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This article presents a new mathematical framework to perform statistical analysis on time-indexed sequences of 2D or 3D shapes. At the core of this statistical analysis is the task of time interpolation of such data. Current models in use…

Imaging features of knee articular cartilage have been shown to be potential imaging biomarkers for knee osteoarthritis. Despite recent methodological advancements in image analysis techniques like image segmentation, registration, and…

We study the patient zero problem in epidemic spreading processes in the independent cascade model and propose a geometric approach for source reconstruction. Using Johnson-Lindenstrauss projections, we embed the contact network into a…

This work presents the spatial error model with heteroskedasticity, which allows the joint modeling of the parameters associated with both the mean and the variance, within a traditional approach to spatial econometrics. The estimation…

The statistical analysis of data lying on a differentiable, locally Euclidean, manifold introduces a variety of challenges because the analogous measures to standard Euclidean statistics are local, that is only defined within a…

The theory of geodesic regression aims to find a geodesic curve which is an optimal fit to a given set of data. In this article we restrict ourselves to the Riemannian manifold of positive definite operators (matrices) on a Hilbert space of…

In this article we introduce a family of elastic metrics on the space of parametrized surfaces in 3D space using a corresponding family of metrics on the space of vector valued one-forms. We provide a numerical framework for the computation…

We consider the problem of estimating a parametric model of 3D human mesh from a single image. While there has been substantial recent progress in this area with direct regression of model parameters, these methods only implicitly exploit…

The Grassmann manifold of linear subspaces is important for the mathematical modelling of a multitude of applications, ranging from problems in machine learning, computer vision and image processing to low-rank matrix optimization problems,…

Many geometric machine learning and image analysis applications, require a left-invariant metric on the 5D homogeneous space of 3D positions and orientations SE(3)/SO(2). This is done in Equivariant Neural Networks (G-CNNs), or in PDE-Based…

In this work, we investigate a novel approach for the simulation of two-dimensional, brittle, quasi-static fracture problems based on a shape optimization approach. In contrast to the commonly-used phase-field approach, this proposed…

Incorporating shape information is essential for the delineation of many organs and anatomical structures in medical images. While previous work has mainly focused on parametric spatial transformations applied on reference template shapes,…

The generalized partially linear models on Riemannian manifolds are introduced. These models, like ordinary generalized linear models, are a generalization of partially linear models on Riemannian manifolds that allow for response variables…

This paper introduces a novel computational framework for modeling and analyzing the spatiotemporal shape variability of tree-like 4D structures whose shapes deform and evolve over time. Tree-like 3D objects, such as botanical trees and…

Osteoarthritis is a degenerative condition affecting bones and cartilage, often leading to osteophyte formation, bone density loss, and joint space narrowing. Treatment options to restore normal joint function vary depending on the severity…

Many biomedical studies collect high-dimensional medical imaging data to identify biomarkers for the detection, diagnosis, and treatment of human diseases. Consequently, it is crucial to develop accurate models that can predict a wide range…

Timelike geodesics on a hyperplane orthogonal to the symmetry axis of the G\"odel spacetime appear to be elliptic-like if standard coordinates naturally adapted to the cylindrical symmetry are used. The orbit can then be suitably described…

Natural objects can be subject to various transformations yet still preserve properties that we refer to as invariants. Here, we use definitions of affine invariant arclength for surfaces in R^3 in order to extend the set of existing…

Osteoarthritis (OA) is a highly prevalent degenerative joint disease, and the knee is the most commonly affected joint. Biomechanical factors, particularly forces exerted during walking, are often measured in modern studies of knee joint…

Knee injuries are frequent, varied and often require the patient to undergo intensive rehabilitation for several months. Treatment protocols usually contemplate some recurrent measurements in order to assess progress, such as goniometry.…