Explicit constructions of operator scaling Gaussian fields

2011/04/05 by Marianne Clausel--Lesourd, Clausel--Lesourd, Marianne, Béatrice Vedel +1
Computer Science · Environmental Science · #FOS: Mathematics #Geochemistry and Geologic Mapping #Medical Image Segmentation Techniques #Probability (math.PR) #Soil Geostatistics and Mapping

paper · doi:10.48550/arxiv.1104.0774

openalex publication_date 2011/04/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We propose an explicit way to generate a large class of Operator scaling Gaussian random fields (OSGRF). Such fields are anisotropic generalizations of selfsimilar fields. More specifically, we are able to construct any Gaussian field belonging to this class with given Hurst index and exponent. Our construction provides - for simulations of texture as well as for detection of anisotropies in an image - a large class of models with controlled anisotropic geometries and structures.

Related

• An optimality result about sample path properties of Operator Scaling Gaussian Random Fields
• A strong optimality result for anisotropic self--similar textures
• Operator Scaling Stable Random Fields
• Riesz-based orientation of localizable Gaussian fields
• Texture Modeling by Gaussian fields with prescribed local orientation