Multifractal Analysis on the Sphere

Abstract

Abstract.A new generation of instruments in astrophysics or vision now provide spherical data. These spherical data may present a selfsimilarity property while no spherical analysis tool is yet available to characterize this property. In this paper we present a first numerical study of the extension of multifractal analysis onto the sphere using spherical wavelet transforms. We use a model of multifractal spherical textures as a reference to test this approach. The results of the spherical analysis appear qualitatively satisfactory but not as accurate as those of the usual 2D multifractal analysis.

Scale invariant images in astronomy through the lens of multifractal modeling

“…(2) can be adapted on the sphere [5]. The mission STEREO launched in 2006 has provided astronomers with images from 2 synchronized spatial telescopes, allowing for the 3D reconstruction of the Sun.…”

“…These images help in testing and choosing the best denoising method. When adapted on the 3D sphere [5] they can be used to calibrate a stereographic reconstruction algorithm. This contribution summarizes a set of works carried out over the last 5 years from the first observation of the multiscaling properties of quiet Sun coronal images to the design of our VSR method and its applications.…”

On Simulation of Manifold Indexed Fractional Gaussian Fields

“…But, some other rough phenomena are not indexed by an Euclidean space, but by a manifold. Let us mention for instance the cosmic microwave background (Marinucci et al 2007; National Aeronautics and Space Administration 2010) or solar data (Koenig and Chainais 2008), that lead to spherical data. Real-world textures are usually not supported by an Euclidean space, but by a surface.…”