Two-dimensional sample entropy: assessing image texture through irregularity

Image texture analysis is a key task in computer vision. Although various methods have been applied to extract texture information, none of them are based on the principles of sample entropy, which is a measurement of entropy rate. This paper proposes a two-dimensional sample entropy method, namely SampEn2D, in order to measure irregularity in pixel patterns. We evaluated the proposed method in three different situations: a set of simulated images generated by a deterministic function corrupted with different levels of a stochastic influence; the Brodatz public texture database; and a real biological image set of rat sural nerve. Evaluation with simulations showed SampEn2D as a robust irregularity measure, closely following sample entropy properties. Results with Brodatz dataset testified superiority of SampEn2D to separate different image categories compared to conventional Haralick and wavelet descriptors. SampEn2D was also capable of discriminating rat sural nerve images by age groups with high accuracy (AUROC = 0.844). No significant difference was found between SampEn2D AUROC and those obtained with the best performed Haralick descriptors, i.e. entropy (AUROC = 0.828), uniformity (AUROC = 0.833), homogeneity (AUROC = 0.938) and Wavelet descriptors, i.e. Haar energy/entropy (AUROC = 0.932) and Daubechies energy/entropy (AUROC = 0.859). In addition, it was shown that SampEn2D computation time increases with image size, being around 1400 s for a 600 × 600 pixels image. In conclusion, SampEn2D showed to be stable and robust enough to be applied as texture feature quantifier and irregularity properties, as measured by SampEn2D, seem to be an important feature for image characterization in biomedical image analysis.