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 - CHAP A1 - Hanik, Martin A1 - Hege, Hans-Christian A1 - von Tycowicz, Christoph T1 - A Nonlinear Hierarchical Model for Longitudinal Data on Manifolds T2 - 2022 IEEE 19th International Symposium on Biomedical Imaging (ISBI) N2 - 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 Bézier 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. Y1 - 2022 U6 - https://doi.org/10.1109/ISBI52829.2022.9761465 SP - 1 EP - 5 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 - THES A1 - Hanik, Martin T1 - Geometric Data Analysis: Advancements of the Statistical Methodology and Applications N2 - Data analysis has become fundamental to our society and comes in multiple facets and approaches. Nevertheless, in research and applications, the focus was primarily on data from Euclidean vector spaces. Consequently, the majority of methods that are applied today are not suited for more general data types. Driven by needs from fields like image processing, (medical) shape analysis, and network analysis, more and more attention has recently been given to data from non-Euclidean spaces---particularly (curved) manifolds. It has led to the field of geometric data analysis whose methods explicitly take the structure (for example, the topology and geometry) of the underlying space into account. This thesis contributes to the methodology of geometric data analysis by generalizing several fundamental notions from multivariate statistics to manifolds. We thereby focus on two different viewpoints. First, we use Riemannian structures to derive a novel regression scheme for general manifolds that relies on splines of generalized Bézier curves. It can accurately model non-geodesic relationships, for example, time-dependent trends with saturation effects or cyclic trends. Since Bézier curves can be evaluated with the constructive de Casteljau algorithm, working with data from manifolds of high dimensions (for example, a hundred thousand or more) is feasible. Relying on the regression, we further develop a hierarchical statistical model for an adequate analysis of longitudinal data in manifolds, and a method to control for confounding variables. We secondly focus on data that is not only manifold- but even Lie group-valued, which is frequently the case in applications. We can only achieve this by endowing the group with an affine connection structure that is generally not Riemannian. Utilizing it, we derive generalizations of several well-known dissimilarity measures between data distributions that can be used for various tasks, including hypothesis testing. Invariance under data translations is proven, and a connection to continuous distributions is given for one measure. A further central contribution of this thesis is that it shows use cases for all notions in real-world applications, particularly in problems from shape analysis in medical imaging and archaeology. We can replicate or further quantify several known findings for shape changes of the femur and the right hippocampus under osteoarthritis and Alzheimer's, respectively. Furthermore, in an archaeological application, we obtain new insights into the construction principles of ancient sundials. Last but not least, we use the geometric structure underlying human brain connectomes to predict cognitive scores. Utilizing a sample selection procedure, we obtain state-of-the-art results. KW - Regression in Riemannian manifolds KW - Bi-invariant statistics KW - Bézier splines KW - Shape analysis KW - Brain connectomes KW - Ancient sundials Y1 - 2023 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:188-refubium-40087-8 PB - Refubium ER - TY - JOUR A1 - Hanik, Martin A1 - Ducke, Benjamin A1 - Hege, Hans-Christian A1 - Fless, Friederike A1 - von Tycowicz, Christoph T1 - Intrinsic shape analysis in archaeology: A case study on ancient sundials JF - Journal on Computing and Cultural Heritage N2 - 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. Y1 - 2023 U6 - https://doi.org/10.1145/3606698 VL - 16 IS - 4 SP - 1 EP - 26 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 - 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 - Nava-Yazdani, Esfandiar A1 - Hege, Hans-Christian A1 - von Tycowicz, Christoph T1 - A Hierarchical Geodesic Model for Longitudinal Analysis on Manifolds JF - Journal of Mathematical Imaging and Vision N2 - 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. Y1 - 2022 U6 - https://doi.org/10.1007/s10851-022-01079-x VL - 64 IS - 4 SP - 395 EP - 407 ER - TY - JOUR A1 - Hanik, Martin A1 - Hege, Hans-Christian A1 - von Tycowicz, Christoph T1 - Bi-invariant Dissimilarity Measures for Sample Distributions in Lie Groups JF - SIAM Journal on Mathematics of Data Science N2 - 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. Y1 - 2022 U6 - https://doi.org/10.1137/21M1410373 VL - 4 IS - 4 SP - 1223 EP - 1249 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 -