Bidimensional Multiscale Fuzzy Entropy and Its Application to Pseudoxanthoma Elasticum

Objective: 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. Method: We developed bidimensional fuzzy entropy (FuzEn(2D)) and its multiscale extension (MSF2D) and then evaluated them on a set of synthetic images and texture datasets. Afterwards, we applied MSF2D to dermoscopic PXE images and compared the results to those obtained by bidimensional multiscale sample entropy (MSE2D). Results: 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 tomore stable results. The tests with the multiscale version show that MSF2D is a proper image complexity measure. When applied to the dermoscopic PXE images, the paired t-test illustrates a significant statistical difference between MSF2D of neck images with papules and normal skin images at a couple of scale factors. Conclusion: 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 MSF2D to recognize dermoscopic images of normal zones from PXE papules zones with a large effect size. Significance: This work introduces new image irregularity and complexity measures and shows the potential for MSF2D to serve as a possible tool helpingmedical doctors in PXE diagnosis.