Multifractal detrended moving average analysis for texture representation

Area of Science:

• Complex systems analysis
• Image texture analysis
• Time series analysis

Background:

• Multifractal Detrended Moving Average analysis (MF-DMA) is a recent technique for analyzing time series.
• Detecting long-range correlations and multifractal properties in stationary and non-stationary data is crucial.
• Existing methods like Multifractal Detrended Fluctuation Analysis (MF-DFA) provide a basis for surface analysis.

Purpose of the Study:

• To propose a novel method for calculating local generalized Hurst exponents for image surfaces using MF-DMA.
• To evaluate the performance of this MF-DMA-based local generalized Hurst exponent (LHq) against MF-DFA.
• To determine the optimal parameters for the MF-DMA approach in texture characterization.

Main Methods:

• Developed the MF-DMA-based local generalized Hurst exponent (LHq) for pixel-wise surface analysis.
• Tested the method on synthetic multifractal surfaces and natural textures.
• Compared MF-DMA-based LHq with MF-DFA-based LHq across backward, centered, and forward analysis cases.
• Investigated the impact of different q values and sub-image sizes.

Main Results:

• The MF-DMA-based LHq demonstrated superior performance compared to MF-DFA-based LHq in segmentation experiments.
• The backward MF-DMA algorithm (θ=0) was found to be more computationally efficient than centered and forward algorithms.
• Local generalized Hurst exponents calculated with q<0 were more effective in characterizing natural texture image features than those with q>0 for both MF-DMA and MF-DFA.

Conclusions:

• The MF-DMA-based local generalized Hurst exponent is a powerful tool for analyzing surface complexity and texture.
• The backward MF-DMA approach offers an efficient and effective method for image analysis.
• Negative q-values provide superior characterization of image features in multifractal analysis.