Related papers: Texture Modeling by Gaussian fields with prescribe…
This article presents a neural network approach for estimating the covariance function of spatial Gaussian random fields defined in a portion of the Euclidean plane. Our proposal builds upon recent contributions, expanding from the purely…
Generative adversarial networks (GANs) are a recent approach to train generative models of data, which have been shown to work particularly well on image data. In the current paper we introduce a new model for texture synthesis based on GAN…
Image inpainting is a fundamental task in computer vision, aiming to restore missing or corrupted regions in images realistically. While recent deep learning approaches have significantly advanced the state-of-the-art, challenges remain in…
We develop a technique for the construction of random fields on algebraic structures. We deal with two general situations: random fields on homogeneous spaces of a compact group and in the spin-line bundles of the 2-sphere. In particular,…
High-quality novel view synthesis for large-scale scenes presents a challenging dilemma in 3D computer vision. Existing methods typically partition large scenes into multiple regions, reconstruct a 3D representation using Gaussian splatting…
We propose a novel discrete method of constructing Gaussian Random Fields (GRF) based on a combination of modified spectral representations, Fourier and Blob. The method is intended for Direct Numerical Simulations of the V-Langevin…
A flexible model for non-stationary Gaussian random fields on hypersurfaces is introduced.The class of random fields on curves and surfaces is characterized by an amplitude spectral density of a second order elliptic differential…
In this paper we will consider the problem of the numerical simulation of non-Gaussian, scalar random fields with a prescribed correlation structure provided either by a theoretical model or computed on a set of observational data.…
Neural radiance fields have achieved remarkable performance in modeling the appearance of 3D scenes. However, existing approaches still struggle with the view-dependent appearance of glossy surfaces, especially under complex lighting of…
Gaussian Splatting has become the method of choice for 3D reconstruction and real-time rendering of captured real scenes. However, fine appearance details need to be represented as a large number of small Gaussian primitives, which can be…
We provide theoretical procedures and practical recipes to simulate non-Gaussian correlated, homogeneous random fields with prescribed marginal distributions and cross-correlation structure, either in a N-dimensional Cartesian space or on…
These are lecture notes from a course given at the CRM in Montreal in 1992. They survey the author's attempts to find and understand canonical probabilistic entities in a local field (e.g. p-adic) setting. We propose answers to the related…
This work addresses the problem of simulating Gaussian random fields that are continuously indexed over a class of metric graphs, termed graphs with Euclidean edges, being more general and flexible than linear networks. We introduce three…
Stochastic process models for spatiotemporal data underlying random fields find substantial utility in a range of scientific disciplines. Subsequent to predictive inference on the values of the random field (or spatial surface indexed…
Neural rendering methods have significantly advanced photo-realistic 3D scene rendering in various academic and industrial applications. The recent 3D Gaussian Splatting method has achieved the state-of-the-art rendering quality and speed…
We describe two classes of Gaussian self-similar random fields: with strictly stationary rectangular increments and with mild stationary rectangular increments. We find explicit spectral and moving average representations for the fields…
The 3D Gaussian splatting method has drawn a lot of attention, thanks to its high performance in training and high quality of the rendered image. However, it uses anisotropic Gaussian kernels to represent the scene. Although such…
In the context of texture segmentation in images, and provide some theoretical guarantees for the prototypical approach which consists in extracting local features in the neighborhood of a pixel and then applying a clustering algorithm for…
The fracture characterization using a geostatistical tool with conditioning data is a computationally efficient tool for subsurface flow and transport applications. The main objective of the paper is to propose a framework of geostatistical…
We define weighted fractional Brownian sheets, which are a class of Gaussian random fields with four parameters that include fractional Brownian sheets as special cases, and we give some of their properties. We show that for certain values…