Related papers: Interactive Design and Optics-Based Visualization …
Recent studies have demonstrated the potential of hyperbolic geometry for capturing complex patterns from interaction data in recommender systems. In this work, we introduce a novel hyperbolic recommendation model that uses geometrical…
Slot attention has emerged as a powerful framework for unsupervised object-centric learning, decomposing visual scenes into a small set of compact vector representations called \emph{slots}, each capturing a distinct region or object.…
We propose a modification of the three-manifold invariant based on the use of Euclidean metric values ascribed to the elements of manifold triangulation. We thus obtain a nontrivial invariant that can, in particular, distinguish…
As an approximate theory that is highly regarded for its computational efficiency, geometrical optics (GO) is widely used for modeling waves in various areas of physics. However, GO fails at caustics, which significantly limits its…
Hypercomplex image processing extends conventional techniques in a unified paradigm encompassing algebraic and geometric principles. This work leverages quaternions and the two-dimensional orthogonal planes split framework (splitting of a…
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…
Eyeglasses play an important role in the perception of identity. Authentic virtual representations of faces can benefit greatly from their inclusion. However, modeling the geometric and appearance interactions of glasses and the face of…
Geometrical optical illusions have been object of many studies due to the possibility they offer to understand the behaviour of low-level visual processing. They consist in situations in which the perceived geometrical properties of an…
Graph representation learning in Euclidean space, despite its widespread adoption and proven utility in many domains, often struggles to effectively capture the inherent hierarchical and complex relational structures prevalent in real-world…
Hyperbolic geometry has recently found applications in social networks, machine learning and computational biology. With the increasing popularity, questions about the best representations of hyperbolic spaces arise, as each representation…
HOLONOMY is a virtual environment based on the mathematical concept of hyperbolic geometry. Unlike other environments, HOLONOMY allows users to seamlessly explore an infinite hyperbolic space by physically walking. They use their body as…
A pseudo-outcrop visualization is demonstrated for borehole and full-diameter rock core images to augment the ubiquitous unwrapped cylinder view and thereby to assist non-specialist interpreters. The pseudo-outcrop visualization is…
Deep neural networks have shown great potential in image reconstruction problems in Euclidean space. However, many reconstruction problems involve imaging physics that are dependent on the underlying non-Euclidean geometry. In this paper,…
``An orbifold is a space which is locally modeled on the quotient of a vector space by a finite group.'' This sentence is so easily said or written that more than one person has missed some of the subtleties hidden by orbifolds. Orbifolds…
Metric learning aims to learn a highly discriminative model encouraging the embeddings of similar classes to be close in the chosen metrics and pushed apart for dissimilar ones. The common recipe is to use an encoder to extract embeddings…
Quadrilateral layouts on surfaces are valuable in texture mapping, and essential in generation of quadrilateral meshes and in fitting splines. Previous work has characterized such layouts as a special metric on a surface or as a meromorphic…
Graph transformers typically embed every node in a single Euclidean space, blurring heterogeneous topologies. We prepend a lightweight Riemannian mixture-of-experts layer that routes each node to various kinds of manifold, mixture of…
Hyperbolic spaces have recently gained momentum in the context of machine learning due to their high capacity and tree-likeliness properties. However, the representational power of hyperbolic geometry is not yet on par with Euclidean…
The goal of this paper is to make the vertex operator algebra approach to mirror symmetry accessible to algebraic geometers. Compared to better-known approaches using moduli spaces of stable maps and special Lagrangian fibrations, this…
We present a new method for visualizing implicit real algebraic curves inside a bounding box in the $2$-D or $3$-D ambient space based on numerical continuation and critical point methods. The underlying techniques work also for tracing…