title: Multifractal detrended moving average analysis for texture representation.
abstract: Multifractal detrended moving average analysis (MF-DMA) is recently employed to detect long-range correlation and multifractal nature in stationary and non-stationary time series. In this paper, we propose a method to calculate the generalized Hurst exponent for each pixel of a surface based on MF-DMA, which we call the MF-DMA-based local generalized Hurst exponent. These exponents form a matrix, which we denote by LHq. These exponents are similar to the multifractal detrended fluctuation analysis (MF-DFA)-based local generalized Hurst exponent. The performance of the calculated LHq is tested for two synthetic multifractal surfaces and ten randomly chosen natural textures with analytical solutions under three cases, namely, backward (θ = 0), centered (θ = 0.5), and forward (θ = 1) with different q values and different sub-image sizes. Two sets of comparison segmentation experiments between the three cases of the MF-DMA-based LHq and the MF-DFA-based LHq show that the MF-DMA-based LHq is superior to the MF-DFA-based LHq. In addition, the backward MF-DMA algorithm is more efficient than the centered and forward algorithms. An interest finding is that the LHq with q < 0 outperforms the LHq with q > 0 in characterizing the image features of natural textures for both the MF-DMA and MF-DFA algorithms.
authors.affiliation: College of Science, Hunan Agricultural University, Changsha 410128, China.
authors.forename: Fang
authors.initials: F
authors.lastname: Wang
authors.affiliation: Department of Mathematics and Statistics, University of New Brunswick, Fredericton, New Brunswick E3B 5A3, Canada.
authors.forename: Lin
authors.initials: L
authors.lastname: Wang
authors.affiliation: College of Science, Hunan Agricultural University, Changsha 410128, China.
authors.forename: Rui-Biao
authors.initials: RB
authors.lastname: Zou