@inproceedings{HanikHegevonTycowicz2022, author = {Hanik, Martin and Hege, Hans-Christian and von Tycowicz, Christoph}, title = {A Nonlinear Hierarchical Model for Longitudinal Data on Manifolds}, booktitle = {2022 IEEE 19th International Symposium on Biomedical Imaging (ISBI)}, arxiv = {http://arxiv.org/abs/2202.01180}, doi = {10.1109/ISBI52829.2022.9761465}, pages = {1 -- 5}, year = {2022}, 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} } @misc{AmbellanHanikvonTycowicz2021, author = {Ambellan, Felix and Hanik, Martin and von Tycowicz, Christoph}, title = {Morphomatics: Geometric morphometrics in non-Euclidean shape spaces}, doi = {10.12752/8544}, year = {2021}, 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} } @article{OehmeMoewisBoethetal.2024, 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}, volume = {12}, journal = {Frontiers in Bioengineering and Biotechnology}, doi = {10.3389/fbioe.2024.1322136}, year = {2024}, language = {en} } @article{DietrichvonTycowiczBrandletal.2026, author = {Dietrich, Laura and von Tycowicz, Christoph and Brandl, Michael and Mayer, Julius and Baunack, Lohengrin and Schmidt, Iris}, title = {Project WEAR: Developing a methodological framework for functional analysis on stone tools through controlled experiments and computational modelling of shape transformations through use}, journal = {Antiquity}, year = {2026}, abstract = {The WEAR project is developing an integrative methodology to analyse and predict use-related shape transformation of Neolithic stone axes from Central Europe with mathematical methods and experimental archaeology.}, 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{MayerBaumAmbellanetal.2024, author = {Mayer, Julius and Baum, Daniel and Ambellan, Felix and von Tycowicz, Christoph and for the Alzheimer's Disease Neuroimaging Initiative,}, title = {Shape-based Disease Grading via Functional Maps and Graph Convolutional Networks with Application to Alzheimer's Disease}, volume = {24}, journal = {BMC Medical Imaging}, doi = {10.1186/s12880-024-01513-z}, year = {2024}, abstract = {Shape analysis provides methods for understanding anatomical structures extracted from medical images. However, the underlying notions of shape spaces that are frequently employed 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 functional maps. Further, we present a graph-based learning approach for morphometric classification of disease states that uses novel shape descriptors based on this concept. We demonstrate the performance of the derived classifier on the open-access ADNI database differentiating normal controls and subjects with Alzheimer's disease. Notably, the experiments show that our approach can improve over state-of-the-art from geometric deep learning.}, language = {en} } @misc{NavaYazdaniHegevonTycowicz2021, 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}, year = {2021}, 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{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{HanikDuckeHegeetal.2023, 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}, volume = {16}, journal = {Journal on Computing and Cultural Heritage}, number = {4}, arxiv = {http://arxiv.org/abs/2305.18960}, doi = {10.1145/3606698}, pages = {1 -- 26}, year = {2023}, 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} } @inproceedings{MaignantConradvonTycowicz2025, author = {Maignant, Elodie and Conrad, Tim and von Tycowicz, Christoph}, title = {Tree inference with varifold distances}, volume = {16034}, booktitle = {Geometric Science of Information. GSI 2025}, arxiv = {http://arxiv.org/abs/2507.11313}, doi = {10.1007/978-3-032-03921-7_30}, year = {2025}, abstract = {In this paper, we consider a tree inference problem motivated by the critical problem in single-cell genomics of reconstructing dynamic cellular processes from sequencing data. In particular, given a population of cells sampled from such a process, we are interested in the problem of ordering the cells according to their progression in the process. This is known as trajectory inference. If the process is differentiation, this amounts to reconstructing the corresponding differentiation tree. One way of doing this in practice is to estimate the shortest-path distance between nodes based on cell similarities observed in sequencing data. Recent sequencing techniques make it possible to measure two types of data: gene expression levels, and RNA velocity, a vector that predicts changes in gene expression. The data then consist of a discrete vector field on a (subset of a) Euclidean space of dimension equal to the number of genes under consideration. By integrating this velocity field, we trace the evolution of gene expression levels in each single cell from some initial stage to its current stage. Eventually, we assume that we have a faithful embedding of the differentiation tree in a Euclidean space, but which we only observe through the curves representing the paths from the root to the nodes. Using varifold distances between such curves, we define a similarity measure between nodes which we prove approximates the shortest-path distance in a tree that is isomorphic to the target tree.}, language = {en} } @inproceedings{AmbellanZachowvonTycowicz2021, author = {Ambellan, Felix and Zachow, Stefan and von Tycowicz, Christoph}, title = {Geodesic B-Score for Improved Assessment of Knee Osteoarthritis}, booktitle = {Proc. Information Processing in Medical Imaging (IPMI)}, arxiv = {http://arxiv.org/abs/2104.01107}, doi = {10.1007/978-3-030-78191-0_14}, pages = {177 -- 188}, year = {2021}, 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} } @article{OehmeMoewisBoethetal.2022, 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}, volume = {12}, journal = {Scientific Reports}, number = {1}, doi = {10.1038/s41598-022-17328-3}, pages = {1 -- 11}, year = {2022}, 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{MoewisKaiserTrepczynskietal.2021, 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}, journal = {Knee Surgery, Sports Traumatology, Arthroscopy}, doi = {10.1007/s00167-021-06749-8}, year = {2021}, 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} } @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{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} } @misc{AmbellanZachowvonTycowicz2021, 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}, year = {2021}, 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{MayerBaumAmbellanetal.2022, 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}, volume = {194}, booktitle = {Proceedings of Machine Learning Research}, pages = {85 -- 95}, year = {2022}, 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} } @article{HanikNavayazdanivonTycowicz2024, author = {Hanik, Martin and Navayazdani, Esfandiar and von Tycowicz, Christoph}, title = {De Casteljau's Algorithm in Geometric Data Analysis: Theory and Application}, volume = {110}, journal = {Computer Aided Geometric Design}, arxiv = {http://arxiv.org/abs/2402.07550}, doi = {10.1016/j.cagd.2024.102288}, pages = {102288}, year = {2024}, 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} } @article{HanikSteidlvonTycowicz2024, author = {Hanik, Martin and Steidl, Gabriele and von Tycowicz, Christoph}, title = {Manifold GCN: Diffusion-based Convolutional Neural Network for Manifold-valued Graphs}, arxiv = {http://arxiv.org/abs/2401.14381}, year = {2024}, 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{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{NavaYazdaniHegevonTycowicz2022, author = {Nava-Yazdani, Esfandiar and Hege, Hans-Christian and von Tycowicz, Christoph}, title = {A Hierarchical Geodesic Model for Longitudinal Analysis on Manifolds}, volume = {64}, journal = {Journal of Mathematical Imaging and Vision}, number = {4}, doi = {10.1007/s10851-022-01079-x}, pages = {395 -- 407}, year = {2022}, 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} }