相关论文: Modelling Character Motions on Infinite-Dimensiona…

Phase plotting is a useful way of visualising functions on complex space. We reinvent the method in the context of hyperbolic geometry, and we use it to plot functions on various representative surfaces for hyperbolic space, illustrating…

In the shape analysis approach to computer vision problems, one treats shapes as points in an infinite-dimensional Riemannian manifold, thereby facilitating algorithms for statistical calculations such as geodesic distance between shapes…

The problem of identifying geometric structure in data is a cornerstone of (unsupervised) learning. As a result, Geometric Representation Learning has been widely applied across scientific and engineering domains. In this work, we…

Choosing the right representation for geometry is crucial for making 3D models compatible with existing applications. Focusing on piecewise-smooth man-made shapes, we propose a new representation that is usable in conventional CAD modeling…

Motion retargeting is the long-standing problem in character animation that consists in transferring and adapting the motion of a source character to another target character. A typical application is the creation of motion sequences from…

In this paper, we propose a novel framework for dynamical analysis of human actions from 3D motion capture data using topological data analysis. We model human actions using the topological features of the attractor of the dynamical system.…

Animation of humanoid characters is essential in various graphics applications, but requires significant time and cost to create realistic animations. We propose an approach to synthesize 4D animated sequences of input static 3D humanoid…

We fully generalize a previously-developed computational geometry tool [1] to perform large-scale simulations of arbitrary two-dimensional faceted surfaces $z = h(x,y)$. Our method uses a three-component facet/edge/junction storage model,…

In this thesis, we propose an alternative characterization of the notion of Configuration Space, which we call Visual Configuration Space (VCS). This new characterization allows an embodied agent (e.g., a robot) to discover its own body…

This communication describes a representation of images as a set of edges characterized by their position and orientation. This representation allows the comparison of two images and the computation of their similarity. The first step in…

We cast shape matching as metric learning with convolutional networks. We break the end-to-end process of image representation into two parts. Firstly, well established efficient methods are chosen to turn the images into edge maps.…

This work presents an instance-agnostic learning framework that fuses vision with dynamics to simultaneously learn shape, pose trajectories, and physical properties via the use of geometry as a shared representation. Unlike many contact…

We address the problem of learning representations from observations of a scene involving an agent and an external object the agent interacts with. To this end, we propose a representation learning framework extracting the location in…

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…

This paper presents a novel framework for visual object recognition using infinite-dimensional covariance operators of input features in the paradigm of kernel methods on infinite-dimensional Riemannian manifolds. Our formulation provides…

We introduce a new technique to visualize complex flowing phenomena by using concepts from shape analysis. Our approach uses techniques that examine the intrinsic geometry of manifolds through their heat kernel, to obtain representations of…

Motion segmentation in dynamic scenes is highly challenging, as conventional methods heavily rely on estimating camera poses and point correspondences from inherently noisy motion cues. Existing statistical inference or iterative…

Learning structured task representations from human demonstrations is essential for understanding long-horizon manipulation behaviors, particularly in bimanual settings where action ordering, object involvement, and interaction geometry can…

This paper is concerned with the computation of an optimal matching between two manifold-valued curves. Curves are seen as elements of an infinite-dimensional manifold and compared using a Riemannian metric that is invariant under the…

Human motion prediction aims to forecast future human poses given a prior pose sequence. The discontinuity of the predicted motion and the performance deterioration in long-term horizons are still the main challenges encountered in current…