Research Article

Image patch analysis of sunspots and active regions

I. Intrinsic dimension and correlation analysis

¹ Electrical Engineering and Computer Science Department, University of Michigan, Ann Arbor, MI 48109, USA
² SIDC, Royal Observatory of Belgium, 1180 Brussels, Belgium
³ National Solar Observatory, Boulder, CO 80303, USA

^* Corresponding author: krmoon@umich.edu

Received: 9 March 2015
Accepted: 13 December 2015

Abstract

Context. The flare productivity of an active region is observed to be related to its spatial complexity. Mount Wilson or McIntosh sunspot classifications measure such complexity but in a categorical way, and may therefore not use all the information present in the observations. Moreover, such categorical schemes hinder a systematic study of an active region’s evolution for example.

Aims. We propose fine-scale quantitative descriptors for an active region’s complexity and relate them to the Mount Wilson classification. We analyze the local correlation structure within continuum and magnetogram data, as well as the cross-correlation between continuum and magnetogram data.

Methods. We compute the intrinsic dimension, partial correlation, and canonical correlation analysis (CCA) of image patches of continuum and magnetogram active region images taken from the SOHO-MDI instrument. We use masks of sunspots derived from continuum as well as larger masks of magnetic active regions derived from magnetogram to analyze separately the core part of an active region from its surrounding part.

Results. We find relationships between the complexity of an active region as measured by its Mount Wilson classification and the intrinsic dimension of its image patches. Partial correlation patterns exhibit approximately a third-order Markov structure. CCA reveals different patterns of correlation between continuum and magnetogram within the sunspots and in the region surrounding the sunspots.

Conclusions. Intrinsic dimension has the potential to distinguish simple from complex active regions. These results also pave the way for patch-based dictionary learning with a view toward automatic clustering of active regions.