# Texture Analysis of Near-Infrared Vein Images During Reactive Hyperemia in Healthy Subjects
## 2 Materials and Methods
### Analytics
\begin{table}
\begin{tabular}{c c c} \hline
**Parameter** & **Description** & **Equation** \\ \hline Contrast & \begin{tabular}{c} A measure of the intensity difference between \\ neighboring pixels; indicates how much texture \\ varies locally. \\ \end{tabular} & \(\sum\limits_{i=0}^{N-1}\sum\limits_{j=0}^{N-1}(i-j)^{2}.P(i,j)\) \\ \hline Correlation & \begin{tabular}{c} A measure of how strongly the intensity of one pixel \\ is related to its neighbor; reflects linear patterns in \\ texture. \\ \end{tabular} & \(\frac{\sum\limits_{i=0}^{N-1}\sum\limits_{j=0}^{N-1}(i-\mu_{i})\left(j-\mu_{j} \right).P(i,j)}{\varepsilon_{i}\sigma_{j}}\) \\ \hline Energy & \begin{tabular}{c} A measure of image uniformity; calculated as the \\ sum of squared values in the co-occurrence matrix. \\ \end{tabular} & \(\sum\limits_{i=0}^{N-1}\sum\limits_{j=0}^{N-1}P(i,j)^{2}\) \\ \hline Homogeneity & \begin{tabular}{c} A measure of the similarity between neighboring \\ pixel intensities; higher values indicate smoother \\ and more uniform textures. \\ \end{tabular} & \(\sum\limits_{i=0}^{N-1}\sum\limits_{j=0}^{N-1}\frac{P(i,j)}{1+|i-j|}\) \\ \hline Entropy & \begin{tabular}{c} A measure of randomness or complexity in the \\ distribution of co-occurring gray levels within the \\ GLCM; higher values indicate greater texture \\ irregularity and disorder. \\ \end{tabular} & \(-\sum\limits_{i=0}^{N-1}\sum\limits_{j=0}^{N-1}P(i,j).log_{2}P(i,j)\) \\ \hline Fractal dimension & \begin{tabular}{c} A non-integer exponent that describes how detail in \\ a pattern changes with scale. Calculated with the \\ box-counting method, where \(\varepsilon\) represents the size \\ (side length) of the box used to cover the structure \\ and \(N(\varepsilon)\) is the number of boxes of size \(\varepsilon\) that are \\ needed to completely cover the object \\ \end{tabular} & \(\frac{\sigma}{\mu^{2}}\) \\ \hline Lacunarity & \begin{tabular}{c} A measure of the amount of texture detail present in \\ relation to the visible size of the vein. \\ \end{tabular} & Entropy/Width \\ \hline Correlation-to-width ratio & \begin{tabular}{c} A measure of the consistency of the texture pattern \\ relative to the vein’s width. \\ \end{tabular} & Correlation/Width \\ \hline Total entropic content & \
\begin{tabular}{c} A measure of the overall texture variation and \\ visual complexity across the entire vein image. \\ \end{tabular} & Entropy \(\times\)Width \\ \hline Correlation-to-entropy ratio &
\begin{tabular}{c} A measure of the amount of order in the texture in \\ relation to its level of complexity. \\ \end{tabular} & Correlation/Entropy \\ \hline \end{tabular}
\end{table} 
Table 2: Description of the texture parameters of hand dorsum veins throughout the procedure (adapted from [PERSON] [31], [PERSON] [32] and [PERSON] [33]. _P(i,j)_ is the (_i,j_)-th entry of the normalized GLCM, representing the joint probability of two pixels with gray levels \(i\) and \(j\) at a defined offset. N is the number of gray levels. \(\mu\) and \(\sigma\) represent the mean and standard deviation of the marginal distributions of _P(i,j)_. Definitions are provided for contrast, correlation, energy, entropy, homogeneity, fractal dimension, and lacunarity.