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 SampEn 2D , 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 SampEn 2D as a robust irregularity measure, closely following sample entropy properties. Results with Brodatz dataset testified superiority of SampEn 2D to separate different image categories compared to conventional Haralick and wavelet descriptors. SampEn 2D was also capable of discriminating rat sural nerve images by age groups with high accuracy (AUROC = 0.844). No significant difference was found between SampEn 2D 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 SampEn 2D computation time increases with image size, being around 1400 s for a 600 × 600 pixels image. In conclusion, SampEn 2D showed to be stable and robust enough to be applied as texture feature quantifier and irregularity properties, as measured by SampEn 2D , seem to be an important feature for image characterization in biomedical image analysis.
Analysis of heart rate variability (HRV) is performed through interbeat interval time series derived from either electrocardiographic or arterial pressure (AP) recordings. However, little attention has been given to the reliability of calculating the time series from different sources, i.e. electrocardiogram (ECG) or pulse intervals (PI). Therefore, the present study aimed to evaluate the correlation between interbeat interval time series obtained from RR, inter-systolic (SS) and inter-diastolic (DD) intervals, as well as their impact on indices of HRV calculated from series of RR or PI. Conscious rats previously instrumented with subcutaneous electrodes and a catheter into the femoral artery were subjected to simultaneous ECG and AP recording for 5 min. Correlation and Bland-Altman plots between RR and PI were evaluated. Moreover, HRV was analyzed in time (mean cardiac interval, SDNN and RMSSD) and frequency domain (power in LF and HF spectral bands) as well as by nonlinear approaches (symbolic dynamics and sample entropy). First, RR showed a stronger correlation with PI calculated by DD than SS. Second, most HRV indices showed similar results when calculated with RR or DD series, but not with SS series. Considering RR interval as the gold standard for the calculation of cardiac cycle, when using PI inter diastolic intervals are the better choice to study HRV. These findings are quite relevant, especially when AP recording is used for HRV analysis.
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