相关论文: Mod\'elisations de textures par champ gaussien \`a…

This paper presents a new framework for oriented texture modeling. We introduce a new class of Gaussian fields, called Locally Anisotropic Fractional Brownian Fields, with prescribed local orientation at any point. These fields are a local…

This paper presents a new model of textures, obtained as realizations of a new class of fractional Brownian fields. These fields, called weighted tensorized fractional Brownian fields, are obtained by a relaxation of the tensor-product…

We propose a curvelet-based model for the generation of Anisotropic Fractional Brownian Fields, that are suited to model systems with orientation-dependent self-similar properties. The synthesis procedure consists of generating coefficients…

Gaussian Splatting has emerged as a powerful representation for high-quality, real-time 3D scene rendering. While recent works extend Gaussians with learnable textures to enrich visual appearance, existing approaches allocate a fixed square…

In previous works, we proposed a method to characterize jointly self-similarity and anisotropy properties of a large class of self--similar Gaussian random fields. We provide here a mathematical analysis of our approach, proving that the…

Recent advances have equipped 3D Gaussian Splatting with texture parameterizations to capture spatially varying attributes, improving the performance of both appearance modeling and downstream tasks. However, the added texture parameters…

We study the sample paths properties of Operator scaling Gaussian random fields. Such fields are anisotropic generalizations of anisotropic self-similar random fields as anisotropic Fractional Brownian Motion. Some characteristic properties…

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…

The variance reduction speed of physically-based rendering is heavily affected by the adopted importance sampling technique. In this paper we propose a novel online framework to learn the spatial-varying density model with a single small…

We consider anisotropic self-similar random fields, in particular, the fractional Brownian sheet. This Gaussian field is an extension of fractional Brownian motion. We prove some properties of covariance function for self-similar fields…

We propose to incorporate grain boundary (GB) anisotropy in phase-field modeling by extending the standard partial differential equations formulation to include a nonlocal functional of an orientation field. Regardless of the number of…

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,…

We explore a generalisation of the L\'evy fractional Brownian field on the Euclidean space based on replacing the Euclidean norm with another norm. A characterisation result for admissible norms yields a complete description of all…

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…

We consider a surface embedded in the Euclidean 3-space and fix a tangential vector $v$ at a given point $p$ on the surface. In this paper, we first review a history of the formula obtained by Mannheim, d'Ocagne and Koenderink, which…

We propose a new method to characterize the geometrical texture of a granular packing at the particle scale including the steric hindrance effect. This method is based on the assumption of a maximum disorder (entropy) compatible both with…

In this paper the whole family of fractional Brownian motions is constructed as a single Gaussian field indexed by time and the Hurst index simultaneously. The field has a simple covariance structure and it is related to two generalizations…

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…

Gaussian random fields (GRFs) constitute an important part of spatial modelling, but can be computationally infeasible for general covariance structures. An efficient approach is to specify GRFs via stochastic partial differential equations…

Suspensions of anisotropic Brownian particles are commonly encountered in a wide array of applications such as drug delivery and manufacturing of fiber-reinforced composites. Technological applications and fundamental studies of small…