Related papers: A Hierarchical Geodesic Model for Longitudinal Ana…

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…

We analytically determine Jacobi fields and parallel transports and compute geodesic regression in Kendall's shape space. Using the derived expressions, we can fully leverage the geometry via Riemannian optimization and thereby reduce the…

Many phenomena are naturally characterized by measuring continuous transformations such as shape changes in medicine or articulated systems in robotics. Modeling the variability in such datasets requires performing statistics on Lie groups,…

We analyze a variational time discretization of geodesic calculus on finite- and certain classes of infinite-dimensional Riemannian manifolds. We investigate the fundamental properties of discrete geodesics, the associated discrete…

In the statistical analysis of shape a goal beyond the analysis of static shapes lies in the quantification of `same' deformation of different shapes. Typically, shape spaces are modelled as Riemannian manifolds on which parallel transport…

Geodesic regression has been proposed for fitting the geodesic curve. However, it cannot automatically choose the dimensionality of data. In this paper, we develop a Bayesian geodesic regression model on Riemannian manifolds (BGRM) model.…

This paper studies robust regression for data on Riemannian manifolds. Geodesic regression is the generalization of linear regression to a setting with a manifold-valued dependent variable and one or more real-valued independent variables.…

Manifolds discovered by machine learning models provide a compact representation of the underlying data. Geodesics on these manifolds define locally length-minimising curves and provide a notion of distance, which are key for reduced-order…

For manifold learning, it is assumed that high-dimensional sample/data points are embedded on a low-dimensional manifold. Usually, distances among samples are computed to capture an underlying data structure. Here we propose a metric…

This paper introduces a set of numerical methods for Riemannian shape analysis of 3D surfaces within the setting of invariant (elastic) second-order Sobolev metrics. More specifically, we address the computation of geodesics and geodesic…

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…

Geodesic distance serves as a reliable means of measuring distance in nonlinear spaces, and such nonlinear manifolds are prevalent in the current multimodal learning. In these scenarios, some samples may exhibit high similarity, yet they…

Models for distributions of shapes contained within images can be widely used in biomedical applications ranging from tumor tracking for targeted radiation therapy to classifying cells in a blood sample. Our focus is on hierarchical…

Mixed effect modeling for longitudinal data is challenging when the observed data are random objects, which are complex data taking values in a general metric space without linear structure. In such settings the classical additive error…

We introduce a new regression framework designed to deal with large-scale, complex data that lies around a low-dimensional manifold with noises. Our approach first constructs a graph representation, referred to as the skeleton, to capture…

This paper proposes a novel framework for multi-group shape analysis relying on a hierarchical graphical statistical model on shapes within a population.The framework represents individual shapes as point setsmodulo translation, rotation,…

The length of the geodesic between two data points along a Riemannian manifold, induced by a deep generative model, yields a principled measure of similarity. Current approaches are limited to low-dimensional latent spaces, due to the…

Mechanistic statistical models are commonly used to study the flow of biological processes. For example, in landscape genetics, the aim is to infer spatial mechanisms that govern gene flow in populations. Existing statistical approaches in…

We consider monotonic, multiple regression for a set of contiguous regions (lattice data). The regression functions permissibly vary between regions and exhibit geographical structure. We develop new Bayesian non-parametric methodology…

Intrinsic and parametric regression models are of high interest for the statistical analysis of manifold-valued data such as images and shapes. The standard linear ansatz has been generalized to geodesic regression on manifolds making it…