The tool calculates the discrete histogram entropy H(X).

$H(X)=-\sum_{i=1}^{n}f(x_i)\cdot\log\left({\frac{f(x_i)}{w(x_i)}}\right)$

where w is the width of the i-th histogram bin and f the frequency of the value x_i.

The macro has originally be intended to be used with the histogram of directions created by the Directionality plugin. It can be used on an image or on a histogram table.

To install the tool save the file discrete_histogram_entropy.ijm into the folder macros/toolsets of your FIJI installation.

Select the "discrete_histogram_entropy" toolset from the >> button of the ImageJ launcher.

Left-click the button to run the tool on the current image. Right-click the button to open the options dialog.

• number of bins - the number of bins of the histogram when the input is an image
• epsilon - a small number used to determine if the sum of the counts in the histogram is close enough to one to consider it normalized
• bin column - the column containing the bin-starts when running on a table
• count column - the column containing the counts when running on a table
• auto - when auto is selected the bin- and count columns are found automatically (either bin start or index and count)

1. Gerson, R., Tu, W., Abreu-Gomez, J., Udare, A., McPhedran, R., Ramsay, T., Schieda, N., 2022. Evaluation of the T2-weighted (T2W) adrenal MRI calculator to differentiate adrenal pheochromocytoma from lipid-poor adrenal adenoma. Eur Radiol 32, 8247–8255. 10.1007/s00330-022-08867-4

2. McPhedran, R., Gerson, R., Alfaleh, H., Sathiadoss, P., Schieda, N., 2022. Inter-individual comparison of diagnostic accuracy of adrenal washout CT compared to chemical shift MRI plus the T2-weighted (T2W) adrenal MRI calculator in indeterminate adrenal masses: a retrospective non-inferiority study. Abdom Radiol 47, 2453–2461.