Characterising Complexity in Solar Magnetogram Data using a Wavelet-based Segmentation Method

TL;DR

This paper introduces a wavelet-based segmentation method to analyze the multifractal complexity of solar magnetogram data, distinguishing active regions from quiet Sun areas by their multifractal properties.

Contribution

It presents a novel multiscale image segmentation technique based on WTMM to characterize and differentiate multifractal features in solar magnetic structures.

Findings

Quiet Sun has an average Hölder exponent of -0.75.

Active regions exhibit an average Hölder exponent of 0.38.

Active region spectra are similar to turbulent flow data.

Abstract

The multifractal nature of solar photospheric magnetic structures are studied using the 2D wavelet transform modulus maxima (WTMM) method. This relies on computing partition functions from the wavelet transform skeleton defined by the WTMM method. This skeleton provides an adaptive space-scale partition of the fractal distribution under study, from which one can extract the multifractal singularity spectrum. We describe the implementation of a multiscale image processing segmentation procedure based on the partitioning of the WT skeleton which allows the disentangling of the information concerning the multifractal properties of active regions from the surrounding quiet-Sun field. The quiet Sun exhibits a average H\"older exponent $\sim -0.75$, with observed multifractal properties due to the supergranular structure. On the other hand, active region multifractal spectra exhibit an average H\"older exponent $\sim 0.38$ similar to those found when studying experimental data from turbulent flows.