@misc{HanikvonTycowicz2022, author = {Hanik, Martin and von Tycowicz, Christoph}, title = {Triangle meshes of shadow-recieving surfaces of ancient sundials}, doi = {10.12752/8425}, year = {2022}, 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{VeldhuijzenVeltkampIkneetal.2024, author = {Veldhuijzen, Ben and Veltkamp, Remco C. and Ikne, Omar and Allaert, Benjamin and Wannous, Hazem and Emporio, Marco and Giachetti, Andrea and LaViola Jr, Joseph J. and He, Ruiwen and Benhabiles, Halim and Cabani, Adnane and Fleury, Anthony and Hammoudi, Karim and Gavalas, Konstantinos and Vlachos, Christoforos and Papanikolaou, Athanasios and Romanelis, Ioannis and Fotis, Vlassis and Arvanitis, Gerasimos and Moustakas, Konstantinos and Hanik, Martin and Nava-Yazdani, Esfandiar and von Tycowicz, Christoph}, title = {SHREC 2024: Recognition Of Dynamic Hand Motions Molding Clay}, volume = {123}, journal = {Computers \& Graphics}, doi = {10.1016/j.cag.2024.104012}, pages = {104012}, year = {2024}, abstract = {Gesture recognition is a tool to enable novel interactions with different techniques and applications, like Mixed Reality and Virtual Reality environments. With all the recent advancements in gesture recognition from skeletal data, it is still unclear how well state-of- the-art techniques perform in a scenario using precise motions with two hands. This paper presents the results of the SHREC 2024 contest organized to evaluate methods for their recognition of highly similar hand motions using the skeletal spatial coordinate data of both hands. The task is the recognition of 7 motion classes given their spatial coordinates in a frame-by-frame motion. The skeletal data has been captured using a Vicon system and pre-processed into a coordinate system using Blender and Vicon Shogun Post. We created a small, novel dataset with a high variety of durations in frames. This paper shows the results of the contest, showing the techniques created by the 5 research groups on this challenging task and comparing them to our baseline method.}, language = {en} } @article{CaputoEmporioGiachettietal.2022, 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}, volume = {107}, journal = {Computers and Graphics}, arxiv = {http://arxiv.org/abs/2207.06706}, doi = {10.1016/j.cag.2022.07.015}, pages = {241 -- 251}, year = {2022}, 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} } @article{SipiranLazoLopezetal.2021, 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}, volume = {100}, journal = {Computers and Graphics}, doi = {10.1016/j.cag.2021.07.010}, pages = {1 -- 20}, year = {2021}, 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{NavayazdaniAmbellanHaniketal.2023, author = {Navayazdani, Esfandiar and Ambellan, Felix and Hanik, Martin and von Tycowicz, Christoph}, title = {Sasaki Metric for Spline Models of Manifold-Valued Trajectories}, volume = {104}, journal = {Computer Aided Geometric Design}, arxiv = {http://arxiv.org/abs/arXiv:2303.17299}, doi = {10.1016/j.cagd.2023.102220}, pages = {102220}, year = {2023}, 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} } @inproceedings{TuerksevenRekikvonTycowiczetal.2023, author = {T{\"u}rkseven, Doğa and Rekik, Islem and von Tycowicz, Christoph and Hanik, Martin}, title = {Predicting Shape Development: A Riemannian Method}, booktitle = {Shape in Medical Imaging}, publisher = {Springer Nature}, arxiv = {http://arxiv.org/abs/2212.04740}, doi = {10.1007/978-3-031-46914-5_17}, pages = {211 -- 222}, year = {2023}, 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{HanikDemirtaşGharsallaouietal.2022, author = {Hanik, Martin and Demirta{\c{s}}, Mehmet Arif and Gharsallaoui, Mohammed Amine and Rekik, Islem}, title = {Predicting cognitive scores with graph neural networks through sample selection learning}, volume = {16}, journal = {Brain Imaging and Behavior}, arxiv = {http://arxiv.org/abs/2106.09408}, doi = {10.1007/s11682-021-00585-7}, pages = {1123 -- 1138}, year = {2022}, abstract = {Analyzing the relation between intelligence and neural activity is of the utmost importance in understanding the working principles of the human brain in health and disease. In existing literature, functional brain connectomes have been used successfully to predict cognitive measures such as intelligence quotient (IQ) scores in both healthy and disordered cohorts using machine learning models. However, existing methods resort to flattening the brain connectome (i.e., graph) through vectorization which overlooks its topological properties. To address this limitation and inspired from the emerging graph neural networks (GNNs), we design a novel regression GNN model (namely RegGNN) for predicting IQ scores from brain connectivity. On top of that, we introduce a novel, fully modular sample selection method to select the best samples to learn from for our target prediction task. However, since such deep learning architectures are computationally expensive to train, we further propose a \emph{learning-based sample selection} method that learns how to choose the training samples with the highest expected predictive power on unseen samples. For this, we capitalize on the fact that connectomes (i.e., their adjacency matrices) lie in the symmetric positive definite (SPD) matrix cone. Our results on full-scale and verbal IQ prediction outperforms comparison methods in autism spectrum disorder cohorts and achieves a competitive performance for neurotypical subjects using 3-fold cross-validation. Furthermore, we show that our sample selection approach generalizes to other learning-based methods, which shows its usefulness beyond our GNN architecture.}, language = {en} } @inproceedings{StokkeBergmannHaniketal.2025, author = {Stokke, Jo Andersson and Bergmann, Ronny and Hanik, Martin and von Tycowicz, Christoph}, title = {p-Laplacians for Manifold-valued Hypergraphs}, volume = {16035}, booktitle = {Geometric Science of Information. GSI 2025}, arxiv = {http://arxiv.org/abs/2507.10335}, doi = {10.1007/978-3-032-03924-8_17}, year = {2025}, abstract = {Hypergraphs extend traditional graphs by enabling the representation of N-ary relationships through higher-order edges. Akin to a common approach of deriving graph Laplacians, we define function spaces and corresponding symmetric products on the nodes and edges to derive hypergraph Laplacians. While this has been done before for Euclidean features, this work generalizes previous hypergraph Laplacian approaches to accommodate manifold-valued hypergraphs for many commonly encountered manifolds.}, language = {en} } @misc{NavaYazdaniHanikAmbellanetal.2022, 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}, year = {2022}, 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} } @inproceedings{HanikHegeHennemuthetal.2020, 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}, booktitle = {Proc. Medical Image Computing and Computer Assisted Intervention (MICCAI)}, publisher = {Springer International Publishing}, address = {Cham}, arxiv = {http://arxiv.org/abs/2007.05275}, doi = {10.1007/978-3-030-59719-1_60}, pages = {617 -- 626}, year = {2020}, 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} }