Related papers: Snapshot of Algebraic Vision
Mathematical objects are generally abstract and not very approachable. Illustrations and interactive visualizations help both students and professionals to comprehend mathematical material and to work with it. This approach lends itself…
Cylindrical algebraic decomposition is a classical construction in real algebraic geometry. Although there are many algorithms to compute a cylindrical algebraic decomposition, their practical performance is still very limited. In this…
These notes contain a survey of some aspects of the theory of graded differential algebras and of noncommutative differential calculi as well as of some applications connected with physics. They also give a description of several new…
Artificial intelligence is beginning to reduce the manual effort in the CAD-to-mesh pipeline. Written for meshing and geometry practitioners with limited AI background, this survey organizes recent work by workflow step. We cover part…
This article is a review of theoretical advances in the research field of algebraic geometry and Bayesian statistics in the last two decades. Many statistical models and learning machines which contain hierarchical structures or latent…
The relation between algebraic and traditional calculations of molecular vibrations is investigated. An explicit connection between interactions in configuration space and the corresponding algebraic interactions is established.
We discuss certain ternary algebraic structures appearing more or less naturally in various domains of theoretical and mathematical physics. Far from being exhaustive, this article is intended above all to draw attention to these algebras,…
We investigate the possibility of 3D scene reconstruction from two or more overlapping webcam streams. A large, and growing, number of webcams observe places of interest and are publicly accessible. The question naturally arises: can we…
Visual object counting is a fundamental computer vision task underpinning numerous real-world applications, from cell counting in biomedicine to traffic and wildlife monitoring. However, existing methods struggle to handle the challenge of…
A tutorial introduction to projective geometric algebra (PGA), a modern, coordinate-free framework for doing euclidean geometry. PGA features: uniform representation of points, lines, and planes; robust, parallel-safe join and meet…
It is not commonly realized that the algebra of complex numbers can be used in an elegant way to represent the images of ordinary 3-dimensional figures, orthographically projected to the plane. We describe these ideas here, both using…
We discuss the geometry of rational maps from a projective space of an arbitrary dimension to the product of projective spaces of lower dimensions induced by linear projections. In particular, we give an algebro-geometric variant of the…
The enduring legacy of Euclidean geometry underpins classical machine learning, which, for decades, has been primarily developed for data lying in Euclidean space. Yet, modern machine learning increasingly encounters richly structured data…
How to understand deep learning systems remains an open problem. In this paper we propose that the answer may lie in the geometrization of deep networks. Geometrization is a bridge to connect physics, geometry, deep network and quantum…
Illumination of scenes is usually generated in computer graphics using polygonal meshes. In this paper, we present a geometric method using projections. Starting from an implicit polynomial equation of a surface in 3-D or a curve in 2-D, we…
Accurately reconstructing a 3D scene including explicit geometry information is both attractive and challenging. Geometry reconstruction can benefit from incorporating differentiable appearance models, such as Neural Radiance Fields and 3D…
Bayesian learning with Gaussian processes demonstrates encouraging regression and classification performances in solving computer vision tasks. However, Bayesian methods on 3D manifold-valued vision data, such as meshes and point clouds,…
The abundance and richness of Internet photos of landmarks and cities has led to significant progress in 3D vision over the past two decades, including automated 3D reconstructions of the world's landmarks from tourist photos. However, a…
In this work we address the challenging problem of multiview 3D surface reconstruction. We introduce a neural network architecture that simultaneously learns the unknown geometry, camera parameters, and a neural renderer that approximates…
Cross-view geo-localization has garnered notable attention in the realm of computer vision, spurred by the widespread availability of copious geotagged datasets and the advancements in machine learning techniques. This paper provides a…