Related papers: Modelling Character Motions on Infinite-Dimensiona…
This paper describes a novel framework for computing geodesic paths in shape spaces of spherical surfaces under an elastic Riemannian metric. The novelty lies in defining this Riemannian metric directly on the quotient (shape) space, rather…
Synthesizing graceful and life-like behaviors for physically simulated characters has been a fundamental challenge in computer animation. Data-driven methods that leverage motion tracking are a prominent class of techniques for producing…
Generating diverse and natural human motion is one of the long-standing goals for creating intelligent characters in the animated world. In this paper, we propose a self-supervised method for generating long-range, diverse and plausible…
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…
Facial animation is one of the most challenging problems in computer graphics, and it is often solved using linear heuristics like blend-shape rigging. More expressive approaches like physical simulation have emerged, but these methods are…
Based on a local approximation of the Riemannian distance on a manifold by a computationally cheap dissimilarity measure, a time discrete geodesic calculus is developed, and applications to shape space are explored. The dissimilarity…
We introduce a novel formulation for geometry on discrete points. It is based on a universal differential calculus, which gives a geometric description of a discrete set by the algebra of functions. We expand this mathematical framework so…
Robotic surface-interaction tasks, such as spray painting or welding, require both accurate geometric planning and precise motion execution. While modern motion planners generate valid geometric paths, they often lack the expert motor…
Incorporating temporal information effectively is important for accurate 3D human motion estimation and generation which have wide applications from human-computer interaction to AR/VR. In this paper, we present MoManifold, a novel human…
Swept volume computation, the determination of regions occupied by moving objects, is essential in graphics, robotics, and manufacturing. Existing approaches either explicitly track surfaces, suffering from robustness issues under complex…
Human motion generation is often learned in Euclidean spaces, although valid motions follow structured non-Euclidean geometry. We present Riemannian Motion Generation (RMG), a unified framework that represents motion on a product manifold…
Motivated by an experimental study of groups generated by reflections in planar patterns of tangent circles, we describe some methods for constructing and studying representation spaces of holonomy groups of infinite volume hyperbolic…
In this paper, the projective geometry is used to describe the features of spherical manifold and discreteness in quantum evolution. As a system evolves in time the state vector changes and it traces out a curve in Hilbert space.…
This paper introduces and demonstrates a computational pipeline for the statistical analysis of shape graph datasets, namely geometric networks embedded in 2D or 3D spaces. Unlike traditional abstract graphs, our purpose is not only to…
Dynamic motions of humans and robots are widely driven by posture-dependent nonlinear interactions between their degrees of freedom. However, these dynamical effects remain mostly overlooked when studying the mechanisms of human movement…
This paper explores visual motion-based invariants, resulting in a new instantaneous domain where: a) the stationary environment is perceived as unchanged, even as the 2D images undergo continuous changes due to camera motion, b) obstacles…
We present an implicit neural representation to learn the spatio-temporal space of kinematic motions. Unlike previous work that represents motion as discrete sequential samples, we propose to express the vast motion space as a continuous…
We define an evolution of multiple particles on a discrete manifold $G$. Each particle alone moves on geodesics and particles can interact if they are on the same facet. They move deterministically and reversibly on the frame bundle $P$ of…
Motivated by the problem of nonparametric inference in high level digital image analysis, we introduce a general extrinsic approach for data analysis on Hilbert manifolds with a focus on means of probability distributions on such sample…
It is shown here how prior estimates on the local shape of the universe can be used to reduce, to a small region, the full parameter space for the search of circles in the sky. This is the first step towards the development of efficient…