key="PeerReviewed">yes</enrichment>
    <enrichment key="opus.source">publish</enrichment>
    <author>Martin Hanik</author>
    <submitter>Martin Hanik</submitter>
    <author>Esfandiar Navayazdani</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="projects" number="DDESAMT">DDESAMT</collection>
    <collection role="projects" number="Math+EF1-18">Math+EF1-18</collection>
  </doc>
  <doc>
    <id>9363</id>
    <completedYear/>
    <publishedYear>2024</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>article</type>
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    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Manifold GCN: Diffusion-based Convolutional Neural Network for Manifold-valued Graphs</title>
    <abstract language="eng">We propose two graph neural network layers for graphs with features in a Riemannian manifold. First, based on a manifold-valued graph diffusion equation, we construct a diffusion layer that can be applied to an arbitrary number of nodes and graph connectivity patterns. Second, we model a tangent multilayer perceptron by transferring ideas from the vector neuron framework to our general setting. Both layers are equivariant with respect to node permutations and isometries of the feature manifold. These properties have been shown to lead to a beneficial inductive bias in many deep learning tasks. Numerical examples on synthetic data as well as on triangle meshes of the right hippocampus to classify Alzheimer's disease demonstrate the very good performance of our layers.</abstract>
    <identifier type="arxiv">2401.14381</identifier>
    <enrichment key="SubmissionStatus">under review</enrichment>
    <enrichment key="opus.source">publish</enrichment>
    <enrichment key="PeerReviewed">no</enrichment>
    <author>Martin Hanik</author>
    <submitter>Martin Hanik</submitter>
    <author>Gabriele Steidl</author>
    <author>Christoph von Tycowicz</author>
    <collection role="persons" number="vontycowicz">Tycowicz, Christoph von</collection>
    <collection role="persons" number="hanik">Hanik, Martin</collection>
    <collection role="institutes" number="VDcC">Visual and Data-centric Computing</collection>
    <collection role="projects" number="Math+EF1-18">Math+EF1-18</collection>
  </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>8615</id>
    <completedYear/>
    <publishedYear>2022</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>1223</pageFirst>
    <pageLast>1249</pageLast>
    <pageNumber/>
    <edition/>
    <issue>4</issue>
    <volume>4</volume>
    <type>article</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2022-11-15</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Bi-invariant Dissimilarity Measures for Sample Distributions in Lie Groups</title>
    <abstract language="eng">Data sets sampled in Lie groups are widespread, and as with multivariate data, it is important for many applications to assess the differences between the sets in terms of their distributions. Indices for this task are usually derived by considering the Lie group as a Riemannian manifold. Then, however, compatibility with the group operation is guaranteed only if a bi-invariant metric exists, which is not the case for most non-compact and non-commutative groups. We show here that if one considers an affine connection structure instead, one obtains bi-invariant generalizations of well-known dissimilarity measures: a Hotelling $T^2$ statistic, Bhattacharyya distance and Hellinger distance. Each of the dissimilarity measures matches its multivariate counterpart for Euclidean data and is translation-invariant, so that biases, e.g., through an arbitrary choice of reference, are avoided. We further derive non-parametric two-sample tests that are bi-invariant and consistent. We demonstrate the potential of these dissimilarity measures by performing group tests on data of knee configurations and epidemiological shape data. Significant differences are revealed in both cases.</abstract>
    <parentTitle language="eng">SIAM Journal on Mathematics of Data Science</parentTitle>
    <identifier type="doi">10.1137/21M1410373</identifier>
    <identifier type="arxiv">2402.12901</identifier>
    <enrichment key="PeerReviewed">yes</enrichment>
    <enrichment key="AcceptedDate">09.03.2022</enrichment>
    <enrichment key="opus.source">publish</enrichment>
    <author>Martin Hanik</author>
    <submitter>Martin Hanik</submitter>
    <author>Hans-Christian Hege</author>
    <author>Christoph von Tycowicz</author>
    <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>
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  <doc>
    <id>8723</id>
    <completedYear/>
    <publishedYear>2022</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>363</pageFirst>
    <pageLast>379</pageLast>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>conferenceobject</type>
    <publisherName>Springer Nature Switzerland</publisherName>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">A Kendall Shape Space Approach to 3D Shape Estimation from 2D Landmarks</title>
    <abstract language="eng">3D shapes provide substantially more information than 2D images. However, the acquisition of 3D shapes is sometimes very difficult or even impossible in comparison with acquiring 2D images, making it necessary to derive the 3D shape from 2D images. Although this is, in general, a mathematically ill-posed problem, it might be solved by constraining the problem formulation using prior information. Here, we present a new approach based on Kendall’s shape space to reconstruct 3D shapes from single monocular 2D images. The work is motivated by an application to study the feeding behavior of the basking shark, an endangered species whose massive size and mobility render 3D shape data nearly impossible to obtain, hampering understanding of their feeding behaviors and ecology. 2D images of these animals in feeding position, however, are readily available. We compare our approach with state-of-the-art shape-based approaches both on human stick models and on shark head skeletons. Using a small set of training shapes, we show that the Kendall shape space approach is substantially more robust than previous methods and always results in plausible shapes. This is essential for the motivating application in which specimens are rare and therefore only few training shapes are available.</abstract>
    <parentTitle language="eng">Computer Vision -- ECCV 2022</parentTitle>
    <identifier type="arxiv">2207.12687</identifier>
    <identifier type="doi">10.1007/978-3-031-20086-1_21</identifier>
    <enrichment key="PeerReviewed">yes</enrichment>
    <enrichment key="AcceptedDate">2022-07-03</enrichment>
    <enrichment key="opus.source">publish</enrichment>
    <author>Martha Paskin</author>
    <submitter>Christoph von Tycowicz</submitter>
    <author>Mason Dean</author>
    <author>Daniel Baum</author>
    <author>Christoph von Tycowicz</author>
    <collection role="institutes" number="vis">Visual Data Analysis</collection>
    <collection role="persons" number="baum">Baum, Daniel</collection>
    <collection role="persons" number="vontycowicz">Tycowicz, Christoph von</collection>
    <collection role="institutes" number="VDcC">Visual and Data-centric Computing</collection>
    <collection role="projects" number="MathPlus-EF2-5">MathPlus-EF2-5</collection>
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