Multiscale permutation entropy for two-dimensional patterns

Complexity measures are important to understand and analyze systems with one dimensional data. However, extension of these methods to images (two dimensional data) are much less usual. Bidimensional multiscale sample entropy (MSE2D) has recently been proposed as a new complexity measure for texture evaluation. However, MSE2D leads to undefined or unreliable values for small-sized textures and requires a long computation time. This is why we herein propose the bidimensional multiscale permutation entropy (MPE2D) to evaluate the complexity of 2D patterns. MPE2D is applied to different synthesized textures, to softwood samples, and to study the texture of breast histopathology images. The results show that MPE2D is a valuable tool for texture analysis and that it is computationally noticeably faster than MSE2D.