Related papers: A Novel Geometric Framework on Gram Matrix Traject…
Knowledge of shape geometry plays a pivotal role in many shape analysis applications. In this paper we introduce a local geometry-inclusive global representation of 3D shapes based on computation of the shortest quasi-geodesic paths between…
The paper proposes a variational-inequality based primal-dual dynamic that has a globally exponentially stable saddle-point solution when applied to solve linear inequality constrained optimization problems. A Riemannian geometric framework…
We present TimeWalker, a novel framework that models realistic, full-scale 3D head avatars of a person on lifelong scale. Unlike current human head avatar pipelines that capture identity at the momentary level(e.g., instant photography or…
The space of graphs is often characterised by a non-trivial geometry, which complicates learning and inference in practical applications. A common approach is to use embedding techniques to represent graphs as points in a conventional…
We propose a new Riemannian geometry for fixed-rank matrices that is specifically tailored to the low-rank matrix completion problem. Exploiting the degree of freedom of a quotient space, we tune the metric on our search space to the…
This work focuses on complete 3D facial geometry prediction, including 3D facial alignment via 3D face modeling and face orientation estimation using the proposed multi-task, multi-modal, and multi-representation landmark refinement network…
As a means of improving analysis of biological shapes, we propose an algorithm for sampling a Riemannian manifold by sequentially selecting points with maximum uncertainty under a Gaussian process model. This greedy strategy is known to be…
Covariance matrices have proven highly effective across many scientific fields. Since these matrices lie within the Symmetric Positive Definite (SPD) manifold - a Riemannian space with intrinsic non-Euclidean geometry, the primary challenge…
The ability to identify and temporally segment fine-grained actions in motion capture sequences is crucial for applications in human movement analysis. Motion capture is typically performed with optical or inertial measurement systems,…
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 develop a new class of distances for objects including lines, hyperplanes, and trajectories, based on the distance to a set of landmarks. These distances easily and interpretably map objects to a Euclidean space, are simple to compute,…
We integrate two powerful ideas, geometry and deep visual representation learning, into recurrent network architectures for mobile visual scene understanding. The proposed networks learn to "lift" and integrate 2D visual features over time…
In [Heimann, Lehrenfeld, Preu{\ss}, SIAM J. Sci. Comp. 45(2), 2023, B139 - B165] new geometrically unfitted space-time Finite Element methods for partial differential equations posed on moving domains of higher-order accuracy in space and…
Despite significant algorithmic advances in vision-based positioning, a comprehensive probabilistic framework to study its performance has remained unexplored. The main objective of this paper is to develop such a framework using ideas from…
This paper presents a new axis-based shape representation scheme along with a matching framework to address the problem of generic shape recognition. The main idea is to define the relative spatial arrangement of local symmetry axes and…
This paper addresses the problem of Simultaneous Localization and Mapping (SLAM) for rigid body systems in three-dimensional space. We introduce a new matrix Lie group SE_{3+n}(3), whose elements are composed of the pose, gravity, linear…
We propose a method for learning landmark detectors for visual objects (such as the eyes and the nose in a face) without any manual supervision. We cast this as the problem of generating images that combine the appearance of the object as…
There has recently been increasing interest in learning representations of temporal knowledge graphs (KGs), which record the dynamic relationships between entities over time. Temporal KGs often exhibit multiple simultaneous non-Euclidean…
We introduce the manifold of {\it restricted} $n\times n$ positive semidefinite matrices of fixed rank $p$, denoted $S(n,p)^{*}$. The manifold itself is an open and dense submanifold of $S(n,p)$, the manifold of $n\times n$ positive…
Vision based localization is a popular approach to carry out manoeuvres particularly in GPS-restricted indoor environments, because vision can complement other activities performed by the robot. The objective is to estimate the current…