@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} } @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} } @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{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} } @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{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} } @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{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{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} }