@misc{AmbellanZachowvonTycowicz2019, author = {Ambellan, Felix and Zachow, Stefan and von Tycowicz, Christoph}, title = {An as-invariant-as-possible GL+(3)-based Statistical Shape Model}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-74566}, year = {2019}, abstract = {We describe a novel nonlinear statistical shape model basedon differential coordinates viewed as elements of GL+(3). We adopt an as-invariant-as possible framework comprising a bi-invariant Lie group mean and a tangent principal component analysis based on a unique GL+(3)-left-invariant, O(3)-right-invariant metric. Contrary to earlier work that equips the coordinates with a specifically constructed group structure, our method employs the inherent geometric structure of the group-valued data and therefore features an improved statistical power in identifying shape differences. We demonstrate this in experiments on two anatomical datasets including comparison to the standard Euclidean as well as recent state-of-the-art nonlinear approaches to statistical shape modeling.}, language = {en} } @misc{NavaYazdaniHegevonTycowicz2019, author = {Nava-Yazdani, Esfandiar and Hege, Hans-Christian and von Tycowicz, Christoph}, title = {A Geodesic Mixed Effects Model in Kendall's Shape Space}, journal = {Proc. 7th MICCAI workshop on Mathematical Foundations of Computational Anatomy (MFCA)}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-74621}, year = {2019}, abstract = {In many applications, geodesic hierarchical models are adequate for the study of temporal observations. We employ such a model derived for manifold-valued data to Kendall's shape space. In particular, instead of the Sasaki metric, we adapt a functional-based metric, which increases the computational efficiency and does not require the implementation of the curvature tensor. We propose the corresponding variational time discretization of geodesics and apply the approach for the estimation of group trends and statistical testing of 3D shapes derived from an open access longitudinal imaging study on osteoarthritis.}, language = {en} } @inproceedings{AmbellanZachowvonTycowicz2019, author = {Ambellan, Felix and Zachow, Stefan and von Tycowicz, Christoph}, title = {An as-invariant-as-possible GL+(3)-based Statistical Shape Model}, volume = {11846}, booktitle = {Proc. 7th MICCAI workshop on Mathematical Foundations of Computational Anatomy (MFCA)}, publisher = {Springer}, doi = {10.1007/978-3-030-33226-6_23}, pages = {219 -- 228}, year = {2019}, abstract = {We describe a novel nonlinear statistical shape model basedon differential coordinates viewed as elements of GL+(3). We adopt an as-invariant-as possible framework comprising a bi-invariant Lie group mean and a tangent principal component analysis based on a unique GL+(3)-left-invariant, O(3)-right-invariant metric. Contrary to earlier work that equips the coordinates with a specifically constructed group structure, our method employs the inherent geometric structure of the group-valued data and therefore features an improved statistical power in identifying shape differences. We demonstrate this in experiments on two anatomical datasets including comparison to the standard Euclidean as well as recent state-of-the-art nonlinear approaches to statistical shape modeling.}, language = {en} } @misc{AmbellanZachowvonTycowicz2019, author = {Ambellan, Felix and Zachow, Stefan and von Tycowicz, Christoph}, title = {A Surface-Theoretic Approach for Statistical Shape Modeling}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-74497}, year = {2019}, abstract = {We present a novel approach for nonlinear statistical shape modeling that is invariant under Euclidean motion and thus alignment-free. By analyzing metric distortion and curvature of shapes as elements of Lie groups in a consistent Riemannian setting, we construct a framework that reliably handles large deformations. Due to the explicit character of Lie group operations, our non-Euclidean method is very efficient allowing for fast and numerically robust processing. This facilitates Riemannian analysis of large shape populations accessible through longitudinal and multi-site imaging studies providing increased statistical power. We evaluate the performance of our model w.r.t. shape-based classification of pathological malformations of the human knee and show that it outperforms the standard Euclidean as well as a recent nonlinear approach especially in presence of sparse training data. To provide insight into the model's ability of capturing natural biological shape variability, we carry out an analysis of specificity and generalization ability.}, language = {en} } @inproceedings{AmbellanZachowvonTycowicz2019, author = {Ambellan, Felix and Zachow, Stefan and von Tycowicz, Christoph}, title = {A Surface-Theoretic Approach for Statistical Shape Modeling}, volume = {11767}, booktitle = {Proc. Medical Image Computing and Computer Assisted Intervention (MICCAI), Part IV}, publisher = {Springer}, doi = {10.1007/978-3-030-32251-9_3}, pages = {21 -- 29}, year = {2019}, abstract = {We present a novel approach for nonlinear statistical shape modeling that is invariant under Euclidean motion and thus alignment-free. By analyzing metric distortion and curvature of shapes as elements of Lie groups in a consistent Riemannian setting, we construct a framework that reliably handles large deformations. Due to the explicit character of Lie group operations, our non-Euclidean method is very efficient allowing for fast and numerically robust processing. This facilitates Riemannian analysis of large shape populations accessible through longitudinal and multi-site imaging studies providing increased statistical power. We evaluate the performance of our model w.r.t. shape-based classification of pathological malformations of the human knee and show that it outperforms the standard Euclidean as well as a recent nonlinear approach especially in presence of sparse training data. To provide insight into the model's ability of capturing natural biological shape variability, we carry out an analysis of specificity and generalization ability.}, language = {en} } @article{AmbellanZachowvonTycowicz2021, author = {Ambellan, Felix and Zachow, Stefan and von Tycowicz, Christoph}, title = {Rigid Motion Invariant Statistical Shape Modeling based on Discrete Fundamental Forms}, volume = {73}, journal = {Medical Image Analysis}, arxiv = {http://arxiv.org/abs/2111.06850}, doi = {10.1016/j.media.2021.102178}, year = {2021}, abstract = {We present a novel approach for nonlinear statistical shape modeling that is invariant under Euclidean motion and thus alignment-free. By analyzing metric distortion and curvature of shapes as elements of Lie groups in a consistent Riemannian setting, we construct a framework that reliably handles large deformations. Due to the explicit character of Lie group operations, our non-Euclidean method is very efficient allowing for fast and numerically robust processing. This facilitates Riemannian analysis of large shape populations accessible through longitudinal and multi-site imaging studies providing increased statistical power. Additionally, as planar configurations form a submanifold in shape space, our representation allows for effective estimation of quasi-isometric surfaces flattenings. We evaluate the performance of our model w.r.t. shape-based classification of hippocampus and femur malformations due to Alzheimer's disease and osteoarthritis, respectively. In particular, we achieve state-of-the-art accuracies outperforming the standard Euclidean as well as a recent nonlinear approach especially in presence of sparse training data. To provide insight into the model's ability of capturing biological shape variability, we carry out an analysis of specificity and generalization ability.}, language = {en} } @article{SchulzTycowiczSeideletal.2014, author = {Schulz, Christian and Tycowicz, Christoph von and Seidel, Hans-Peter and Hildebrandt, Klaus}, title = {Animating Deformable Objects Using Sparse Spacetime Constraints}, volume = {33}, journal = {ACM Transactions on Graphics}, number = {4}, doi = {10.1145/2601097.2601156}, pages = {109:1 -- 109:10}, year = {2014}, abstract = {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.}, language = {en} } @inproceedings{KraemerHerrmannBoethetal.2015, 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}, booktitle = {ISMRM (International Society for Magnetic Resonance in Medicine), 23rd Annual Meeting 2015, Toronto, Canada}, year = {2015}, language = {en} } @article{TycowiczSchulzSeideletal.2013, author = {Tycowicz, Christoph von and Schulz, Christian and Seidel, Hans-Peter and Hildebrandt, Klaus}, title = {An Efficient Construction of Reduced Deformable Objects}, volume = {32}, journal = {ACM Transactions on Graphics}, number = {6}, publisher = {ACM}, doi = {10.1145/2508363.2508392}, pages = {213:1 -- 213:10}, year = {2013}, abstract = {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.}, language = {en} } @article{HildebrandtSchulzTycowiczetal.2012, author = {Hildebrandt, Klaus and Schulz, Christian and Tycowicz, Christoph von and Polthier, Konrad}, title = {Interactive spacetime control of deformable objects}, volume = {31}, journal = {ACM Transactions on Graphics}, number = {4}, publisher = {ACM}, doi = {10.1145/2185520.2185567}, pages = {71:1 -- 71:8}, year = {2012}, abstract = {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.}, language = {en} } @article{HildebrandtSchulzTycowiczetal.2011, author = {Hildebrandt, Klaus and Schulz, Christian and Tycowicz, Christoph von and Polthier, Konrad}, title = {Interactive surface modeling using modal analysis}, volume = {30}, journal = {ACM Transactions on Graphics}, number = {5}, doi = {10.1145/2019627.2019638}, pages = {119:1 -- 119:11}, year = {2011}, abstract = {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].}, language = {en} } @article{HildebrandtSchulzTycowiczetal.2012, author = {Hildebrandt, Klaus and Schulz, Christian and Tycowicz, Christoph von and Polthier, Konrad}, title = {Modal Shape Analysis beyond Laplacian}, volume = {29}, journal = {Computer Aided Geometric Design}, number = {5}, doi = {10.1016/j.cagd.2012.01.001}, pages = {204 -- 2018}, year = {2012}, abstract = {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.}, language = {en} } @article{TycowiczKaelbererPolthier2011, author = {Tycowicz, Christoph von and K{\"a}lberer, Felix and Polthier, Konrad}, title = {Context-based Coding of Adaptive Multiresolution Meshes}, volume = {30}, journal = {Computer Graphics Forum}, number = {8}, doi = {10.1111/j.1467-8659.2011.01972.x}, pages = {2231 -- 2245}, year = {2011}, abstract = {Multiresolution meshes provide an efficient and structured representation of geometric objects. To increase the mesh resolution only at vital parts of the object, adaptive refinement is widely used. We propose a lossless compression scheme for these adaptive structures that exploits the parent-child relationships inherent to the mesh hierarchy. We use the rules that correspond to the adaptive refinement scheme and store bits only where some freedom of choice is left, leading to compact codes that are free of redundancy. Moreover, we extend the coder to sequences of meshes with varying refinement. The connectivity compression ratio of our method exceeds that of state-of-the-art coders by a factor of 2 to 7. For efficient compression of vertex positions we adapt popular wavelet-based coding schemes to the adaptive triangular and quadrangular cases to demonstrate the compatibility with our method. Akin to state-of-the-art coders, we use a zerotree to encode the resulting coefficients. Using improved context modeling we enhanced the zerotree compression, cutting the overall geometry data rate by 7\% below those of the successful Progressive Geometry Compression. More importantly, by exploiting the existing refinement structure we achieve compression factors that are 4 times greater than those of coders which can handle irregular meshes.}, language = {en} } @misc{HildebrandtSchulzTycowiczetal.2010, author = {Hildebrandt, Klaus and Schulz, Christian and Tycowicz, Christoph von and Polthier, Konrad}, title = {Eigenmodes of Surface Energies for Shape Analysis}, volume = {6130}, journal = {Advances in Geometric Modeling and Processing (Proceedings of Geometric Modeling and Processing 2010)}, editor = {Mourrain, Bernard and Schaefer, Scott and Xu, Guoliang}, publisher = {Springer Berlin / Heidelberg}, doi = {10.1007/978-3-642-13411-1_20}, pages = {296 -- 314}, year = {2010}, abstract = {In this work, we study the spectra and eigenmodes of the Hessian of various discrete surface energies and discuss applications to shape analysis. In particular, we consider a physical model that describes the vibration modes and frequencies of a surface through the eigenfunctions and eigenvalues of the Hessian of a deformation energy, and we derive a closed form representation for the Hessian (at the rest state of the energy) for a general class of deformation energies. Furthermore, we design a quadratic energy, such that the eigenmodes of the Hessian of this energy are sensitive to the extrinsic curvature of the surface. 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 the surface. In addition, we discuss a spectral quadrangulation scheme for surfaces.}, language = {en} } @article{TycowiczSchulzSeideletal.2015, author = {Tycowicz, Christoph von and Schulz, Christian and Seidel, Hans-Peter and Hildebrandt, Klaus}, title = {Real-time Nonlinear Shape Interpolation}, volume = {34}, journal = {ACM Transactions on Graphics}, number = {3}, doi = {10.1145/2729972}, pages = {34:1 -- 34:10}, year = {2015}, 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.2015, author = {Schulz, Christian and Tycowicz, Christoph von and Seidel, Hans-Peter and Hildebrandt, Klaus}, title = {Animating articulated characters using wiggly splines}, booktitle = {ACM SIGGRAPH / Eurographics Symposium on Computer Animation}, doi = {10.1145/2786784.2786799}, pages = {101 -- 109}, year = {2015}, 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{KaelbererTycowiczPolthier2009, author = {K{\"a}lberer, Felix and Tycowicz, Christoph von and Polthier, Konrad}, title = {Lossless Compression of Adaptive Multiresolution Meshes}, booktitle = {XXII Brazilian Symposium on Computer Graphics and Image Processing}, doi = {10.1109/SIBGRAPI.2009.53}, pages = {80 -- 87}, year = {2009}, abstract = {We present a novel coder for lossless compression of adaptive multiresolution meshes that exploits their special hierarchical structure. The heart of our method is a new progressive connectivity coder that can be combined with leading geometry encoding techniques. The compressor uses the parent/child relationships inherent to the hierarchical mesh. We use the rules that accord to the refinement scheme and store bits only where it leaves freedom of choice, leading to compact codes that are free of redundancy. To illustrate our scheme we chose the widespread red-green refinement, but the underlying concepts can be directly transferred to other adaptive refinement schemes as well. The compression ratio of our method exceeds that of state-of-the-art coders by a factor of 2 to 3 on most of our benchmark models.}, language = {en} } @inproceedings{TycowiczLoviscach2008, author = {Tycowicz, Christoph von and Loviscach, J{\"o}rn}, title = {Measuring and Enhancing the Legibility of GPU-rendered Text}, booktitle = {Eurographics 2008 Short Papers}, pages = {45 -- 48}, year = {2008}, abstract = {The limited spatial resolution of standard computer displays impedes the legibility of text. To improve the rendering, we have developed a number of strategies that employ GPU-based shader programs and appropriate preprocessing steps. We devised and implemented a set of methods that may be used alone or in combination ranging from simple measures such as gamma-correct MIPmapping to complex ones such as RGB subpixel rendering combined with supersampling. We have researched into their performance in terms of both legibility and speed. We difinded a psychovisual test that quantifies legibility quickly enough to compare a selection of promising techniques. The results allow to choose the optimum blend of rendering methods for a given set of requirements.}, language = {en} } @inproceedings{GreenhalghBenfordDrozdetal.2007, author = {Greenhalgh, Chris and Benford, Steve and Drozd, Adam and Flintham, Martin and Hampshire, Alastair and Oppermann, Leif and Smith, Keir and Tycowicz, Christoph von}, title = {Addressing Mobile Phone Diversity in Ubicomp Experience Development}, volume = {4717}, booktitle = {UbiComp 2007: Ubiquitous Computing, 9th International Conference}, doi = {10.1007/978-3-540-74853-3_26}, pages = {447 -- 464}, year = {2007}, abstract = {Mobile phones are a widely-available class of device with supporting communications infrastructure which can be appropriated and exploited to support ubicomp experiences. However mobile phones vary hugely in their capabilities. We explore how a single dimension of phone application type embodies the critical trade-off between capability and availability, i.e. between what can be done and the fraction of potential participants' phones that can do this. We describe four different mobile phone ubicomp experiences that illustrate different points along this continuum (SMS, WAP/Web, and J2ME, Python and native applications) and the common software platform/toolkit, EQUIP2, that has been co-developed to support them. From this we propose four development strategies for addressing mobile phone diversity: prioritise support for server development (including web integration), migrate functionality between server(s) and handset(s), support flexible communication options, and use a loosely coupled (data-driven and component-based) software approach.}, language = {en} } @phdthesis{Tycowicz2014, author = {Tycowicz, Christoph von}, title = {Concepts and Algorithms for the Deformation, Analysis, and Compression of Digital Shapes}, doi = {10.17169/refubium-4697}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:188-fudissthesis000000096721-7}, year = {2014}, abstract = {This thesis concerns model reduction techniques for the efficient numerical treatment of physical systems governing the deformation behavior of geometrically complex shapes. We present new strategies for the construction of simplified, low-dimensional models that capture the main features of the original complex system and are suitable for use in interactive computer graphics applications. To demonstrate the effectiveness of the new techniques we propose frameworks for real-time simulation and interactive deformation-based modeling of elastic solids and shells and compare them to alternative approaches. In addition, we investigate differential operators that are derived from the physical models and hence can serve as alternatives to the Laplace-Beltrami operator for applications in modal shape analysis. Furthermore, this thesis addresses the compression of digital shapes. In particular, we present a lossless compression scheme that is adapted to the special characteristics of adaptively refined, hierarchical meshes.}, language = {en} } @incollection{PolthierBobenkoHildebrandtetal.2014, author = {Polthier, Konrad and Bobenko, Alexander and Hildebrandt, Klaus and Kornhuber, Ralf and Tycowicz, Christoph von and Yserentant, Harry and Ziegler, G{\"u}nter M.}, title = {Geometry processing}, volume = {1}, booktitle = {MATHEON - Mathematics for Key Technologies}, publisher = {EMS Publishing House}, isbn = {978-3-03719-137-8}, doi = {10.4171/137}, pages = {341 -- 355}, year = {2014}, language = {en} }