相关论文: Geometrical Optical Illusion via Sub-Riemannian Ge…

All that structure from motion algorithms "see" are sets of 2D points. We show that these impoverished views of the world can be faked for the purpose of reconstructing objects in challenging settings, such as from a single image, or from a…

Recently, "visual o1" began to enter people's vision, with expectations that this slow-thinking design can solve visual reasoning tasks, especially geometric math problems. However, the reality is that current LVLMs (Large Vision Language…

The Expanding Hole Illusion is a compelling visual phenomenon in which a static, concentric pattern evokes a strong perception of continuous forward motion. Despite its simplicity, this illusion challenges our understanding of how the brain…

In a recent paper on Cortical Dynamics, Francis and Grossberg raise the question how visual forms and motion information are integrated to generate a coherent percept of moving forms? In their investigation of illusory contours (which are,…

Effectively modeling multimodal spatial omics data is critical for understanding tissue complexity and underlying biological mechanisms. While spatial transcriptomics, proteomics, and epigenomics capture molecular features, they lack…

We investigate the geometrical structure of probabilistic generative dimensionality reduction models using the tools of Riemannian geometry. We explicitly define a distribution over the natural metric given by the models. We provide the…

The goal of this study is to provide a method for computing the following: Given a network of curves in 3d (satisfying a condition at the intersection points), compute efficiently a smooth surface such that the curves are geodesics on it.…

Implicit Neural Representations (INRs) are widely used for modeling continuous 2D images, enabling high-fidelity reconstruction, super-resolution, and compression. Architectures such as SIREN, WIRE, and FINER demonstrate their ability to…

Geodesic currents on closed hyperbolic surfaces are measures on the unit tangent bundle invariant under geodesic flow and orientation reversal. Every geodesic current induces a dual function on curves via the geometric intersection pairing.…

We prove that a foliation $(M, F)$ of codimension $q$ on a $n$-dimen\-sio\-nal pseudo-Riemannian manifold is pseudo-Riemannian if and only if any geodesic that is orthogonal at one point to a leaf is orthogonal to every leaf it intersects.…

AI-driven geometric problem solving is a complex vision-language task that requires accurate diagram interpretation, mathematical reasoning, and robust cross-modal grounding. A foundational yet underexplored capability for this task is the…

In this article, we examine the geometry of a group of Fourier-integral operators, which is the central extension of $Diff(S^1)$ with a group of classical pseudo-differential operators of any order. Several subgroups are considered, and the…

This paper presents a novel method, named geodesic deformable networks (GDN), that for the first time enables the learning of geodesic flows of deformation fields derived from images. In particular, the capability of our proposed GDN being…

We provide a self-contained geometric description of the geodesic flow in the three-dimensional Lie group $\mathrm{Sol}$, one of Thurston's eight model geometries. The geometry of geodesics is governed by a single invariant $k\in[0,1]$, its…

The geodesic motion in a Lorentzian spacetime can be described by trajectories in a $3-$dimensional Riemannian metric. In this article we present a generalized Jacobi metric obtained from projecting a Lorentzian metric over the directions…

The last decade has witnessed an experimental revolution in data science and machine learning, epitomised by deep learning methods. Indeed, many high-dimensional learning tasks previously thought to be beyond reach -- such as computer…

We propose CG-HOI, the first method to address the task of generating dynamic 3D human-object interactions (HOIs) from text. We model the motion of both human and object in an interdependent fashion, as semantically rich human motion rarely…

In order to compare and interpolate signals, we investigate a Riemannian geometry on the space of signals. The metric allows discontinuous signals and measures both horizontal (thus providing many benefits of the Wasserstein metric) and…

Electromagnetism in an inhomogeneous dielectric medium at rest is described using the methods of differential geometry. In contrast to a general relativistic approach the electromagnetic fields are discussed in three-dimensional space only.…

Reconstructing dynamic scenes with complex human-object interactions is a fundamental challenge in computer vision and graphics. Existing Gaussian Splatting methods either rely on human pose priors while neglecting dynamic objects, or…