The Multifractal Gaussian Mixture Model for unsupervised segmentation of complex data sets

作     者：Jacyna, Garry Frezza, Damon Slater, David M. Thompson, James R. 

作者机构：Mitre Corp 7515 Colshire Dr Mclean VA 22201 USA 

出 版 物：《SPATIAL STATISTICS》 (Spat. Stat.)

年 卷 期：2025年第66卷

核心收录：

学科分类：0202[经济学-应用经济学] 02[经济学] 020208[经济学-统计学] 07[理学] 0708[理学-地球物理学] 0816[工学-测绘科学与技术] 0714[理学-统计学（可授理学、经济学学位）] 0701[理学-数学] 

主　　题：Multifractal analysis Data segmentation Gaussian mixture models Image analysis 

摘      要：We derive the Multifractal Gaussian Mixture Model algorithm for decomposing data sets into different multifractal regimes building on the empirical observation that simulated multifractals have log wavelet leaders that are well-approximated by a Gaussian distribution. We test the algorithm on composite images constructed from multifractal random walks with known multifractal spectra. The algorithm is able to correctly segment the pixels corresponding to different multifractals when the constituent multifractals are most distinct from each other. It also estimates the multifractal parameters with minimal error when compared to the theoretical spectra used to generate the original multifractal random walks. We also apply the algorithm to satellite images with varying degrees of cloud cover taken from the LandSat 8 Cloud Validation Data set. The algorithm is able to segment the pixels into their corresponding cloud mask category, and it detects different texture and features in the images that are unrelated to clouds. The results indicate that the Multifractal Gaussian Mixture Model algorithm is well-suited for semi-automated unsupervised data segmentation when the data being analyzed exhibit complex, scale-invariant characteristics.