Related papers: A Riemannian Approach for Spatiotemporal Analysis …

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…

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…

How can one analyze detailed 3D biological objects, such as neurons and botanical trees, that exhibit complex geometrical and topological variation? In this paper, we develop a novel mathematical framework for representing, comparing, and…

We consider the statistical analysis of trajectories on Riemannian manifolds that are observed under arbitrary temporal evolutions. Past methods rely on cross-sectional analysis, with the given temporal registration, and consequently may…

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…

Spatiotemporal forecasting of complex three-dimensional phenomena (4D: 3D + time) is fundamental to applications in medical imaging, fluid and material dynamics, and geophysics. In contrast to unconstrained neural forecasting models, we…

In this paper, we propose a novel space-time geometric representation of human landmark configurations and derive tools for comparison and classification. We model the temporal evolution of landmarks as parametrized trajectories on the…

In this work, a new model for macroscopic plant tissue growth based on dynamical Riemannian geometry is presented. We treat 1D and 2D tissues as continuous, deformable, growing geometries for sizes larger than 1mm. The dynamics of the…

We investigate a challenging task of dynamic scene geometry estimation, which requires representing both spatial and temporal features. Typically, existing methods align the two features into a unified latent space to model scene geometry.…

We provide a novel approach to model space-time random fields where the temporal argument is decomposed into two parts. The former captures the linear argument, which is related, for instance, to the annual evolution of the field. The…

Even though Non-rigid Structure-from-Motion (NRSfM) has been extensively studied and great progress has been made, there are still key challenges that hinder their broad real-world applications: 1) the inherent motion/rotation ambiguity…

We introduce a novel geometric framework for separating the phase and the amplitude variability in functional data of the type frequently studied in growth curve analysis. This framework uses the Fisher-Rao Riemannian metric to derive a…

Multivariate time-series have become abundant in recent years, as many data-acquisition systems record information through multiple sensors simultaneously. In this paper, we assume the variables pertain to some geometry and present an…

In this paper, we propose a Bayesian matrix-variate spatiotemporal modeling framework for jointly analyzing multiple response variables observed at spatial locations over time. The approach relaxes the standard assumption of spatial…

In constrained solution spaces with a huge number of homotopy classes, stand-alone sampling-based kinodynamic planners suffer low efficiency in convergence. Local optimization is integrated to alleviate this problem. In this paper, we…

Visual observations of dynamic phenomena, such as human actions, are often represented as sequences of smoothly-varying features . In cases where the feature spaces can be structured as Riemannian manifolds, the corresponding…

Plants are dynamic organisms and understanding temporal variations in vegetation is an essential problem for robots in the wild. However, associating repeated 3D scans of plants across time is challenging. A key step in this process is…

Sampling-based motion planning has emerged as a powerful approach for robotics, enabling exploration of complex, high-dimensional configuration spaces. When combined with Signal Temporal Logic (STL), a temporal logic widely used for…

Temporal alignment of multiple signals through time warping is crucial in many fields, such as classification within speech recognition or robot motion learning. Almost all related works are limited to data in Euclidean space. Although an…

We propose a novel Transformer-based architecture for the task of generative modelling of 3D human motion. Previous work commonly relies on RNN-based models considering shorter forecast horizons reaching a stationary and often implausible…