@inproceedings{MyersUtpalaTalbaretal., author = {Myers, Adele and Utpala, Saiteja and Talbar, Shubham and Sanborn, Sophia and Shewmake, Christian and Donnat, Claire and Mathe, Johan and Lupo, Umberto and Sonthalia, Rishi and Cui, Xinyue and Szwagier, Tom and Pignet, Arthur and Bergsson, Andri and Hauberg, S{\o}ren and Nielsen, Dmitriy and Sommer, Stefan and Klindt, David and Hermansen, Erik and Vaupel, Melvin and Dunn, Benjamin and Xiong, Jeffrey and Aharony, Noga and Pe'er, Itsik and Ambellan, Felix and Hanik, Martin and Navayazdani, Esfandiar and Tycowicz, Christoph von and Miolane, Nina}, title = {ICLR 2022 Challenge for Computational Geomerty \& Topology: Design and Results}, series = {Proceedings of Topology, Algebra, and Geometry in Learning}, volume = {196}, booktitle = {Proceedings of Topology, Algebra, and Geometry in Learning}, publisher = {PMLR}, pages = {269 -- 276}, language = {en} } @article{CaputoEmporioGiachettietal., author = {Caputo, Ariel and Emporio, Marco and Giachetti, Andrea and Cristani, Marco and Borghi, Guido and D'Eusanio, Andrea and Le, Minh-Quan and Nguyen, Hai-Dang and Tran, Minh-Triet and Ambellan, Felix and Hanik, Martin and Navayazdani, Esfandiar and Tycowicz, Christoph von}, title = {SHREC 2022 Track on Online Detection of Heterogeneous Gestures}, series = {Computers and Graphics}, volume = {107}, journal = {Computers and Graphics}, doi = {10.1016/j.cag.2022.07.015}, pages = {241 -- 251}, abstract = {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.}, language = {en} } @inproceedings{KraemerMaggioniTycowiczetal., author = {Kr{\"a}mer, Martin and Maggioni, Marta and Tycowicz, Christoph von and Brisson, Nick and Zachow, Stefan and Duda, Georg and Reichenbach, J{\"u}rgen}, title = {Ultra-short echo-time (UTE) imaging of the knee with curved surface reconstruction-based extraction of the patellar tendon}, series = {ISMRM (International Society for Magnetic Resonance in Medicine), 26th Annual Meeting 2018, Paris, France}, booktitle = {ISMRM (International Society for Magnetic Resonance in Medicine), 26th Annual Meeting 2018, Paris, France}, abstract = {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.}, language = {en} } @misc{BrandtTycowiczHildebrandt, author = {Brandt, Christopher and Tycowicz, Christoph von and Hildebrandt, Klaus}, title = {Geometric Flows of Curves in Shape Space for Processing Motion of Deformable Objects}, issn = {1438-0064}, doi = {10.1111/cgf.12832}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-59504}, abstract = {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 "B{\´e}zier curves" by executing de Casteljau's algorithm in shape space.}, language = {en} } @article{BrandtTycowiczHildebrandt, author = {Brandt, Christopher and Tycowicz, Christoph von and Hildebrandt, Klaus}, title = {Geometric Flows of Curves in Shape Space for Processing Motion of Deformable Objects}, series = {Computer Graphics Forum}, volume = {35}, journal = {Computer Graphics Forum}, number = {2}, doi = {10.1111/cgf.12832}, abstract = {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 B{\´e}zier curves by executing de Casteljau's algorithm in shape space.}, language = {en} } @misc{TycowiczAmbellanMukhopadhyayetal., author = {Tycowicz, Christoph von and Ambellan, Felix and Mukhopadhyay, Anirban and Zachow, Stefan}, title = {A Riemannian Statistical Shape Model using Differential Coordinates}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-61175}, abstract = {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.}, language = {en} } @article{TycowiczSchulzSeideletal., author = {Tycowicz, Christoph von and Schulz, Christian and Seidel, Hans-Peter and Hildebrandt, Klaus}, title = {Real-time Nonlinear Shape Interpolation}, series = {ACM Transactions on Graphics}, volume = {34}, journal = {ACM Transactions on Graphics}, number = {3}, doi = {10.1145/2729972}, pages = {34:1 -- 34:10}, abstract = {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.}, language = {en} } @inproceedings{SchulzTycowiczSeideletal., author = {Schulz, Christian and Tycowicz, Christoph von and Seidel, Hans-Peter and Hildebrandt, Klaus}, title = {Animating articulated characters using wiggly splines}, series = {ACM SIGGRAPH / Eurographics Symposium on Computer Animation}, booktitle = {ACM SIGGRAPH / Eurographics Symposium on Computer Animation}, doi = {10.1145/2786784.2786799}, pages = {101 -- 109}, abstract = {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.}, language = {en} } @inproceedings{GoetschelTycowiczPolthieretal., author = {G{\"o}tschel, Sebastian and Tycowicz, Christoph von and Polthier, Konrad and Weiser, Martin}, title = {Reducing Memory Requirements in Scientific Computing and Optimal Control}, series = {Multiple Shooting and Time Domain Decomposition Methods}, booktitle = {Multiple Shooting and Time Domain Decomposition Methods}, editor = {Carraro, T. and Geiger, M. and Koerkel, S. and Rannacher, R.}, publisher = {Springer}, pages = {263 -- 287}, language = {en} } @inproceedings{KraemerHerrmannBoethetal., author = {Kr{\"a}mer, Martin and Herrmann, Karl-Heinz and Boeth, Heide and Tycowicz, Christoph von and K{\"o}nig, Christian and Zachow, Stefan and Ehrig, Rainald and Hege, Hans-Christian and Duda, Georg and Reichenbach, J{\"u}rgen}, title = {Measuring 3D knee dynamics using center out radial ultra-short echo time trajectories with a low cost experimental setup}, series = {ISMRM (International Society for Magnetic Resonance in Medicine), 23rd Annual Meeting 2015, Toronto, Canada}, booktitle = {ISMRM (International Society for Magnetic Resonance in Medicine), 23rd Annual Meeting 2015, Toronto, Canada}, language = {en} }