TY - GEN A1 - Hanik, Martin A1 - von Tycowicz, Christoph T1 - Triangle meshes of shadow-recieving surfaces of ancient sundials N2 - 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. Y1 - 2022 U6 - https://doi.org/10.12752/8425 ER - TY - JOUR A1 - Caputo, Ariel A1 - Emporio, Marco A1 - Giachetti, Andrea A1 - Cristani, Marco A1 - Borghi, Guido A1 - D'Eusanio, Andrea A1 - Le, Minh-Quan A1 - Nguyen, Hai-Dang A1 - Tran, Minh-Triet A1 - Ambellan, Felix A1 - Hanik, Martin A1 - Navayazdani, Esfandiar A1 - Tycowicz, Christoph von T1 - SHREC 2022 Track on Online Detection of Heterogeneous Gestures JF - Computers and Graphics N2 - This paper presents the outcomes of a contest organized to evaluate methods for the online recognition of heterogeneous gestures from sequences of 3D hand poses. The task is the detection of gestures belonging to a dictionary of 16 classes characterized by different pose and motion features. The dataset features continuous sequences of hand tracking data where the gestures are interleaved with non-significant motions. The data have been captured using the Hololens 2 finger tracking system in a realistic use-case of mixed reality interaction. The evaluation is based not only on the detection performances but also on the latency and the false positives, making it possible to understand the feasibility of practical interaction tools based on the algorithms proposed. The outcomes of the contest's evaluation demonstrate the necessity of further research to reduce recognition errors, while the computational cost of the algorithms proposed is sufficiently low. Y1 - 2022 U6 - https://doi.org/10.1016/j.cag.2022.07.015 VL - 107 SP - 241 EP - 251 ER - TY - JOUR A1 - Sipiran, Ivan A1 - Lazo, Patrick A1 - Lopez, Cristian A1 - Bagewadi, Nihar A1 - Bustos, Benjamin A1 - Dao, Hieu A1 - Gangisetty, Shankar A1 - Hanik, Martin A1 - Ho-Thi, Ngoc-Phuong A1 - Holenderski, Mike A1 - Jarnikov, Dmitri A1 - Labrada, Arniel A1 - Lengauer, Stefan A1 - Licandro, Roxane A1 - Nguyen, Dinh-Huan A1 - Nguyen-Ho, Thang-Long A1 - Pérez Rey, Luis A. A1 - Pham, Bang-Dang A1 - Pham, Minh-Khoi A1 - Preiner, Reinhold A1 - Schreck, Tobias A1 - Trinh, Quoc-Huy A1 - Tonnaer, Loek A1 - von Tycowicz, Christoph A1 - Vu-Le, The-Anh T1 - SHREC 2021: Retrieval of Cultural Heritage Objects JF - Computers and Graphics N2 - 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. Y1 - 2021 U6 - https://doi.org/10.1016/j.cag.2021.07.010 VL - 100 SP - 1 EP - 20 ER - TY - JOUR A1 - Navayazdani, Esfandiar A1 - Ambellan, Felix A1 - Hanik, Martin A1 - von Tycowicz, Christoph T1 - Sasaki Metric for Spline Models of Manifold-Valued Trajectories JF - Computer Aided Geometric Design N2 - 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 Bézier 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. Y1 - 2023 U6 - https://doi.org/10.1016/j.cagd.2023.102220 VL - 104 SP - 102220 ER - TY - CHAP A1 - Türkseven, Doğa A1 - Rekik, Islem A1 - von Tycowicz, Christoph A1 - Hanik, Martin T1 - Predicting Shape Development: A Riemannian Method T2 - Shape in Medical Imaging N2 - 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. Y1 - 2023 U6 - https://doi.org/10.1007/978-3-031-46914-5_17 SP - 211 EP - 222 PB - Springer Nature ER - TY - JOUR A1 - Hanik, Martin A1 - Demirtaş, Mehmet Arif A1 - Gharsallaoui, Mohammed Amine A1 - Rekik, Islem T1 - Predicting cognitive scores with graph neural networks through sample selection learning JF - Brain Imaging and Behavior N2 - 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. Y1 - 2022 U6 - https://doi.org/10.1007/s11682-021-00585-7 VL - 16 SP - 1123 EP - 1138 ER - TY - GEN A1 - Nava-Yazdani, Esfandiar A1 - Hanik, Martin A1 - Ambellan, Felix A1 - von Tycowicz, Christoph T1 - On Gradient Formulas in an Algorithm for the Logarithm of the Sasaki Metric N2 - 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. T3 - ZIB-Report - 22-12 Y1 - 2022 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-87174 SN - 1438-0064 ER - TY - CHAP A1 - Hanik, Martin A1 - Hege, Hans-Christian A1 - Hennemuth, Anja A1 - von Tycowicz, Christoph T1 - Nonlinear Regression on Manifolds for Shape Analysis using Intrinsic Bézier Splines T2 - Proc. Medical Image Computing and Computer Assisted Intervention (MICCAI) N2 - 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 Bézier 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 Bézier spline regression as an effective and flexible tool for manifold-valued regression. Y1 - 2020 U6 - https://doi.org/10.1007/978-3-030-59719-1_60 SP - 617 EP - 626 PB - Springer International Publishing CY - Cham ER - TY - GEN A1 - Ambellan, Felix A1 - Hanik, Martin A1 - von Tycowicz, Christoph T1 - Morphomatics: Geometric morphometrics in non-Euclidean shape spaces N2 - 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. KW - shape analysis KW - geometric statistics KW - geometric morphometrics Y1 - 2021 U6 - https://doi.org/10.12752/8544 N1 - https://morphomatics.github.io/ ER - TY - JOUR A1 - Hanik, Martin A1 - Steidl, Gabriele A1 - von Tycowicz, Christoph T1 - Manifold GCN: Diffusion-based Convolutional Neural Network for Manifold-valued Graphs N2 - 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. Y1 - 2024 ER -