Modification of multifractal analysis based on multiplicative cascade image

Abstract

In this paper, we propose a two-dimensional multifractal detrended fluctuation norm (2D MF-DFN) method which is based on multifractal detrended fluctuation analysis (MF-DFA) with the norm constraints. The proposed 2D MF-DFN method is defined to adjust the internal structure of 2D MF-DFA by Lp-norm constraint on the basis of 2D MF-DFA, thus improving the performance. In addition, the multiplicative cascade method is used to construct the image, the 2D MF-DFN algorithm is used to analyze and test the constructed image, and the calculated multifractal features are compared with the results of 2D MF-DFA. The superiority of the proposed model is measured by the multifractal properties such as the generalized Hurst exponents H and mass exponent spectrums τ. We calculate the numerical solutions of the 2D MF-DFA and 2D MF-DFN of the image and compare them with the multifractal analytical solutions of the image. The results show that the numerical results of 2D MF-DFA can be optimized by controlling the norm constraint value so that the calculation results are more consistent with the real multifractal feature solution of the image. In addition, in the optimal norm selection test, we found that, when the numerical curve of 2D MF-DFA is below the analytical solution, the norm value needs to be increased so that the numerical curve can move up close to the analytical solution and vice versa. Through the test, we can obtain the appropriate norm value and construct the corresponding 2D MF-DFN model. The test results show that the performance of the proposed model is significantly better than that of 2D MF-DFA. Furthermore, we compare the performance of the two approaches when transforming the construction parameters of multiplicative cascade images. The numerical results show that 2D MF-DFN is more accurate. In addition, we apply the proposed method to the classification of medical images and the high classification accuracy demonstrates the robustness of the proposed method.