Recurrence entropy-based characterization of spatial patterns

Abstract The identification and characterization of spatial patterns play an important role in fields ranging from medical imaging and materials science to laser physics and complex systems. Here, we introduce a recurrence-based framework for the analysis of two-dimensional patterns by extending concepts originally developed for nonlinear time series analysis. Spatial recurrence data are generated from pixel arrays and decomposed into recurrence motifs, whose statistical distribution is used to construct entropy-based descriptors of spatial organization. By systematically varying the recurrence threshold, we obtain a two-dimensional representation defined by the threshold and its associated recurrence entropy, providing a compact and interpretable feature space for pattern characterization. The proposed framework is validated using synthetic datasets, including fractional Brownian surfaces and Turing patterns, as well as real-world textures from the Kylberg dataset. The results show that recurrence entropy provides a complementary description of spatial organization, capturing structural changes associated with variations in spatial correlations and texture organization.