Related papers: Geodesic analysis in Kendall's shape space with ep…

We propose a novel framework to learn the spatiotemporal variability in longitudinal 3D shape data sets, which contain observations of objects that evolve and deform over time. This problem is challenging since surfaces come with arbitrary…

Leveraging geodesic distances and the geometrical information they convey is key for many data-oriented applications in imaging. Geodesic distance computation has been used for long for image segmentation using Image based metrics. We…

We present Geodesic Semantic Search (GSS), a retrieval system that learns node-specific Riemannian metrics on citation graphs to enable geometry-aware semantic search. Unlike standard embedding-based retrieval that relies on fixed Euclidean…

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…

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…

We introduce the shape module of the Python package Geomstats to analyze shapes of objects represented as landmarks, curves and surfaces across fields of natural sciences and engineering. The shape module first implements widely used shape…

Accurate prediction of knee osteoarthritis (KOA) progression from structural MRI has a potential to enhance disease understanding and support clinical trials. Prior art focused on manually designed imaging biomarkers, which may not fully…

The automatic segmentation of human knee cartilage from 3D MR images is a useful yet challenging task due to the thin sheet structure of the cartilage with diffuse boundaries and inhomogeneous intensities. In this paper, we present an…

In this paper the space of images is considered as a Riemannian manifold using the metamorphosis approach, where the underlying Riemannian metric simultaneously measures the cost of image transport and intensity variation. A robust and…

Recurrence plot based methods are highly efficient and widely accepted tools for the investigation of time series or one-dimensional data. We present an extension of the recurrence plots and their quantifications in order to study recurrent…

We review a simple but instructive application of the formalism of covariant bitensors, to use a deviation vector field along a fiducial geodesic to describe a neighboring worldline, in an exact and manifestly covariant manner, via the…

In fields ranging from computer vision to signal processing and statistics, increasing computational power allows a move from classical linear models to models that incorporate non-linear phenomena. This shift has created interest in…

Regression analysis for responses taking values in general metric spaces has received increasing attention, particularly for settings with Euclidean predictors $X \in \mathbb{R}^p$ and non-Euclidean responses $Y$ in metric spaces. While…

Shape affects both the physical and chemical properties of a material. Characterizing the roughness, convexity, and general geometry of a material can yield information on its catalytic efficiency, solubility, elasticity, porosity, and…

This paper proposes a generalized framework with joint normalization which learns lower-dimensional subspaces with maximum discriminative power by making use of the Riemannian geometry. In particular, we model the similarity/dissimilarity…

This work presents a new method for generating impulsive trajectories in restricted two-body systems by leveraging Riemannian geometry. The proposed method transforms the standard trajectory optimization problem into a purely geometric one…

Understanding feature-outcome associations in high-dimensional data remains challenging when relationships vary across subpopulations, yet standard methods assuming global associations miss context-dependent patterns, reducing statistical…

In medical image analysis, automated segmentation of multi-component anatomical structures, which often have a spectrum of potential anomalies and pathologies, is a challenging task. In this work, we develop a multi-step approach using…

We propose a framework for 2D shape analysis using positive definite kernels defined on Kendall's shape manifold. Different representations of 2D shapes are known to generate different nonlinear spaces. Due to the nonlinearity of these…

The geodesic motion in a Lorentzian spacetime can be described by trajectories in a $3-$dimensional Riemannian metric. In this article we present a generalized Jacobi metric obtained from projecting a Lorentzian metric over the directions…