<?xml version="1.0" encoding="utf-8"?>
<export-example>
  <doc>
    <id>6117</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>2016-11-29</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">A Riemannian Statistical Shape Model using Differential Coordinates</title>
    <abstract language="eng">We propose a novel Riemannian framework for statistical analysis of shapes that is able to account for the nonlinearity in shape variation. By adopting a physical perspective, we introduce a differential representation that puts the local geometric variability into focus. We model these differential coordinates as elements of a Lie group thereby endowing our shape space with a non-Euclidian structure. A key advantage of our framework is that statistics in a manifold shape space become numerically tractable improving performance by several orders of magnitude over state-of-the-art. We show that our Riemannian model is well suited for the identification of intra-population variability as well as inter-population differences. In particular, we demonstrate the superiority of the proposed model in experiments on specificity and generalization ability. We further derive a statistical shape descriptor that outperforms the standard Euclidian approach in terms of shape-based classification of morphological disorders.</abstract>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-61175</identifier>
    <identifier type="url">https://opus4.kobv.de/opus4-zib/frontdoor/index/index/docId/6485</identifier>
    <author>Christoph von Tycowicz</author>
    <submitter>Felix Ambellan</submitter>
    <author>Felix Ambellan</author>
    <author>Anirban Mukhopadhyay</author>
    <author>Stefan Zachow</author>
    <series>
      <title>ZIB-Report</title>
      <number>16-69</number>
    </series>
    <collection role="ccs" number="">Statistical computing</collection>
    <collection role="ccs" number="I.3.5">Computational Geometry and Object Modeling</collection>
    <collection role="msc" number="53-04">Explicit machine computation and programs (not the theory of computation or programming)</collection>
    <collection role="msc" number="62-04">Explicit machine computation and programs (not the theory of computation or programming)</collection>
    <collection role="msc" number="68U05">Computer graphics; computational geometry [See also 65D18]</collection>
    <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="projects" number="BMBF-TOKMIS">BMBF-TOKMIS</collection>
    <collection role="projects" number="DFG-Knee-Laxity">DFG-Knee-Laxity</collection>
    <collection role="persons" number="vontycowicz">Tycowicz, Christoph von</collection>
    <collection role="persons" number="ambellan">Ambellan, Felix</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/6117/ZIBReport_16-69.pdf</file>
  </doc>
  <doc>
    <id>4611</id>
    <completedYear/>
    <publishedYear>2015</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>263</pageFirst>
    <pageLast>287</pageLast>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>conferenceobject</type>
    <publisherName>Springer</publisherName>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Reducing Memory Requirements in Scientific Computing and Optimal Control</title>
    <parentTitle language="eng">Multiple Shooting and Time Domain Decomposition Methods</parentTitle>
    <enrichment key="PeerReviewed">yes</enrichment>
    <enrichment key="FulltextUrl">https://nbn-resolving.org/urn:nbn:de:0297-zib-42695</enrichment>
    <author>Sebastian Götschel</author>
    <submitter>Sebastian Götschel</submitter>
    <editor>T. Carraro</editor>
    <author>Christoph von Tycowicz</author>
    <editor>M. Geiger</editor>
    <author>Konrad Polthier</author>
    <editor>S. Koerkel</editor>
    <author>Martin Weiser</author>
    <editor>R. Rannacher</editor>
    <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>
    <collection role="persons" number="vontycowicz">Tycowicz, Christoph von</collection>
  </doc>
  <doc>
    <id>5950</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>2016-05-25</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Geometric Flows of Curves in Shape Space for Processing Motion of Deformable Objects</title>
    <abstract language="eng">We introduce techniques for the processing of motion and animations of non-rigid shapes. The idea is to regard animations of deformable objects as curves in shape space. Then, we use the geometric structure on shape space to transfer concepts from curve processing in R^n to the processing of motion of non-rigid shapes. Following this principle, we introduce a discrete geometric flow for curves in shape space. The flow iteratively replaces every shape with a weighted average shape of a local neighborhood and thereby globally decreases an energy whose minimizers are discrete geodesics in shape space. Based on the flow, we devise a novel smoothing filter for motions and animations of deformable shapes. By shortening the length in shape space of an animation, it systematically regularizes the deformations between consecutive frames of the animation. The scheme can be used for smoothing and noise removal, e.g., for reducing jittering artifacts in motion capture data. We introduce a reduced-order method for the computation of the flow. In addition to being efficient for the smoothing of curves, it is a novel scheme for computing geodesics in shape space. We use the scheme to construct non-linear “Bézier curves” by executing de Casteljau’s algorithm in shape space.</abstract>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-59504</identifier>
    <identifier type="doi">10.1111/cgf.12832</identifier>
    <author>Christopher Brandt</author>
    <submitter>Christoph von Tycowicz</submitter>
    <author>Christoph von Tycowicz</author>
    <author>Klaus Hildebrandt</author>
    <series>
      <title>ZIB-Report</title>
      <number>16-29</number>
    </series>
    <collection role="msc" number="53-XX">DIFFERENTIAL GEOMETRY (For differential topology, see 57Rxx. For foundational questions of differentiable manifolds, see 58Axx)</collection>
    <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="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/5950/ZIB-Report.pdf</file>
  </doc>
  <doc>
    <id>6923</id>
    <completedYear/>
    <publishedYear>2018</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>conferenceobject</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Ultra-short echo-time (UTE) imaging of the knee with curved surface reconstruction-based extraction of the patellar tendon</title>
    <abstract language="eng">Due to very short T2 relaxation times, imaging of tendons is typically performed using ultra-short echo-time (UTE) acquisition techniques. In this work, we combined an echo-train shifted multi-echo 3D UTE imaging sequence with a 3D curved surface reconstruction to virtually extract the patellar tendon from an acquired 3D UTE dataset. Based on the analysis of the acquired multi-echo data, a T2* relaxation time parameter map was calculated and interpolated to the curved surface of the patellar tendon.</abstract>
    <parentTitle language="eng">ISMRM (International Society for Magnetic Resonance in Medicine), 26th Annual Meeting 2018, Paris, France</parentTitle>
    <enrichment key="PeerReviewed">yes</enrichment>
    <enrichment key="AcceptedDate">2018-02-03</enrichment>
    <author>Martin Krämer</author>
    <submitter>Christoph von Tycowicz</submitter>
    <author>Marta Maggioni</author>
    <author>Christoph von Tycowicz</author>
    <author>Nick Brisson</author>
    <author>Stefan Zachow</author>
    <author>Georg Duda</author>
    <author>Jürgen Reichenbach</author>
    <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="projects" number="DFG_KneeKinematics">DFG_KneeKinematics</collection>
    <collection role="institutes" number="VDcC">Visual and Data-centric Computing</collection>
  </doc>
  <doc>
    <id>5452</id>
    <completedYear/>
    <publishedYear>2014</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>109:1</pageFirst>
    <pageLast>109:10</pageLast>
    <pageNumber/>
    <edition/>
    <issue>4</issue>
    <volume>33</volume>
    <type>article</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Animating Deformable Objects Using Sparse Spacetime Constraints</title>
    <abstract language="eng">We propose a scheme for animating deformable objects based on spacetime optimization. The main feature is that it robustly and quickly (within a few seconds) generates interesting motion from a sparse set of spacetime constraints. Providing only partial (as opposed to full) keyframes for positions and velocities is sufficient. The computed motion satisfies the constraints and the remaining degrees of freedom are determined by physical principles using elasticity and the spacetime constraints paradigm. Our modeling of the spacetime optimization problem combines dimensional reduction, modal coordinates, wiggly splines, and rotation strain warping. Controlling the warped motion requires the derivative of the warp map. We derive a representation of the derivative that can be efficiently and robustly evaluated. Our solver is based on a theorem that characterizes the solutions of the optimization problem and allows us to restrict the optimization to very low-dimensional search spaces. This treatment of the optimization problem avoids a time discretization and the resulting method can robustly deal with sparse input and wiggly motion.</abstract>
    <parentTitle language="eng">ACM Transactions on Graphics</parentTitle>
    <identifier type="doi">10.1145/2601097.2601156</identifier>
    <enrichment key="PeerReviewed">yes</enrichment>
    <author>Christian Schulz</author>
    <submitter>Christoph von Tycowicz</submitter>
    <author>Christoph von Tycowicz</author>
    <author>Hans-Peter Seidel</author>
    <author>Klaus Hildebrandt</author>
    <collection role="institutes" number="vis">Visual Data Analysis</collection>
    <collection role="institutes" number="medplan">Therapy Planning</collection>
    <collection role="persons" number="vontycowicz">Tycowicz, Christoph von</collection>
    <collection role="institutes" number="VDcC">Visual and Data-centric Computing</collection>
  </doc>
  <doc>
    <id>5473</id>
    <completedYear/>
    <publishedYear>2015</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>conferenceobject</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Measuring 3D knee dynamics using center out radial ultra-short echo time trajectories with a low cost experimental setup</title>
    <parentTitle language="deu">ISMRM (International Society for Magnetic Resonance in Medicine), 23rd Annual Meeting 2015, Toronto, Canada</parentTitle>
    <enrichment key="PeerReviewed">yes</enrichment>
    <author>Martin Krämer</author>
    <submitter> Stötzel</submitter>
    <author>Karl-Heinz Herrmann</author>
    <author>Heide Boeth</author>
    <author>Christoph von Tycowicz</author>
    <author>Christian König</author>
    <author>Stefan Zachow</author>
    <author>Rainald Ehrig</author>
    <author>Hans-Christian Hege</author>
    <author>Georg Duda</author>
    <author>Jürgen Reichenbach</author>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="institutes" number="vis">Visual Data Analysis</collection>
    <collection role="institutes" number="compsys">Computational Systems Biology</collection>
    <collection role="persons" number="ehrig">Ehrig, Rainald</collection>
    <collection role="persons" number="hege">Hege, Hans-Christian</collection>
    <collection role="persons" number="zachow">Zachow, Stefan</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>
  </doc>
  <doc>
    <id>5477</id>
    <completedYear/>
    <publishedYear>2013</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>213:1</pageFirst>
    <pageLast>213:10</pageLast>
    <pageNumber/>
    <edition/>
    <issue>6</issue>
    <volume>32</volume>
    <type>article</type>
    <publisherName>ACM</publisherName>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">An Efficient Construction of Reduced Deformable Objects</title>
    <abstract language="eng">Many efficient computational methods for physical simulation are based on model reduction. We propose new model reduction techniques for the approximation of reduced forces and for the construction of reduced shape spaces of deformable objects that accelerate the construction of a reduced dynamical system, increase the accuracy of the approximation, and simplify the implementation of model reduction. Based on the techniques, we introduce schemes for real-time simulation of deformable objects and interactive deformation-based editing of triangle or tet meshes. We demonstrate the effectiveness of the new techniques in different experiments with elastic solids and shells and compare them to alternative approaches.</abstract>
    <parentTitle language="eng">ACM Transactions on Graphics</parentTitle>
    <identifier type="doi">10.1145/2508363.2508392</identifier>
    <enrichment key="PeerReviewed">yes</enrichment>
    <author>Christoph von Tycowicz</author>
    <submitter>Christoph von Tycowicz</submitter>
    <author>Christian Schulz</author>
    <author>Hans-Peter Seidel</author>
    <author>Klaus Hildebrandt</author>
    <collection role="institutes" number="vis">Visual Data Analysis</collection>
    <collection role="persons" number="vontycowicz">Tycowicz, Christoph von</collection>
    <collection role="institutes" number="VDcC">Visual and Data-centric Computing</collection>
  </doc>
  <doc>
    <id>5479</id>
    <completedYear/>
    <publishedYear>2012</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>71:1</pageFirst>
    <pageLast>71:8</pageLast>
    <pageNumber/>
    <edition/>
    <issue>4</issue>
    <volume>31</volume>
    <type>article</type>
    <publisherName>ACM</publisherName>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Interactive spacetime control of deformable objects</title>
    <abstract language="eng">Creating motions of objects or characters that are physically plausible and follow an animator’s intent is a key task in computer animation. The spacetime constraints paradigm is a valuable approach to this problem, but it suffers from high computational costs. Based on spacetime constraints, we propose a technique that controls the motion of deformable objects and offers an interactive response. This is achieved by a model reduction of the underlying variational problem, which combines dimension reduction, multipoint linearization, and decoupling of ODEs. After a preprocess, the cost for creating or editing a motion is reduced to solving a number of one-dimensional spacetime problems, whose solutions are the wiggly splines introduced by Kass and Anderson [2008]. We achieve interactive response using a new fast and robust numerical scheme for solving a set of one-dimensional problems based on an explicit representation of the wiggly splines.</abstract>
    <parentTitle language="eng">ACM Transactions on Graphics</parentTitle>
    <identifier type="doi">10.1145/2185520.2185567</identifier>
    <enrichment key="PeerReviewed">yes</enrichment>
    <author>Klaus Hildebrandt</author>
    <submitter>Christoph von Tycowicz</submitter>
    <author>Christian Schulz</author>
    <author>Christoph von Tycowicz</author>
    <author>Konrad Polthier</author>
    <collection role="institutes" number="vis">Visual Data Analysis</collection>
    <collection role="institutes" number="visalgo">Visual Data Analysis in Science and Engineering</collection>
    <collection role="persons" number="vontycowicz">Tycowicz, Christoph von</collection>
    <collection role="institutes" number="VDcC">Visual and Data-centric Computing</collection>
  </doc>
  <doc>
    <id>5480</id>
    <completedYear/>
    <publishedYear>2011</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>119:1</pageFirst>
    <pageLast>119:11</pageLast>
    <pageNumber/>
    <edition/>
    <issue>5</issue>
    <volume>30</volume>
    <type>article</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Interactive surface modeling using modal analysis</title>
    <abstract language="eng">We propose a framework for deformation-based surface modeling that is interactive, robust and intuitive to use. The deformations are described by a non-linear optimization problem that models static states of elastic shapes under external forces which implement the user input. Interactive response is achieved by a combination of model reduction, a robust energy approximation, and an efficient quasi-Newton solver. Motivated by the observation that a typical modeling session requires only a fraction of the full shape space of the underlying model, we use second and third derivatives of a deformation energy to construct a low-dimensional shape space that forms the feasible set for the optimization. Based on mesh coarsening, we propose an energy approximation scheme with adjustable approximation quality. The quasi-Newton solver guarantees superlinear convergence without the need of costly Hessian evaluations during modeling. We demonstrate the effectiveness of the approach on different examples including the test suite introduced in [Botsch and Sorkine 2008].</abstract>
    <parentTitle language="eng">ACM Transactions on Graphics</parentTitle>
    <identifier type="doi">10.1145/2019627.2019638</identifier>
    <enrichment key="PeerReviewed">yes</enrichment>
    <enrichment key="PreprintUrn">https://nbn-resolving.org/urn:nbn:de:0296-matheon-8349</enrichment>
    <author>Klaus Hildebrandt</author>
    <submitter>Christoph von Tycowicz</submitter>
    <author>Christian Schulz</author>
    <author>Christoph von Tycowicz</author>
    <author>Konrad Polthier</author>
    <collection role="institutes" number="vis">Visual Data Analysis</collection>
    <collection role="persons" number="vontycowicz">Tycowicz, Christoph von</collection>
    <collection role="institutes" number="VDcC">Visual and Data-centric Computing</collection>
  </doc>
  <doc>
    <id>5481</id>
    <completedYear/>
    <publishedYear>2012</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>204</pageFirst>
    <pageLast>2018</pageLast>
    <pageNumber/>
    <edition/>
    <issue>5</issue>
    <volume>29</volume>
    <type>article</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Modal Shape Analysis beyond Laplacian</title>
    <abstract language="eng">In recent years, substantial progress in shape analysis has been achieved through methods that use the spectra and eigenfunctions of discrete Laplace operators. In this work, we study spectra and eigenfunctions of discrete differential operators that can serve as an alternative to the discrete Laplacians for applications in shape analysis. We construct such operators as the Hessians of surface energies, which operate on a function space on the surface, or of deformation energies, which operate on a shape space. In particular, we design a quadratic energy such that, on the one hand, its Hessian equals the Laplace operator if the surface is a part of the Euclidean plane, and, on the other hand, the Hessian eigenfunctions are sensitive to the extrinsic curvature (e.g. sharp bends) on curved surfaces. Furthermore, we consider eigenvibrations induced by deformation energies, and we derive a closed form representation for the Hessian (at the rest state of the energy) for a general class of deformation energies. Based on these spectra and eigenmodes, we derive two shape signatures. One that measures the similarity of points on a surface, and another that can be used to identify features of surfaces.</abstract>
    <parentTitle language="eng">Computer Aided Geometric Design</parentTitle>
    <identifier type="doi">10.1016/j.cagd.2012.01.001</identifier>
    <enrichment key="PeerReviewed">yes</enrichment>
    <enrichment key="FulltextUrl">https://nbn-resolving.org/urn:nbn:de:0296-matheon-9678</enrichment>
    <author>Klaus Hildebrandt</author>
    <submitter>Christoph von Tycowicz</submitter>
    <author>Christian Schulz</author>
    <author>Christoph von Tycowicz</author>
    <author>Konrad Polthier</author>
    <collection role="institutes" number="vis">Visual Data Analysis</collection>
    <collection role="persons" number="vontycowicz">Tycowicz, Christoph von</collection>
    <collection role="institutes" number="VDcC">Visual and Data-centric Computing</collection>
  </doc>
</export-example>
