@article{KoflerWaldKolbitschetal., author = {Kofler, Andreas and Wald, Christian and Kolbitsch, Christoph and von Tycowicz, Christoph and Ambellan, Felix}, title = {Joint Reconstruction and Segmentation in Undersampled 3D Knee MRI combining Shape Knowledge and Deep Learning}, series = {Physics in Medicine and Biology}, journal = {Physics in Medicine and Biology}, doi = {10.1088/1361-6560/ad3797}, abstract = {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. 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. 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). 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. 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. 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.}, language = {en} } @misc{GoetschelvonTycowiczPolthieretal., author = {G{\"o}tschel, Sebastian and von Tycowicz, Christoph and Polthier, Konrad and Weiser, Martin}, title = {Reducing Memory Requirements in Scientific Computing and Optimal Control}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-42695}, abstract = {In high accuracy numerical simulations and optimal control of time-dependent processes, often both many time steps and fine spatial discretizations are needed. Adjoint gradient computation, or post-processing of simulation results, requires the storage of the solution trajectories over the whole time, if necessary together with the adaptively refined spatial grids. In this paper we discuss various techniques to reduce the memory requirements, focusing first on the storage of the solution data, which typically are double precision floating point values. We highlight advantages and disadvantages of the different approaches. Moreover, we present an algorithm for the efficient storage of adaptively refined, hierarchic grids, and the integration with the compressed storage of solution data.}, language = {en} } @article{vonTycowiczAmbellanMukhopadhyayetal., author = {von Tycowicz, Christoph and Ambellan, Felix and Mukhopadhyay, Anirban and Zachow, Stefan}, title = {An Efficient Riemannian Statistical Shape Model using Differential Coordinates}, series = {Medical Image Analysis}, volume = {43}, journal = {Medical Image Analysis}, number = {1}, doi = {10.1016/j.media.2017.09.004}, pages = {1 -- 9}, 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-Euclidean structure. A key advantage of our framework is that statistics in a manifold shape space becomes 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 Euclidean approach in terms of shape-based classification of morphological disorders.}, 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} } @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} } @phdthesis{Tycowicz, 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}, 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., 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}, series = {MATHEON - Mathematics for Key Technologies}, 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}, language = {en} } @incollection{OppermannJacobsWatkinsetal., author = {Oppermann, Leif and Jacobs, R. and Watkins, M. and Shackford, R. and Tycowicz, Christoph von and Wright, M. and Capra, M. and Greenhalgh, Chris and Benford, Steve}, title = {Love City: A Text-Driven, Location-Based Mobile Phone Game Played Between 3 Cities}, series = {Pervasive Gaming Applications - A Reader for Pervasive Gaming Research}, volume = {2}, booktitle = {Pervasive Gaming Applications - A Reader for Pervasive Gaming Research}, publisher = {Shaker Verlag}, isbn = {978-3-8322-6224-2}, pages = {285 -- 312}, language = {en} } @incollection{GreenhalghBenfordDrozdetal., 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 = {EQUIP2: A Platform for Mobile Phone-based Game Development}, series = {Concepts and Technologies for Pervasive Games - A Reader for Pervasive Gaming Research}, volume = {1}, booktitle = {Concepts and Technologies for Pervasive Games - A Reader for Pervasive Gaming Research}, publisher = {Shaker Verlag}, isbn = {978-3-8322-6223-5}, pages = {153 -- 178}, language = {en} } @article{SchulzTycowiczSeideletal., author = {Schulz, Christian and Tycowicz, Christoph von and Seidel, Hans-Peter and Hildebrandt, Klaus}, title = {Animating Deformable Objects Using Sparse Spacetime Constraints}, series = {ACM Transactions on Graphics}, volume = {33}, journal = {ACM Transactions on Graphics}, number = {4}, doi = {10.1145/2601097.2601156}, pages = {109:1 -- 109:10}, 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} } @article{TycowiczSchulzSeideletal., author = {Tycowicz, Christoph von and Schulz, Christian and Seidel, Hans-Peter and Hildebrandt, Klaus}, title = {An Efficient Construction of Reduced Deformable Objects}, series = {ACM Transactions on Graphics}, volume = {32}, journal = {ACM Transactions on Graphics}, number = {6}, publisher = {ACM}, doi = {10.1145/2508363.2508392}, pages = {213:1 -- 213:10}, 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., author = {Hildebrandt, Klaus and Schulz, Christian and Tycowicz, Christoph von and Polthier, Konrad}, title = {Interactive spacetime control of deformable objects}, series = {ACM Transactions on Graphics}, volume = {31}, journal = {ACM Transactions on Graphics}, number = {4}, publisher = {ACM}, doi = {10.1145/2185520.2185567}, pages = {71:1 -- 71:8}, 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., author = {Hildebrandt, Klaus and Schulz, Christian and Tycowicz, Christoph von and Polthier, Konrad}, title = {Interactive surface modeling using modal analysis}, series = {ACM Transactions on Graphics}, volume = {30}, journal = {ACM Transactions on Graphics}, number = {5}, doi = {10.1145/2019627.2019638}, pages = {119:1 -- 119:11}, 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., author = {Hildebrandt, Klaus and Schulz, Christian and Tycowicz, Christoph von and Polthier, Konrad}, title = {Modal Shape Analysis beyond Laplacian}, series = {Computer Aided Geometric Design}, volume = {29}, journal = {Computer Aided Geometric Design}, number = {5}, doi = {10.1016/j.cagd.2012.01.001}, pages = {204 -- 2018}, 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{TycowiczKaelbererPolthier, author = {Tycowicz, Christoph von and K{\"a}lberer, Felix and Polthier, Konrad}, title = {Context-based Coding of Adaptive Multiresolution Meshes}, series = {Computer Graphics Forum}, volume = {30}, journal = {Computer Graphics Forum}, number = {8}, doi = {10.1111/j.1467-8659.2011.01972.x}, pages = {2231 -- 2245}, 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., author = {Hildebrandt, Klaus and Schulz, Christian and Tycowicz, Christoph von and Polthier, Konrad}, title = {Eigenmodes of Surface Energies for Shape Analysis}, series = {Advances in Geometric Modeling and Processing (Proceedings of Geometric Modeling and Processing 2010)}, 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}, 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} } @inproceedings{KaelbererTycowiczPolthier, author = {K{\"a}lberer, Felix and Tycowicz, Christoph von and Polthier, Konrad}, title = {Lossless Compression of Adaptive Multiresolution Meshes}, series = {XXII Brazilian Symposium on Computer Graphics and Image Processing}, booktitle = {XXII Brazilian Symposium on Computer Graphics and Image Processing}, doi = {10.1109/SIBGRAPI.2009.53}, pages = {80 -- 87}, 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{TycowiczLoviscach, author = {Tycowicz, Christoph von and Loviscach, J{\"o}rn}, title = {Measuring and Enhancing the Legibility of GPU-rendered Text}, series = {Eurographics 2008 Short Papers}, booktitle = {Eurographics 2008 Short Papers}, pages = {45 -- 48}, 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., 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}, series = {UbiComp 2007: Ubiquitous Computing, 9th International Conference}, volume = {4717}, booktitle = {UbiComp 2007: Ubiquitous Computing, 9th International Conference}, doi = {10.1007/978-3-540-74853-3_26}, pages = {447 -- 464}, 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} } @misc{NavaYazdaniHegevonTycowicz, author = {Nava-Yazdani, Esfandiar and Hege, Hans-Christian and von Tycowicz, Christoph}, title = {A Geodesic Mixed Effects Model in Kendall's Shape Space}, series = {Proc. 7th MICCAI workshop on Mathematical Foundations of Computational Anatomy (MFCA)}, 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}, 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{AmbellanZachowvonTycowicz, author = {Ambellan, Felix and Zachow, Stefan and von Tycowicz, Christoph}, title = {An as-invariant-as-possible GL+(3)-based Statistical Shape Model}, series = {Proc. 7th MICCAI workshop on Mathematical Foundations of Computational Anatomy (MFCA)}, 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}, 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{AmbellanZachowvonTycowicz, 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}, 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} } @misc{AmbellanZachowvonTycowicz, 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}, 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} } @inproceedings{HanikHegevonTycowicz, author = {Hanik, Martin and Hege, Hans-Christian and von Tycowicz, Christoph}, title = {Bi-invariant Two-Sample Tests in Lie Groups for Shape Analysis}, series = {Shape in Medical Imaging}, booktitle = {Shape in Medical Imaging}, publisher = {Springer International Publishing}, address = {Cham}, doi = {10.1007/978-3-030-61056-2_4}, pages = {44 -- 54}, abstract = {We propose generalizations of the T²-statistics of Hotelling and the Bhattacharayya distance for data taking values in Lie groups. A key feature of the derived measures is that they are compatible with the group structure even for manifolds that do not admit any bi-invariant metric. This property, e.g., assures analysis that does not depend on the reference shape, thus, preventing bias due to arbitrary choices thereof. Furthermore, the generalizations agree with the common definitions for the special case of flat vector spaces guaranteeing consistency. Employing a permutation test setup, we further obtain nonparametric, two-sample testing procedures that themselves are bi-invariant and consistent. We validate our method in group tests revealing significant differences in hippocampal shape between individuals with mild cognitive impairment and normal controls.}, language = {en} } @inproceedings{HanikHegeHennemuthetal., author = {Hanik, Martin and Hege, Hans-Christian and Hennemuth, Anja and von Tycowicz, Christoph}, title = {Nonlinear Regression on Manifolds for Shape Analysis using Intrinsic B{\´e}zier Splines}, series = {Proc. Medical Image Computing and Computer Assisted Intervention (MICCAI)}, booktitle = {Proc. Medical Image Computing and Computer Assisted Intervention (MICCAI)}, publisher = {Springer International Publishing}, address = {Cham}, doi = {10.1007/978-3-030-59719-1_60}, pages = {617 -- 626}, abstract = {Intrinsic and parametric regression models are of high interest for the statistical analysis of manifold-valued data such as images and shapes. The standard linear ansatz has been generalized to geodesic regression on manifolds making it possible to analyze dependencies of random variables that spread along generalized straight lines. Nevertheless, in some scenarios, the evolution of the data cannot be modeled adequately by a geodesic. We present a framework for nonlinear regression on manifolds by considering Riemannian splines, whose segments are B{\´e}zier curves, as trajectories. Unlike variational formulations that require time-discretization, we take a constructive approach that provides efficient and exact evaluation by virtue of the generalized de Casteljau algorithm. We validate our method in experiments on the reconstruction of periodic motion of the mitral valve as well as the analysis of femoral shape changes during the course of osteoarthritis, endorsing B{\´e}zier spline regression as an effective and flexible tool for manifold-valued regression.}, language = {en} } @article{NavaYazdaniHegeSullivanetal., author = {Nava-Yazdani, Esfandiar and Hege, Hans-Christian and Sullivan, T. J. and von Tycowicz, Christoph}, title = {Geodesic Analysis in Kendall's Shape Space with Epidemiological Applications}, series = {Journal of Mathematical Imaging and Vision}, volume = {62}, journal = {Journal of Mathematical Imaging and Vision}, number = {4}, doi = {10.1007/s10851-020-00945-w}, pages = {549 -- 559}, abstract = {We analytically determine Jacobi fields and parallel transports and compute geodesic regression in Kendall's shape space. Using the derived expressions, we can fully leverage the geometry via Riemannian optimization and thereby reduce the computational expense by several orders of magnitude over common, nonlinear constrained approaches. The methodology is demonstrated by performing a longitudinal statistical analysis of epidemiological shape data. As an example application we have chosen 3D shapes of knee bones, reconstructed from image data of the Osteoarthritis Initiative (OAI). Comparing subject groups with incident and developing osteoarthritis versus normal controls, we find clear differences in the temporal development of femur shapes. This paves the way for early prediction of incident knee osteoarthritis, using geometry data alone.}, language = {en} } @inproceedings{NavaYazdaniHegevonTycowicz, author = {Nava-Yazdani, Esfandiar and Hege, Hans-Christian and von Tycowicz, Christoph}, title = {A Geodesic Mixed Effects Model in Kendall's Shape Space}, series = {Proc. 7th MICCAI workshop on Mathematical Foundations of Computational Anatomy (MFCA)}, volume = {11846}, booktitle = {Proc. 7th MICCAI workshop on Mathematical Foundations of Computational Anatomy (MFCA)}, doi = {10.1007/978-3-030-33226-6_22}, pages = {209 -- 218}, 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} } @article{AmbellanZachowvonTycowicz, author = {Ambellan, Felix and Zachow, Stefan and von Tycowicz, Christoph}, title = {Rigid Motion Invariant Statistical Shape Modeling based on Discrete Fundamental Forms}, series = {Medical Image Analysis}, volume = {73}, journal = {Medical Image Analysis}, doi = {10.1016/j.media.2021.102178}, 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} } @misc{AmbellanZachowvonTycowicz, author = {Ambellan, Felix and Zachow, Stefan and von Tycowicz, Christoph}, title = {Geodesic B-Score for Improved Assessment of Knee Osteoarthritis}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-81930}, abstract = {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.}, language = {en} } @inproceedings{AmbellanZachowvonTycowicz, author = {Ambellan, Felix and Zachow, Stefan and von Tycowicz, Christoph}, title = {Geodesic B-Score for Improved Assessment of Knee Osteoarthritis}, series = {Proc. Information Processing in Medical Imaging (IPMI)}, booktitle = {Proc. Information Processing in Medical Imaging (IPMI)}, doi = {10.1007/978-3-030-78191-0_14}, pages = {177 -- 188}, abstract = {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.}, language = {en} } @misc{AmbellanLameckervonTycowiczetal., author = {Ambellan, Felix and Lamecker, Hans and von Tycowicz, Christoph and Zachow, Stefan}, title = {Statistical Shape Models - Understanding and Mastering Variation in Anatomy}, issn = {1438-0064}, doi = {10.1007/978-3-030-19385-0_5}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-72699}, abstract = {In our chapter we are describing how to reconstruct three-dimensional anatomy from medical image data and how to build Statistical 3D Shape Models out of many such reconstructions yielding a new kind of anatomy that not only allows quantitative analysis of anatomical variation but also a visual exploration and educational visualization. Future digital anatomy atlases will not only show a static (average) anatomy but also its normal or pathological variation in three or even four dimensions, hence, illustrating growth and/or disease progression. Statistical Shape Models (SSMs) are geometric models that describe a collection of semantically similar objects in a very compact way. SSMs represent an average shape of many three-dimensional objects as well as their variation in shape. The creation of SSMs requires a correspondence mapping, which can be achieved e.g. by parameterization with a respective sampling. If a corresponding parameterization over all shapes can be established, variation between individual shape characteristics can be mathematically investigated. We will explain what Statistical Shape Models are and how they are constructed. Extensions of Statistical Shape Models will be motivated for articulated coupled structures. In addition to shape also the appearance of objects will be integrated into the concept. Appearance is a visual feature independent of shape that depends on observers or imaging techniques. Typical appearances are for instance the color and intensity of a visual surface of an object under particular lighting conditions, or measurements of material properties with computed tomography (CT) or magnetic resonance imaging (MRI). A combination of (articulated) statistical shape models with statistical models of appearance lead to articulated Statistical Shape and Appearance Models (a-SSAMs).After giving various examples of SSMs for human organs, skeletal structures, faces, and bodies, we will shortly describe clinical applications where such models have been successfully employed. Statistical Shape Models are the foundation for the analysis of anatomical cohort data, where characteristic shapes are correlated to demographic or epidemiologic data. SSMs consisting of several thousands of objects offer, in combination with statistical methods ormachine learning techniques, the possibility to identify characteristic clusters, thus being the foundation for advanced diagnostic disease scoring.}, language = {en} } @inproceedings{AmbellanZachowvonTycowicz, author = {Ambellan, Felix and Zachow, Stefan and von Tycowicz, Christoph}, title = {A Surface-Theoretic Approach for Statistical Shape Modeling}, series = {Proc. Medical Image Computing and Computer Assisted Intervention (MICCAI), Part IV}, 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}, 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} } @incollection{AmbellanLameckervonTycowiczetal., author = {Ambellan, Felix and Lamecker, Hans and von Tycowicz, Christoph and Zachow, Stefan}, title = {Statistical Shape Models - Understanding and Mastering Variation in Anatomy}, series = {Biomedical Visualisation}, volume = {3}, booktitle = {Biomedical Visualisation}, number = {1156}, editor = {Rea, Paul M.}, edition = {1}, publisher = {Springer Nature Switzerland AG}, isbn = {978-3-030-19384-3}, doi = {10.1007/978-3-030-19385-0_5}, pages = {67 -- 84}, abstract = {In our chapter we are describing how to reconstruct three-dimensional anatomy from medical image data and how to build Statistical 3D Shape Models out of many such reconstructions yielding a new kind of anatomy that not only allows quantitative analysis of anatomical variation but also a visual exploration and educational visualization. Future digital anatomy atlases will not only show a static (average) anatomy but also its normal or pathological variation in three or even four dimensions, hence, illustrating growth and/or disease progression. Statistical Shape Models (SSMs) are geometric models that describe a collection of semantically similar objects in a very compact way. SSMs represent an average shape of many three-dimensional objects as well as their variation in shape. The creation of SSMs requires a correspondence mapping, which can be achieved e.g. by parameterization with a respective sampling. If a corresponding parameterization over all shapes can be established, variation between individual shape characteristics can be mathematically investigated. We will explain what Statistical Shape Models are and how they are constructed. Extensions of Statistical Shape Models will be motivated for articulated coupled structures. In addition to shape also the appearance of objects will be integrated into the concept. Appearance is a visual feature independent of shape that depends on observers or imaging techniques. Typical appearances are for instance the color and intensity of a visual surface of an object under particular lighting conditions, or measurements of material properties with computed tomography (CT) or magnetic resonance imaging (MRI). A combination of (articulated) statistical shape models with statistical models of appearance lead to articulated Statistical Shape and Appearance Models (a-SSAMs).After giving various examples of SSMs for human organs, skeletal structures, faces, and bodies, we will shortly describe clinical applications where such models have been successfully employed. Statistical Shape Models are the foundation for the analysis of anatomical cohort data, where characteristic shapes are correlated to demographic or epidemiologic data. SSMs consisting of several thousands of objects offer, in combination with statistical methods ormachine learning techniques, the possibility to identify characteristic clusters, thus being the foundation for advanced diagnostic disease scoring.}, language = {en} } @misc{AmbellanHanikvonTycowicz, author = {Ambellan, Felix and Hanik, Martin and von Tycowicz, Christoph}, title = {Morphomatics: Geometric morphometrics in non-Euclidean shape spaces}, doi = {10.12752/8544}, abstract = {Morphomatics is an open-source Python library for (statistical) shape analysis developed within the geometric data analysis and processing research group at Zuse Institute Berlin. It contains prototype implementations of intrinsic manifold-based methods that are highly consistent and avoid the influence of unwanted effects such as bias due to arbitrary choices of coordinates.}, language = {en} } @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} } @misc{NavaYazdaniHegevonTycowiczetal., author = {Nava-Yazdani, Esfandiar and Hege, Hans-Christian and von Tycowicz, Christoph and Sullivan, T. J.}, title = {A Shape Trajectories Approach to Longitudinal Statistical Analysis}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-69759}, abstract = {For Kendall's shape space we determine analytically Jacobi fields and parallel transport, and compute geodesic regression. Using the derived expressions, we can fully leverage the geometry via Riemannian optimization and reduce the computational expense by several orders of magnitude. The methodology is demonstrated by performing a longitudinal statistical analysis of epidemiological shape data. As application example we have chosen 3D shapes of knee bones, reconstructed from image data of the Osteoarthritis Initiative. Comparing subject groups with incident and developing osteoarthritis versus normal controls, we find clear differences in the temporal development of femur shapes. This paves the way for early prediction of incident knee osteoarthritis, using geometry data only.}, 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{SipiranLazoLopezetal., author = {Sipiran, Ivan and Lazo, Patrick and Lopez, Cristian and Bagewadi, Nihar and Bustos, Benjamin and Dao, Hieu and Gangisetty, Shankar and Hanik, Martin and Ho-Thi, Ngoc-Phuong and Holenderski, Mike and Jarnikov, Dmitri and Labrada, Arniel and Lengauer, Stefan and Licandro, Roxane and Nguyen, Dinh-Huan and Nguyen-Ho, Thang-Long and P{\´e}rez Rey, Luis A. and Pham, Bang-Dang and Pham, Minh-Khoi and Preiner, Reinhold and Schreck, Tobias and Trinh, Quoc-Huy and Tonnaer, Loek and von Tycowicz, Christoph and Vu-Le, The-Anh}, title = {SHREC 2021: Retrieval of Cultural Heritage Objects}, series = {Computers and Graphics}, volume = {100}, journal = {Computers and Graphics}, doi = {10.1016/j.cag.2021.07.010}, pages = {1 -- 20}, abstract = {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.}, 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{vonTycowicz, author = {von Tycowicz, Christoph}, title = {Towards Shape-based Knee Osteoarthritis Classification using Graph Convolutional Networks}, series = {2020 IEEE 17th International Symposium on Biomedical Imaging (ISBI 2020)}, booktitle = {2020 IEEE 17th International Symposium on Biomedical Imaging (ISBI 2020)}, doi = {10.1109/ISBI45749.2020.9098687}, abstract = {We present a transductive learning approach for morphometric osteophyte grading based on geometric deep learning. We formulate the grading task as semi-supervised node classification problem on a graph embedded in shape space. To account for the high-dimensionality and non-Euclidean structure of shape space we employ a combination of an intrinsic dimension reduction together with a graph convolutional neural network. We demonstrate the performance of our derived classifier in comparisons to an alternative extrinsic approach.}, language = {en} } @article{MoewisKaiserTrepczynskietal., author = {Moewis, Philippe and Kaiser, Ren{\´e} and Trepczynski, Adam and von Tycowicz, Christoph and Krahl, Leonie and Ilg, Ansgar and Holz, Johannes and Duda, Georg}, title = {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}, series = {Knee Surgery, Sports Traumatology, Arthroscopy}, journal = {Knee Surgery, Sports Traumatology, Arthroscopy}, doi = {10.1007/s00167-021-06749-8}, abstract = {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 Methods. Retrospective study design. Fluoroscopic analyses during high flexion activities (unloaded flexion-extension and loaded lunge) were conducted at >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). 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. 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.}, language = {en} } @inproceedings{MayerBaumAmbellanetal., author = {Mayer, Julius and Baum, Daniel and Ambellan, Felix and von Tycowicz, Christoph}, title = {A Soft-Correspondence Approach to Shape-based Disease Grading with Graph Convolutional Networks}, series = {Proceedings of Machine Learning Research}, volume = {194}, booktitle = {Proceedings of Machine Learning Research}, pages = {85 -- 95}, abstract = {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.}, 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} } @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{NavaYazdaniHanikAmbellanetal., author = {Nava-Yazdani, Esfandiar and Hanik, Martin and Ambellan, Felix and von Tycowicz, Christoph}, title = {On Gradient Formulas in an Algorithm for the Logarithm of the Sasaki Metric}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-87174}, abstract = {The Sasaki metric is the canonical metric on the tangent bundle TM of a Riemannian manifold M. It is highly useful for data analysis in TM (e.g., when one is interested in the statistics of a set of geodesics in M). To this end, computing the Riemannian logarithm is often necessary, and an iterative algorithm was proposed by Muralidharan and Fletcher. In this note, we derive approximation formulas of the energy gradients in their algorithm that we use with success.}, language = {en} } @misc{NavaYazdaniHegevonTycowicz, author = {Nava-Yazdani, Esfandiar and Hege, Hans-Christian and von Tycowicz, Christoph}, title = {A Hierarchical Geodesic Model for Longitudinal Analysis on Manifolds}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-85187}, 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 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.}, language = {en} } @inproceedings{HanikHegevonTycowicz, author = {Hanik, Martin and Hege, Hans-Christian and von Tycowicz, Christoph}, title = {A Nonlinear Hierarchical Model for Longitudinal Data on Manifolds}, series = {2022 IEEE 19th International Symposium on Biomedical Imaging (ISBI)}, booktitle = {2022 IEEE 19th International Symposium on Biomedical Imaging (ISBI)}, doi = {10.1109/ISBI52829.2022.9761465}, pages = {1 -- 5}, abstract = {Large longitudinal studies provide lots of valuable information, especially in medical applications. A problem which must be taken care of in order to utilize their full potential is that of correlation between intra-subject measurements taken at different times. For data in Euclidean space this can be done with hierarchical models, that is, models that consider intra-subject and between-subject variability in two different stages. Nevertheless, data from medical studies often takes values in nonlinear manifolds. Here, as a first step, geodesic hierarchical models have been developed that generalize the linear ansatz by assuming that time-induced intra-subject variations occur along a generalized straight line in the manifold. However, this is often not the case (e.g., periodic motion or processes with saturation). We propose a hierarchical model for manifold-valued data that extends this to include trends along higher-order curves, namely B{\´e}zier splines in the manifold. To this end, we present a principled way of comparing shape trends in terms of a functional-based Riemannian metric. Remarkably, this metric allows efficient, yet simple computations by virtue of a variational time discretization requiring only the solution of regression problems. We validate our model on longitudinal data from the osteoarthritis initiative, including classification of disease progression.}, language = {en} } @inproceedings{TuerksevenRekikvonTycowiczetal., author = {T{\"u}rkseven, Doğa and Rekik, Islem and von Tycowicz, Christoph and Hanik, Martin}, title = {Predicting Shape Development: A Riemannian Method}, series = {Shape in Medical Imaging}, booktitle = {Shape in Medical Imaging}, publisher = {Springer Nature}, doi = {10.1007/978-3-031-46914-5_17}, pages = {211 -- 222}, abstract = {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.}, language = {en} } @article{NavaYazdaniHegevonTycowicz, author = {Nava-Yazdani, Esfandiar and Hege, Hans-Christian and von Tycowicz, Christoph}, title = {A Hierarchical Geodesic Model for Longitudinal Analysis on Manifolds}, series = {Journal of Mathematical Imaging and Vision}, volume = {64}, journal = {Journal of Mathematical Imaging and Vision}, number = {4}, doi = {10.1007/s10851-022-01079-x}, pages = {395 -- 407}, 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 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.}, language = {en} } @misc{HanikvonTycowicz, author = {Hanik, Martin and von Tycowicz, Christoph}, title = {Triangle meshes of shadow-recieving surfaces of ancient sundials}, doi = {10.12752/8425}, abstract = {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.}, language = {en} } @article{HanikDuckeHegeetal., author = {Hanik, Martin and Ducke, Benjamin and Hege, Hans-Christian and Fless, Friederike and von Tycowicz, Christoph}, title = {Intrinsic shape analysis in archaeology: A case study on ancient sundials}, series = {Journal on Computing and Cultural Heritage}, volume = {16}, journal = {Journal on Computing and Cultural Heritage}, number = {4}, doi = {10.1145/3606698}, pages = {1 -- 26}, abstract = {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.}, language = {en} } @article{OehmeMoewisBoethetal., author = {Oehme, Stephan and Moewis, Philippe and Boeth, Heide and Bartek, Benjamin and Lippert, Annika and von Tycowicz, Christoph and Ehrig, Rainald and Duda, Georg and Jung, Tobias}, title = {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}, series = {Scientific Reports}, volume = {12}, journal = {Scientific Reports}, number = {1}, doi = {10.1038/s41598-022-17328-3}, pages = {1 -- 11}, language = {en} } @article{HanikHegevonTycowicz, author = {Hanik, Martin and Hege, Hans-Christian and von Tycowicz, Christoph}, title = {Bi-invariant Dissimilarity Measures for Sample Distributions in Lie Groups}, series = {SIAM Journal on Mathematics of Data Science}, volume = {4}, journal = {SIAM Journal on Mathematics of Data Science}, number = {4}, doi = {10.1137/21M1410373}, pages = {1223 -- 1249}, abstract = {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.}, language = {en} } @article{NavayazdaniAmbellanHaniketal., author = {Navayazdani, Esfandiar and Ambellan, Felix and Hanik, Martin and von Tycowicz, Christoph}, title = {Sasaki Metric for Spline Models of Manifold-Valued Trajectories}, series = {Computer Aided Geometric Design}, volume = {104}, journal = {Computer Aided Geometric Design}, doi = {10.1016/j.cagd.2023.102220}, pages = {102220}, abstract = {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 B{\´e}zier 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.}, language = {en} } @article{HanikSteidlvonTycowicz, author = {Hanik, Martin and Steidl, Gabriele and von Tycowicz, Christoph}, title = {Manifold GCN: Diffusion-based Convolutional Neural Network for Manifold-valued Graphs}, abstract = {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.}, language = {en} } @article{OehmeMoewisBoethetal., author = {Oehme, Stephan and Moewis, Philippe and Boeth, Heide and Bartek, Benjamin and von Tycowicz, Christoph and Ehrig, Rainald and Duda, Georg and Jung, Tobias}, title = {Altered knee kinematics after posterior cruciate single-bundle reconstruction - a comprehensive prospective biomechanical in vivo analysis}, series = {Frontiers in Bioengineering and Biotechnology}, volume = {12}, journal = {Frontiers in Bioengineering and Biotechnology}, doi = {10.3389/fbioe.2024.1322136}, language = {en} } @inproceedings{PaskinDeanBaumetal., author = {Paskin, Martha and Dean, Mason and Baum, Daniel and von Tycowicz, Christoph}, title = {A Kendall Shape Space Approach to 3D Shape Estimation from 2D Landmarks}, series = {Computer Vision -- ECCV 2022}, booktitle = {Computer Vision -- ECCV 2022}, publisher = {Springer Nature Switzerland}, doi = {10.1007/978-3-031-20086-1_21}, pages = {363 -- 379}, abstract = {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.}, language = {en} } @misc{PaskinBaumDeanetal., author = {Paskin, Martha and Baum, Daniel and Dean, Mason N. and von Tycowicz, Christoph}, title = {A Kendall Shape Space Approach to 3D Shape Estimation from 2D Landmarks -- Source Code and Data}, doi = {10.12752/8730}, abstract = {Source code and novel dataset of basking shark head skeletons facilitating the reproduction of the results presented in 'A Kendall Shape Space Approach to 3D Shape Estimation from 2D Landmarks' - ECCV 2022.}, language = {en} } @article{HanikNavayazdanivonTycowicz, author = {Hanik, Martin and Navayazdani, Esfandiar and von Tycowicz, Christoph}, title = {De Casteljau's Algorithm in Geometric Data Analysis: Theory and Application}, series = {Computer Aided Geometric Design}, volume = {110}, journal = {Computer Aided Geometric Design}, doi = {10.1016/j.cagd.2024.102288}, pages = {102288}, abstract = {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.}, language = {en} }