Related papers: Geometric-optical illusions and Riemannian geometr…
We geometrically analyze the problem of estimating parameters related to the shape and size of a two-dimensional target object on the plane by using randomly distributed distance sensors whose locations are unknown. Based on the analysis…
Obtaining complete information about the shape of an object by looking at it from a single direction is impossible in general. In this paper, we theoretically study obtaining differential geometric information of an object from orthogonal…
Hallucinations in deployed language models can have real consequences for downstream decisions in domains such as healthcare, legal, and financial services. In production, detection has to run on what the deployed system can see: the query,…
The basic laws of geometrical optics can be deduced from energy-momentum conservation for electromagnetic waves, without other wave concepts. However, the concept of quanta is required; it arises naturally, hence such a hypothesis could…
In general relativity, spatial light rays of static spherically symmetric spacetimes are geodesics of surfaces in Riemannian optical geometry. In this paper, we apply results on the isoperimetric problem to show that length-minimizing…
In this paper, we introduce Geometric Algebra-Informed 3D Gaussian Splatting (GAI-GS), a framework for wireless modeling that couples 3D Gaussian splatting with a geometric algebra-based attention mechanism to explicitly model ray-object…
The ultimate goal of many image-based modeling systems is to render photo-realistic novel views of a scene without visible artifacts. Existing evaluation metrics and benchmarks focus mainly on the geometric accuracy of the reconstructed…
General object composition (GOC) aims to seamlessly integrate a target object into a background scene with desired geometric properties, while simultaneously preserving its fine-grained appearance details. Recent approaches derive semantic…
We will show the usefulness of the tools of Symplectic and Presymplectic Geometry and the corresponding Lie algebraic methods in different problems in Geometric Optics.
We tackle the challenge of efficiently reconstructing 3D scenes with high detail on objects of interest. Existing 3D Gaussian Splatting (3DGS) methods allocate resources uniformly across the scene, limiting fine detail to Regions Of…
In this article, we propose a new dimensionality-independent and gradient-free sampler, called Geometric Optics Approximation Sampling, which is based on the reflector antenna system. The core idea is to construct a reflecting surface that…
The biological characteristics of human visual processing can be investigated through the study of optical illusions and their perception, giving rise to intuitions that may improve computer vision to match human performance. Geometric…
3D scene reconstruction is a foundational problem in computer vision. Despite recent advancements in Neural Implicit Representations (NIR), existing methods often lack editability and compositional flexibility, limiting their use in…
Hyperbolic geometry, a Riemannian manifold endowed with constant sectional negative curvature, has been considered an alternative embedding space in many learning scenarios, \eg, natural language processing, graph learning, \etc, as a…
The geometry of generative models serves as the basis for interpolation, model inspection, and more. Unfortunately, most generative models lack a principal notion of geometry without restrictive assumptions on either the model or the data…
The performance of modern object detectors drops when the test distribution differs from the training one. Most of the methods that address this focus on object appearance changes caused by, e.g., different illumination conditions, or gaps…
We describe the invariant metrics on real flag manifolds and classify those with the following property: every geodesic is the orbit of a one-parameter subgroup. Such a metric is called g.o. (geodesic orbit). In contrast to the complex…
A geodesic orbit manifold (GO manifold) is a Riemannian manifold (M,g) with the property that any geodesic in M is an orbit of a one-parameter subgroup of a group G of isometries of (M,g). The metric g is then called a G-GO metric in M. For…
We present a system for generating inconspicuous-looking textures that, when displayed in the physical world as digital or printed posters, cause visual object tracking systems to become confused. For instance, as a target being tracked by…
The main purpose of this article is to develop an explicit derived deformation theory of algebraic structures at a high level of generality, encompassing in a common framework various kinds of algebras (associative, commutative, Poisson...)…