Adaptive multifractal correlation analyses and its variants for classification of complex image

Conventional two-dimensional multifractal analysis suffers from boundary effects and imprecise detrending, preventing accurate quantification of the generalized Hurst exponent and limiting its efficacy for image classification. To overcome these challenges, we propose two novel two-dimensional multifractal analysis methods. The first, Two-dimensional Multiscale Adaptive Multifractal Analysis (2D-MAMFA), enhances the traditional 2D-MFDFA by incorporating adaptive surface partitioning with overlapping regions and a weighted fusion process for cumulative sums. This innovation mitigates boundary effects and yields a more accurate estimation of the generalized Hurst exponent. The second algorithm, Two-dimensional Adaptive Multifractal Detrended Cross-Correlation Analysis (2D-AMFDCCA), extends this adaptive framework to the cross-correlation analysis of two image surfaces. Compared to the conventional algorithms, they both demonstrates superior performance on simulated data and real-world images. Therefore, the proposed methods provide robust tools for complex image texture analysis and classification, with promising applications in biomedicine and materials science.