相关论文: Computing higher direct images in Macaulay2
Synthesizing photo-realistic images from a point cloud is challenging because of the sparsity of point cloud representation. Recent Neural Radiance Fields and extensions are proposed to synthesize realistic images from 2D input. In this…
We provide a user's guide to version 1.0 of the software package CYTools, which we designed to compute the topological data of Calabi-Yau hypersurfaces in toric varieties. CYTools has strong capabilities in analyzing and triangulating…
We prove that the topological recursion formalism can be used to compute the WKB expansion of solutions of second order differential operators obtained by quantization of any hyper-elliptic curve. We express this quantum curve in terms of…
This paper presents an unpaired method for creating line drawings from photographs. Current methods often rely on high quality paired datasets to generate line drawings. However, these datasets often have limitations due to the subjects of…
The first part of this paper discusses general procedures for finding numerical approximations to distinguished Kahler metrics, such as Calabi-Yau metrics, on complex projective manifolds. These procedures are closely related to ideas from…
We discuss the local freeness and the numerical semipositivity of direct images of relative pluricanonical bundles for surjective morphisms between smooth projective varieties with connected fibers. We give a desirable semipositivity…
The Integral Image algorithm is often applied in tasks that require efficient integration over images, such as object detection. In this paper we discuss theoretical aspects of the algorithm's continuous version. We suggest to define the…
Given a unipotent bundle of smooth manifolds we construct its secondary transfer map and show that this map determines the higher smooth torsion of the bundle. This approach to higher torsion provides a new perspective on some of its…
Contours are salient features for image description, but the detection and localization of boundary contours is still considered a challenging problem. This paper introduces a new tool for edge processing implementing the Gestaltism idea of…
By using the $\mathbb R$-filtration approach of Arakelov geometry, one establishes explicit upper bounds for geometric and arithmetic Hilbert-Samuel function for line bundles on projective varieties and hermitian line bundles on arithmetic…
We give a classification of all possible $2$-adic images of Galois representations associated to elliptic curves over $\mathbb{Q}$. To this end, we compute the 'arithmetically maximal' tower of 2-power level modular curves, develop…
Reductions of higher tangent bundles of Lie groupoids provide natural examples of geometric structures which we would like to call higher algebroids. Such objects can be also constructed abstractly starting from an arbitrary almost Lie…
Numerical algebraic geometry is the field of computational mathematics concerning the numerical solution of polynomial systems of equations. Bertini, a popular software package for computational applications of this field, includes…
We present a novel technique for estimating disk parameters (the centre and the radius) from its 2D image. It is based on the maximal likelihood approach utilising both edge pixels coordinates and the image intensity gradients. We emphasise…
We present {\tt RandomPoints}, a package in \emph{Macaulay2} designed mainly to identify rational and geometric points in a variety over a finite field. We provide tools to estimate the dimension of a variety. We also present methods to…
In this note, we obtain various formulas for the curvature of the $L^2$ metric on the direct image of the relative canonical bundle twisted by a holomorphic line bundle endowed with a positively curved metric with analytic singularities,…
We introduce the notion of tropical Lagrangian multi-sections over a fan and study its relation with toric vector bundles. We also introduce a "SYZ-type" construction for toric vector bundles which gives a reinterpretation of Kaneyama's…
We present a new method for vectorization of technical line drawings, such as floor plans, architectural drawings, and 2D CAD images. Our method includes (1) a deep learning-based cleaning stage to eliminate the background and imperfections…
Iterative methods for tomographic image reconstruction have great potential for enabling high quality imaging from low-dose projection data. The computational burden of iterative reconstruction algorithms, however, has been an impediment in…
We introduce a theoretical framework for differentiable surface evolution that allows discrete topology changes through the use of topological derivatives for variational optimization of image functionals. While prior methods for inverse…