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

Correlation matrices are fundamental summaries of functional brain networks, yet standard analyses often treat entries independently, ignoring the curved geometry of correlation space. Existing geometric methods frequently lack closed-form…

Although modern object detectors rely heavily on a significant amount of training data, humans can easily detect novel objects using a few training examples. The mechanism of the human visual system is to interpret spatial relationships…

The geometric approach to optimal transport and information theory has triggered the interpretation of probability densities as an infinite-dimensional Riemannian manifold. The most studied Riemannian structures are Otto's metric, yielding…

In Riemannian geometry geodesics are integral curves of the Riemannian distance gradient. We extend this classical result to the framework of Information Geometry. In particular, we prove that the rays of level-sets defined by a…

Geometrical optics (GO) is widely used for reduced modeling of waves in plasmas but fails near reflection points, where it predicts a spurious singularity of the wave amplitude. We show how to avoid this singularity by adopting a different…

The visual systems of many mammals, including humans, is able to integrate the geometric information of visual stimuli and to perform cognitive tasks already at the first stages of the cortical processing. This is thought to be the result…

This paper presents, for the first time, a Geometry of Interaction (GoI) interpretation inspired from Hughes-vanGlabbeek (HvG) proof-nets for multiplicative additive linear logic (MALL). Our GoI dynamically captures HvG's geometric…

We present an extension of the ergodic, mixing and Bernoulli levels of the ergodic hierarchy in dynamical systems, the information geometric ergodic hierarchy (IGEH), making use of statistical models on curved manifolds in the context of…

In this paper we study the notion of geodesic curvature of smooth horizontal curves parametrized by arc lenght in the Heisenberg group, that is the simplest sub-Riemannian structure. Our goal is to give a metric interpretation of this…

Over the last decade, a variety of new neurophysiological experiments have led to new insights as to how, when and where retinal processing takes place, and the nature of the retinal representation encoding sent to the cortex for further…

Human-object interaction (HOI) synthesis is crucial for creating immersive and realistic experiences for applications such as virtual reality. Existing methods often rely on simplified object representations, such as the object's centroid…

This thesis is concerned with extending the idea of geodesic completeness from pseudo-Riemannian to complex geometry: we take, however a completely holomorphicpoint of view; that is to say, a 'metric' will be a (meromorphic) symmetric…

The geometric phase (GP) is a fundamental quantum effect arising from conical intersections (CIs), with profound consequences for vibronic energy levels. Standard imaginary-time path integral molecular dynamics (PIMD) based on the…

In recent decades, advancements in motion learning have enabled robots to acquire new skills and adapt to unseen conditions in both structured and unstructured environments. In practice, motion learning methods capture relevant patterns and…

Imaging systems are represented as linear operators, and their singular value spectra describe the structure recoverable at the operator level. Building on an operator-based information-theoretic framework, this paper introduces a minimal…

We present a new learning-based framework to recover vehicle pose in SO(3) from a single RGB image. In contrast to previous works that map from local appearance to observation angles, we explore a progressive approach by extracting…

Geometrical optics provides an instructive insight into Brownian motion, ``pushed" into a large-deviations regime by imposed constraints. Here we extend geometrical optics of Brownian motion by accounting for diffusion inhomogeneity in…

Noise injection has been proved to be one of the key technique advances in generating high-fidelity images. Despite its successful usage in GANs, the mechanism of its validity is still unclear. In this paper, we propose a geometric…

We address the task of open-world class-agnostic object detection, i.e., detecting every object in an image by learning from a limited number of base object classes. State-of-the-art RGB-based models suffer from overfitting the training…

Geometrical optics (GO) is often used to model wave propagation in weakly inhomogeneous media and quantum-particle motion in the semiclassical limit. However, GO predicts spurious singularities of the wavefield near reflection points and,…