Bidimensional Multiscale Fuzzy Entropy and Its Application to Pseudoxanthoma Elasticum

We propose a new bidimensional entropy measure and its multiscale form and evaluate their behavior using various synthetic and real images. The bidimensional multiscale measure finds application in helping clinicians for pseudoxanthoma elasticum (PXE) detection in dermoscopic images.

We developed bidimensional fuzzy entropy ( FuzEn_2D) and its multiscale extension ( MSF_2D) and then evaluated them on a set of synthetic images and texture datasets. Afterwards, we applied MSF_2D to dermoscopic PXE images and compared the results to those obtained by bidimensional multiscale sample entropy ( MSE_2D).

The results for the synthetic images illustrate that FuzEn_2D has the ability to quantify images irregularity. Moreover, FuzEn_2D, compared with bidimensional sample entropy ( SampEn_2D), leads to more stable results. The tests with the multiscale version show that MSF_2D is a proper image complexity measure. When applied to the dermoscopic PXE images, the paired t-test illustrates a significant statistical difference between MSF_2D of neck images with papules and normal skin images at a couple of scale factors.

The results for the synthetic data illustrate that FuzEn_2D is an image irregularity measure that overcomes SampEn_2D in terms of reliability, especially for small-sized images, and stability of results. The results for the PXE dermoscopic images demonstrate the ability of MSF_2D to recognize dermoscopic images of normal zones from PXE papules zones with a large effect size.

This work introduces new image irregularity and complexity measures and shows the potential for MSF_2D to serve as a possible tool helping medical doctors in PXE diagnosis.