Related papers: Mapping on the HEALPix grid
Compact representations of objects is a common concept in computer science. Automated planning can be viewed as a case of this concept: a planning instance is a compact implicit representation of a graph and the problem is to find a path (a…
Superpixels serve as a powerful preprocessing tool in numerous computer vision tasks. By using superpixel representation, the number of image primitives can be largely reduced by orders of magnitudes. With the rise of deep learning in…
For real application and theoretical investigation of ordinary hypergraphs and non-ordinary hypergraphs, researchers need to establish standard rules and feasible operating methods. We propose a visualization tool for investigating…
A new method SREAG (spherical rectangular equal-area grid) is proposed to divide a spherical surface into equal-area cells. The method is based on dividing a sphere into latitudinal rings of near-constant width with further splitting each…
We develop an algebraic and operational framework for quantum isomorphisms of hypergraphs, using tools from compact quantum group theory. We introduce a new synchronous version of the hypergraph isomorphism game whose game algebra uniformly…
Grasping objects of different shapes and sizes - a foundational, effortless skill for humans - remains a challenging task in robotics. Although model-based approaches can predict stable grasp configurations for known object models, they…
Superpixel segmentation is a foundation for many higher-level computer vision tasks, such as image segmentation, object recognition, and scene understanding. Existing graph-based superpixel segmentation methods typically concentrate on the…
Self-supervised representation learning has been highly promising for histopathology image analysis with numerous approaches leveraging their patient-slide-patch hierarchy to learn better representations. In this paper, we explore how the…
In the present paper, as we did previously in [7], we investigate the relations between the geometric properties of tilings and the algebraic properties of associated relational structures. Our study is motivated by the existence of…
We introduce the polygonalisation complex of a surface, a cube complex whose vertices correspond to polygonalisations. This is a geometric model for the mapping class group and it is motivated by works of Harer, Mosher and Penner. Using…
Geometrical modelling generally provides the geometrical description of a special structure and a set of services to "navigate" through its structure. HEP geometrical modellers are designed to handle high complexity detector geometries and…
Multidimensional Projection is a fundamental tool for high-dimensional data analytics and visualization. With very few exceptions, projection techniques are designed to map data from a high-dimensional space to a visual space so as to…
The torus T of projective space also acts on the Hilbert scheme of subschemes of projective space. The T-graph of the Hilbert scheme has vertices the fixed points of this action, and edges connecting pairs of fixed points in the closure of…
The space of smooth genus 0 curves in projective space has a natural smooth compactification: the moduli space of stable maps, which may be seen as the generalization of the classical space of complete conics. In arbitrary genus, no such…
Open vocabulary models (e.g. CLIP) have shown strong performance on zero-shot classification through their ability generate embeddings for each class based on their (natural language) names. Prior work has focused on improving the accuracy…
Phase plotting is a useful way of visualising functions on complex space. We reinvent the method in the context of hyperbolic geometry, and we use it to plot functions on various representative surfaces for hyperbolic space, illustrating…
We define and study a natural category of graph limits. The objects are pairs $(\pi,\mu)$, where $\pi$ (the distribution of vertices) is an abstract probability measure on some abstract measurable space $(X,\mathcal{A})$ and $\mu$ (the…
Second-order superintegrable systems in dimensions two and three are essentially classified. With increasing dimension, however, the non-linear partial differential equations employed in current methods become unmanageable. Here we propose…
We define a graph structure associated in a natural way to finite fields that nevertheless distinguishes between different models of isomorphic fields.
We already saw in [A1] that the space of dynamically marked rational maps can be identified to a subspace of the space of covers between trees of spheres on which there is a notion of convergence that makes it sequentially compact. In the…