Local multifractal detrended fluctuation analysis for non-stationary image's texture segmentation

Abstract Feature extraction plays a great important role in image processing and pattern recognition. As a power tool, multifractal theory is recently employed for this job. However, traditional multifractal methods are proposed to analyze the objects with stationary measure and cannot for non-stationary measure. The works of this paper is twofold. First, the definition of stationary image and 2D image feature detection methods are proposed. Second, a novel feature extraction scheme for non-stationary image is proposed by local multifractal detrended fluctuation analysis (Local MF-DFA), which is based on 2D MF-DFA. A set of new multifractal descriptors, called local generalized Hurst exponent ( Lh q ) is defined to characterize the local scaling properties of textures. To test the proposed method, both the novel texture descriptor and other two multifractal indicators, namely, local Holder coefficients based on capacity measure and multifractal dimension D q based on multifractal differential box-counting (MDBC) method, are compared in segmentation experiments. The first experiment indicates that the segmentation results obtained by the proposed Lh q are better than the MDBC-based D q slightly and superior to the local Holder coefficients significantly. The results in the second experiment demonstrate that the Lh q can distinguish the texture images more effectively and provide more robust segmentations than the MDBC-based D q significantly.