A5073020214- Morphological variations and asymmetry
- 3D Shape Modeling and Analysis
- Image Processing and 3D Reconstruction
- Advanced Numerical Analysis Techniques
- Advanced Graph Neural Networks
- Hand Gesture Recognition Systems
- Topological and Geometric Data Analysis
- Human Pose and Action Recognition
- Bayesian Methods and Mixture Models
- Functional Brain Connectivity Studies
- Bioinformatics and Genomic Networks
- Machine Learning in Healthcare
- Advanced Vision and Imaging
- Hydrology and Sediment Transport Processes
- Hydrology and Drought Analysis
- Advanced Neuroimaging Techniques and Applications
- Advanced Measurement and Metrology Techniques
- Cultural Heritage Materials Analysis
- Landslides and related hazards
- Statistical Methods and Inference
- Advanced Image and Video Retrieval Techniques
- advanced mathematical theories
- Gait Recognition and Analysis
- Geological Modeling and Analysis
- 3D Surveying and Cultural Heritage
Freie Universität Berlin
2022-2024
Technische Universität Berlin
2024
Zuse Institute Berlin
2020-2023
Istanbul Technical University
2021
University of Dundee
2021
Tunisia Polytechnic School
2021
Many phenomena are naturally characterized by measuring continuous transformations such as shape changes in medicine or articulated systems robotics. Modeling the variability datasets requires performing statistics on Lie groups, that is, manifolds carrying an additional group structure. As captures symmetries data, it is essential from a theoretical and practical perspective to ask for statistical methods respect these symmetries; this way they insensitive confounding effects, e.g., due...
We propose two graph neural network layers for graphs with features in a Riemannian manifold. First, based on manifold-valued diffusion equation, we construct layer that can be applied to an arbitrary number of nodes and connectivity patterns. Second, model tangent multilayer perceptron by transferring ideas from the vector neuron framework our general setting. Both are equivariant respect node permutations isometries feature These properties have been shown lead beneficial inductive bias...
For decades, de Casteljau's algorithm has been used as a fundamental building block in curve and surface design found wide range of applications fields such scientific computing discrete geometry, to name but few. With increasing interest nonlinear data science, its constructive approach shown provide principled way generalize parametric smooth curves manifolds. These have remarkable new the analysis parameter-dependent, geometric data. This article provides survey recent theoretical...
Analyzing the relation between intelligence and neural activity is of utmost importance in understanding working principles human brain health disease. In existing literature, functional connectomes have been used successfully to predict cognitive measures such as quotient (IQ) scores both healthy disordered cohorts using machine learning models. However, methods resort flattening connectome (i.e., graph) through vectorization which overlooks its topological properties. To address this...
Gesture recognition is a tool to enable novel interactions with different techniques and applications, like Mixed Reality Virtual environments. With all the recent advancements in gesture from skeletal data, it still unclear how well state-of-the-art perform scenario using precise motions two hands. This paper presents results of SHREC 2024 contest organized evaluate methods for their highly similar hand spatial coordinate data both The task 7 motion classes given coordinates frame-by-frame...
Large longitudinal studies provide information that is particularly valuable in medical studies. A problem must be solved order to realize the full potential correlation between intra-subject measurements taken at different times. For data Euclidean space this can achieved with hierarchical models, i.e., models account for and between-subject variability two levels. How-ever, from often take values nonlinear manifolds. such data, as a first step, geodesic have been developed generalize...
For decades, de Casteljau's algorithm has been used as a fundamental building block in curve and surface design found wide range of applications fields such scientific computing, discrete geometry to name but few. With increasing interest nonlinear data science, its constructive approach shown provide principled way generalize parametric smooth curves manifolds. These have remarkable new the analysis parameter-dependent, geometric data. This article provides survey recent theoretical...
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 other hand, it is also a major analytical challenge uncover these trends disentagle them in an unbiased way. This article explores novel mathematical approach extract archaeological insights from ensembles similar artifact shapes. We show by considering all shape find collection , possible...
Abstract Analyzing the relation between intelligence and neural activity is of utmost importance in understanding working principles human brain health disease. In existing literature, functional connectomes have been used successfully to predict cognitive measures such as quotient (IQ) scores both healthy disordered cohorts using machine learning models. However, methods resort flattening connectome (i.e., graph) through vectorization which overlooks its topological properties. To address...
Data sets sampled in Lie groups are widespread, and as with multivariate data, it is important for many applications to assess the differences between terms of their distributions. Indices this task usually derived by considering group a Riemannian manifold. Then, however, compatibility operation guaranteed only if bi-invariant metric exists, which not case most non-compact non-commutative groups. We show here that one considers an affine connection structure instead, obtains generalizations...
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 manifold by composite B\' ezier splines, natural metric induced the Sasaki compare trajectories, estimate average as group-wise trends. evaluate our comparison state-of-the-art methods within qualitative quantitative experiments on...
This paper explores a novel mathematical approach to extract archaeological insights from ensembles of similar artifact shapes. We show that by considering all the shape information in find collection, it is possible identify patterns would be difficult discern artifacts individually or classifying shapes into predefined types and analyzing associated distinguishing characteristics. Recently, series high-resolution digital representations have become available, we explore their potential on...
Large longitudinal studies provide lots of valuable information, especially in medical applications. A problem which must be taken care order to utilize their full potential is that correlation between intra-subject measurements at different times. For data Euclidean space this can done with hierarchical models, is, models consider and between-subject variability two stages. Nevertheless, from often takes values nonlinear manifolds. Here, as a first step, geodesic have been developed...
This paper presents the computational challenge on differential geometry and topology that was hosted within ICLR 2022 workshop ``Geometric Topological Representation Learning". The competition asked participants to provide implementations of machine learning algorithms manifolds would respect API open-source software Geomstats (manifold part) Scikit-Learn (machine or PyTorch. attracted seven teams in its two month duration. describes design summarizes main findings.
Predicting the future development of an anatomical shape from a single baseline observation is challenging task. But it can be essential for clinical decision-making. Research has shown that should tackled in curved spaces, as (e.g., disease-related) changes frequently expose nonlinear characteristics. We thus propose novel prediction method encodes whole Riemannian space. It then learns simple technique founded on hierarchical statistical modeling longitudinal training data. When applied to...