Bitemporal Spatial Autocorrelation Matrix for Change Detection in Multispectral Imagery: A Case Study on the Drying of a Lake in Southern Italy

Abstract. Multispectral satellite imagery provides an essential source of information for monitoring environmental transformations, yet robust unsupervised change detection remains challenging due to radiometric variability and seasonal dynamics. At the same time, supervised approaches based on Deep Learning are often constrained by the need for computationally expensive accelerated hardware and the limited availability of high-quality annotated datasets. This work introduces a framework based on the Bitemporal Spatial Autocorrelation (BSAC) matrix, that rather than relying on pixel-wise spectral differencing or data-intensive Deep Learning models, it is designed to quantify structural changes by evaluating the symmetry properties of the spatial autocorrelation across multiple spatial lags. Three complementary metrics are derived from the BSAC representation: a binary change/no-change trigger (χ) that identifies structural discontinuities, an asymmetry magnitude (Δ) that measures the intensity of change, and a normalized Symmetry Index (SI) obtained via singular value decomposition to characterize the geometric coherence of the correlation structure. The methodology is applied to Sentinel-2 imagery of Lake Fanaco (Sicily, Italy), which experienced severe desiccation during the 2024 drought. Experiments conducted using NDWI and NDVI confirm the index-agnostic nature of the framework, capturing both hydrological contraction and vegetation stress. Comparison with an unsupervised K-means segmentation baseline shows strong spatial agreement in identifying the affected areas. Thanks to its unsupervised formulation and near-linear computational complexity, the BSAC framework represents a scalable and interpretable approach for operational change monitoring in Earth observation.