相关论文: Virtual Manifolds and Localization

These course notes are about computing modular forms and some of their arithmetic properties. Their aim is to explain and prove the modular symbols algorithm in as elementary and as explicit terms as possible, and to enable the devoted…

We study toroidal orbifold models with topologically invariant terms in the path integral formalism and give physical interpretations of the terms from an operator formalism point of view. We briefly discuss a possibility of a new class of…

We develop a geometric version of the inverse problem of the calculus of variations for discrete mechanics and constrained discrete mechanics. The geometric approach consists of using suitable Lagrangian and isotropic submanifolds. We also…

We construct the moduli space of r-jets at a point of Riemannian metrics on a smooth manifold. The construction is closely related to the problem of classification of jet metrics via differential invariants. The moduli space is proved to be…

This paper proposes a novel approach to scaling distributed collaboration in mixed reality by virtualizing collaborative tasks as independent, installable environments. By mapping group activities into dedicated virtual spaces that adapt to…

Recent literature has shown that symbolic data, such as text and graphs, is often better represented by points on a curved manifold, rather than in Euclidean space. However, geometrical operations on manifolds are generally more complicated…

This paper presents a new technique for the virtual reality (VR) visu-alization of complex volume images obtained from computer tomography (CT) and Magnetic Resonance Imaging (MRI) by combining three-dimensional (3D) mesh processing and…

This paper proposed a new interaction paradigm in the virtual reality (VR) environments, which consists of a virtual mirror or window projected onto a virtual surface, representing the correct perspective geometry of a mirror or window…

Deformable objects manipulation can benefit from representations that seamlessly integrate vision and touch while handling occlusions. In this work, we present a novel approach for, and real-world demonstration of, multimodal visuo-tactile…

We present and discuss applications of the category of probabilistic morphisms, initially developed in \cite{Le2023}, as well as some geometric methods to several classes of problems in statistical, machine and manifold learning which shall…

Recent learning-based approaches have achieved impressive results in the field of single-shot camera localization. However, how best to fuse multiple modalities (e.g., image and depth) and to deal with degraded or missing input are less…

This is a survey paper based on my talk at the Workshop on Orbifolds and String Theory, the goal of which was to explain the role of groupoids and their classifying spaces as a foundation for the theory of orbifolds.

These lecture notes consist of an introduction to moduli spaces in algebraic geometry, with a strong emphasis placed on examples related to the theory of quiver representations. The goal is to provide the background necessary to understand…

Enumerative invariants in Algebraic Geometry 'count' $\tau$-(semi)stable objects $E$ with fixed topological invariants $[E]=a$ in some geometric problem, using a virtual class $[{\cal M}_a^{\rm ss}(\tau)]_{\rm virt}$ in homology, for the…

Moduli spaces of stable sheaves on smooth projective surfaces are in general singular. Nonetheless, they carry a virtual class, which -- in analogy with the classical case of Hilbert schemes of points -- can be used to define intersection…

The interest in virtualization has been growing rapidly in the IT industry because of inherent benefits like better resource utilization and ease of system manageability. The experimentation and use of virtualization as well as the…

Visual object localization is the key step in a series of object detection tasks. In the literature, high localization accuracy is achieved with the mainstream strongly supervised frameworks. However, such methods require object-level…

We give a canonical description of the formal moduli space of a vector bundle on a variety; as an application, we prove the closedness of certain differential forms on moduli corresponding to the trace form on the endomorphism algebra of…

The present contribution suggests the use of a multidimensional scaling (MDS) algorithm as a visualization tool for manifold-valued elements. A visualization tool of this kind is useful in signal processing and machine learning whenever…

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…