Two-dimensional multi-scale permutation entropy algorithm based on uniform quantization

In order to solve the problem that equal values in the subsequence lead to an increase in the probability of certain ordinal patterns when extending the permutation entropy algorithm to two-dimensional domain, a two-dimensional multi-scale permutation entropy based on uniform quantization (MUPE_2D) algorithm based on uniform quantization was proposed. By redefining the ordinal patterns based on uniform quantization, the effect of equal values on the calculation was eliminated. The MUPE_2D algorithm was used to investigate various synthetic textures, MIX_2D(<italic>p</italic>) images and encrypted images. The results reveal that MUPE_2D is able to effectively quantify the complexity and information concealment capabilities of encrypted images even if there are a large number of equal values. Consequently, the MUPE_2D algorithm provides an effective means for evaluating images.