相关论文: Computing higher direct images in Macaulay2

In this paper, we propose an incremental abstraction method for dynamically over-approximating nonlinear systems in a bounded domain by solving a sequence of linear programs, resulting in a sequence of affine upper and lower hyperplanes…

This work aims at the precise and efficient computation of the x-ray projection of an image represented by a linear combination of general shifted basis functions that typically overlap. We achieve this with a suitable adaptation of ray…

Ray tracing is a widely used technique for modeling optical systems, involving sequential surface-by-surface computations, which can be computationally intensive. We propose Ray2Ray, a novel method that leverages implicit neural…

We explain a method for calculating the cohomology of line bundles on a toric variety in terms of the cohomology of certain constructible sheaves on the polytope. We show its effective use by means of some examples.

One of the most fundamental ingredients in mixed-integer nonlinear programming solvers is the well-known McCormick relaxation for a product of two variables x and y over a box-constrained domain. The starting point of this paper is the fact…

This paper presents a comprehensive survey of computational imaging (CI) techniques and their transformative impact on computer vision (CV) applications. Conventional imaging methods often fail to deliver high-fidelity visual data in…

We present a modular differentiable renderer design that yields performance superior to previous methods by leveraging existing, highly optimized hardware graphics pipelines. Our design supports all crucial operations in a modern graphics…

Deep learning models have a large number of free parameters that must be estimated by efficient training of the models on a large number of training data samples to increase their generalization performance. In real-world applications, the…

LiDAR Upsampling is a challenging task for the perception systems of robots and autonomous vehicles, due to the sparse and irregular structure of large-scale scene contexts. Recent works propose to solve this problem by converting LiDAR…

Recent advances in 3D vision have demonstrated the strengths of photometric bundle adjustment. By directly minimizing reprojected pixel errors, instead of geometric reprojection errors, such methods can achieve sub-pixel alignment accuracy…

A parameterized surface can be represented as a projection from a certain toric surface. This generalizes the classical homogeneous and bihomogeneous parameterizations. We extend to the toric case two methods for computing the implicit…

We use a generalization of Horrocks monads for arithmetic Cohen-Macaulay (ACM) varieties to establish a cohomological characterization of linear and Steiner bundles over projective spaces and quadric hypersurfaces. We also study resolutions…

Mathematical morphology is a theory and technique to collect features like geometric and topological structures in digital images. Given a target image, determining suitable morphological operations and structuring elements is a cumbersome…

A new multifocus image fusion approach is presented in this paper. First the contourlet transform is used to decompose the source images into different components. Then, some salient features are extracted from components. In order to…

We give a computational algorithm for computing Ext groups between bounded complexes of coherent sheaves on a projective variety, and we describe an implementation of this algorithm in Macaulay2. In particular, our results yield methods for…

We propose an approach to study logarithmic sheaves T(-log A) associated with a hyperplane arrangements A on the projective space, based on projective duality, direct image functors and vector bundles methods. We focus on freeness of line…

This paper presents a high discriminative texture analysis method based on the fusion of complex networks and randomized neural networks. In this approach, the input image is modeled as a complex networks and its topological properties as…

We present an approach to enhancing the realism of synthetic images. The images are enhanced by a convolutional network that leverages intermediate representations produced by conventional rendering pipelines. The network is trained via a…

A Python package for post-processing of plane two-dimensional data from computational fluid dynamics simulations is presented. The package, called turbulucid, provides means for scripted, reproducible analysis of large simulation campaigns…

A new approach to analyzing visual images is proposed, based on the idea of converting an optical image into a spatially varying pattern of polarized squeezed light, which is then used to produce a pattern of chiral edge currents in a thin…