TY - CHAP A1 - Myers, Adele A1 - Utpala, Saiteja A1 - Talbar, Shubham A1 - Sanborn, Sophia A1 - Shewmake, Christian A1 - Donnat, Claire A1 - Mathe, Johan A1 - Lupo, Umberto A1 - Sonthalia, Rishi A1 - Cui, Xinyue A1 - Szwagier, Tom A1 - Pignet, Arthur A1 - Bergsson, Andri A1 - Hauberg, Søren A1 - Nielsen, Dmitriy A1 - Sommer, Stefan A1 - Klindt, David A1 - Hermansen, Erik A1 - Vaupel, Melvin A1 - Dunn, Benjamin A1 - Xiong, Jeffrey A1 - Aharony, Noga A1 - Pe’er, Itsik A1 - Ambellan, Felix A1 - Hanik, Martin A1 - Navayazdani, Esfandiar A1 - Tycowicz, Christoph von A1 - Miolane, Nina T1 - ICLR 2022 Challenge for Computational Geomerty & Topology: Design and Results T2 - Proceedings of Topology, Algebra, and Geometry in Learning Y1 - 2022 VL - 196 SP - 269 EP - 276 PB - PMLR ER - TY - JOUR A1 - Caputo, Ariel A1 - Emporio, Marco A1 - Giachetti, Andrea A1 - Cristani, Marco A1 - Borghi, Guido A1 - D'Eusanio, Andrea A1 - Le, Minh-Quan A1 - Nguyen, Hai-Dang A1 - Tran, Minh-Triet A1 - Ambellan, Felix A1 - Hanik, Martin A1 - Navayazdani, Esfandiar A1 - Tycowicz, Christoph von T1 - SHREC 2022 Track on Online Detection of Heterogeneous Gestures JF - Computers and Graphics N2 - This paper presents the outcomes of a contest organized to evaluate methods for the online recognition of heterogeneous gestures from sequences of 3D hand poses. The task is the detection of gestures belonging to a dictionary of 16 classes characterized by different pose and motion features. The dataset features continuous sequences of hand tracking data where the gestures are interleaved with non-significant motions. The data have been captured using the Hololens 2 finger tracking system in a realistic use-case of mixed reality interaction. The evaluation is based not only on the detection performances but also on the latency and the false positives, making it possible to understand the feasibility of practical interaction tools based on the algorithms proposed. The outcomes of the contest's evaluation demonstrate the necessity of further research to reduce recognition errors, while the computational cost of the algorithms proposed is sufficiently low. Y1 - 2022 U6 - https://doi.org/10.1016/j.cag.2022.07.015 VL - 107 SP - 241 EP - 251 ER - TY - CHAP A1 - Krämer, Martin A1 - Maggioni, Marta A1 - Tycowicz, Christoph von A1 - Brisson, Nick A1 - Zachow, Stefan A1 - Duda, Georg A1 - Reichenbach, Jürgen T1 - Ultra-short echo-time (UTE) imaging of the knee with curved surface reconstruction-based extraction of the patellar tendon T2 - ISMRM (International Society for Magnetic Resonance in Medicine), 26th Annual Meeting 2018, Paris, France N2 - 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. Y1 - 2018 ER - TY - GEN A1 - Brandt, Christopher A1 - Tycowicz, Christoph von A1 - Hildebrandt, Klaus T1 - Geometric Flows of Curves in Shape Space for Processing Motion of Deformable Objects N2 - 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. T3 - ZIB-Report - 16-29 Y1 - 2016 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-59504 SN - 1438-0064 ER - TY - JOUR A1 - Brandt, Christopher A1 - Tycowicz, Christoph von A1 - Hildebrandt, Klaus T1 - Geometric Flows of Curves in Shape Space for Processing Motion of Deformable Objects JF - Computer Graphics Forum N2 - 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 Rn 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. Y1 - 2016 U6 - https://doi.org/10.1111/cgf.12832 VL - 35 IS - 2 ER - TY - GEN A1 - Tycowicz, Christoph von A1 - Ambellan, Felix A1 - Mukhopadhyay, Anirban A1 - Zachow, Stefan T1 - A Riemannian Statistical Shape Model using Differential Coordinates N2 - 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. T3 - ZIB-Report - 16-69 Y1 - 2016 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-61175 UR - https://opus4.kobv.de/opus4-zib/frontdoor/index/index/docId/6485 SN - 1438-0064 ER - TY - JOUR A1 - Tycowicz, Christoph von A1 - Schulz, Christian A1 - Seidel, Hans-Peter A1 - Hildebrandt, Klaus T1 - Real-time Nonlinear Shape Interpolation JF - ACM Transactions on Graphics N2 - We introduce a scheme for real-time nonlinear interpolation of a set of shapes. The scheme exploits the structure of the shape interpolation problem, in particular, the fact that the set of all possible interpolated shapes is a low-dimensional object in a high-dimensional shape space. The interpolated shapes are defined as the minimizers of a nonlinear objective functional on the shape space. Our approach is to construct a reduced optimization problem that approximates its unreduced counterpart and can be solved in milliseconds. To achieve this, we restrict the optimization to a low-dimensional subspace that is specifically designed for the shape interpolation problem. The construction of the subspace is based on two components: a formula for the calculation of derivatives of the interpolated shapes and a Krylov-type sequence that combines the derivatives and the Hessian of the objective functional. To make the computational cost for solving the reduced optimization problem independent of the resolution of the example shapes, we combine the dimensional reduction with schemes for the efficient approximation of the reduced nonlinear objective functional and its gradient. In our experiments, we obtain rates of 20-100 interpolated shapes per second even for the largest examples which have 500k vertices per example shape. Y1 - 2015 U6 - https://doi.org/10.1145/2729972 VL - 34 IS - 3 SP - 34:1 EP - 34:10 ER - TY - CHAP A1 - Schulz, Christian A1 - Tycowicz, Christoph von A1 - Seidel, Hans-Peter A1 - Hildebrandt, Klaus T1 - Animating articulated characters using wiggly splines T2 - ACM SIGGRAPH / Eurographics Symposium on Computer Animation N2 - We propose a new framework for spacetime optimization that can generate artistic motion with a long planning horizon for complex virtual characters. The scheme can be used for generating general types of motion and neither requires motion capture data nor an initial motion that satisfies the constraints. Our modeling of the spacetime optimization combines linearized dynamics and a novel warping scheme for articulated characters. We show that the optimal motions can be described using a combination of vibration modes, wiggly splines, and our warping scheme. This enables us to restrict the optimization to low-dimensional spaces of explicitly parametrized motions. Thereby the computation of an optimal motion is reduced to a low-dimensional non-linear least squares problem, which can be solved with standard solvers. We show examples of motions created by specifying only a few constraints for positions and velocities. Y1 - 2015 U6 - https://doi.org/10.1145/2786784.2786799 SP - 101 EP - 109 ER - TY - CHAP A1 - Götschel, Sebastian A1 - Tycowicz, Christoph von A1 - Polthier, Konrad A1 - Weiser, Martin ED - Carraro, T. ED - Geiger, M. ED - Koerkel, S. ED - Rannacher, R. T1 - Reducing Memory Requirements in Scientific Computing and Optimal Control T2 - Multiple Shooting and Time Domain Decomposition Methods Y1 - 2015 SP - 263 EP - 287 PB - Springer ER - TY - CHAP A1 - Krämer, Martin A1 - Herrmann, Karl-Heinz A1 - Boeth, Heide A1 - Tycowicz, Christoph von A1 - König, Christian A1 - Zachow, Stefan A1 - Ehrig, Rainald A1 - Hege, Hans-Christian A1 - Duda, Georg A1 - Reichenbach, Jürgen T1 - Measuring 3D knee dynamics using center out radial ultra-short echo time trajectories with a low cost experimental setup T2 - ISMRM (International Society for Magnetic Resonance in Medicine), 23rd Annual Meeting 2015, Toronto, Canada Y1 - 2015 ER -