Related papers: Mapping on the HEALPix grid
Time series imputation benefits from leveraging cross-feature correlations, yet existing attention-based methods re-discover feature relationships at each layer, lacking persistent anchors to maintain consistent representations. To address…
The hyperelliptic mapping class group has been studied in various contexts within topology and algebraic geometry. What makes this study tractable is that there is a surjective map from the hyperelliptic mapping class group to a mapping…
The "butterfly" projection is constructed as the polar layout of the HEALPix projection with (H,K) = (4,3). This short article formalises its representation in FITS.
In various astronomical projects it is crucial to have coordinates indexed tables. All sky optical and IR catalogues have up to 1 billion objects that will increase with forthcoming projects. Also partial sky surveys at various wavelengths…
The lack of proper class discrimination among the Hyperspectral (HS) data points poses a potential challenge in HS classification. To address this issue, this paper proposes an optimal geometry-aware transformation for enhancing the…
We introduce a natural stratification of the space of projective classes of measured laminations on a complete hyperbolic surface of finite area. We prove a rigidity result, namely, the group of self-homeomorphisms of the space of…
We define a natural class of graphs by generalizing prior notions of visibility, allowing the representing regions and sightlines to be arbitrary. We consider mainly the case of compact connected representing regions, proving two results…
We describe an algorithm that associates to each positive real number $r$ and each finite collection $C_r$ of planar pixels of size $r$ a planar piecewise linear set $S_r$ with the following additional property: if $C_r$ is the collection…
A classical approach for surface classification is to find a compact algebraic representation for each surface that would be similar for objects within the same class and preserve dissimilarities between classes. We introduce Self…
We illustrate the generative power of the lifting property (orthogonality of morphisms in a category) as means of defining natural elementary mathematical concepts by giving a number of examples in various categories, in particular showing…
We study a natural generalization of covering projections defined in terms of unique lifting properties. A map $p:E\to X$ has the "continuous path-covering property" if all paths in $X$ lift uniquely and continuously (rel. basepoint) with…
Gorski et al (1999b) have earlier presented the outline of a pixelisation-to-spherical-coordinate transformation scheme which simultaneously satisfies three properties which are especially useful for rapid analyses of maps on a sphere: (i)…
Hyperatlas is an open standard intended to facilitate the large-scale federation of image-based data. The subject of hyperatlas is the space of sphere-to-plane projection mappings (the FITS-WCS information), and the standard consists of…
We completely classify the locally finite, infinite graphs with pure mapping class groups admitting a coarsely bounded generating set. We also study algebraic properties of the pure mapping class group: We establish a semidirect product…
We give a local parametric description of all holomorphic hypersurfaces in complex Euclidean and projective spaces with constant index of relative nullity, together with applications. This is a complex analogue to the parametrization for…
The homography matrix is a key component in various vision-based robotic tasks. Traditionally, homography estimation algorithms are classified into feature- or intensity-based. The main advantages of the latter are their versatility,…
Persistent homology is a tool that can be employed to summarize the shape of data by quantifying homological features. When the data is an object in $\mathbb{R}^d$, the (augmented) persistent homology transform ((A)PHT) is a family of…
We introduce a class of maps from an affine flat into a Riemannian manifold that solve an elliptic system defined by the natural second order elliptic operator of the affine structure and the nonlinear Riemann geometry of the target. These…
A new technique for approximating the entire solution set for a nonlinear system of relations (nonlinear equations, inequalities, etc. involving algebraic, smooth, or even continuous functions) is presented. The technique is to first plot…
Let S be a compact surface, and M be the double of a handlebody. Given a homotopy class of maps from S to M inducing an isomorphism of fundamental groups, we describe a canonical uniformly lipschitz retraction of the sphere graph of M to…