**To build discretized values, it is necessary to determine a bin width ("bin" parameter). The indices derived from these indices will depend on this bin width parameter.**

A quartile is a type of quantile which divides the number of data points into four more or less equal parts, or quarters.

Due to the fact that the data needs to be ordered from smallest to largest in order to compute quartiles, quartiles are a form of Order statistic.**INTENSITY-HISTOGRAM_Q1**: The first quartile (Q1) is defined as the middle number between the smallest number and the median of the data set. It is also known as the lower quartile or the 25th empirical quartile and it marks where 25% of the data is below or to the left of it (if data is ordered on a timeline from smallest to largest).

**INTENSITY-HISTOGRAM_Q2** :The second quartile (Q2) is the median of a data set and 50% of the data lies below this point.

**INTENSITY-HISTOGRAM_Q3** :The third quartile (Q3) is the middle value between the median and the highest value of the data set. It is also known as the upper quartile or the 75th empirical quartile and 75% of the data lies below this point.

**INTENSITY-HISTOGRAM_min** reflects the minimum intensity value in the Volume of Interest. Intensity I might be SUV for PET, HU (Hounsfield Units) for CT, aso.

\begin{equation}

INTENSITY-HISTOGRAM\_min=\min_{i}I_i

\end{equation}

**INTENSITY-HISTOGRAM_mean** reflects the average intensity value in the Volume of Interest.

\begin{equation}

INTENSITY-HISTOGRAM\_mean=\frac{1}{N}\sum_{i}I_i

\end{equation}

**INTENSITY-HISTOGRAM_max** reflects the maximum intensity value in the Volume of Interest.

\begin{equation}

INTENSITY-HISTOGRAM\_max=\max_{i}I_i

\end{equation}

**LOCAL-INTENSITY-HISTOGRAM_peak** reflects the mean intensity value in a sphere with a volume of ~0.5 or ~1 mL and located so that the average intensity value in the VOI is maximum.

**INTENSITY-HISTOGRAM_calciumAgatstonScore** reflects the Agatston Score of the ROI. This feature is only available on CT images: see UserGuide of LIFEx "Calcium Quantitation - Agatston Score" for more information (Documentation).

**INTENSITY-HISTOGRAM_TLG** (mL) is the total signal (Total Lesion Glycolysis in FDG PET) defined as the product of \(Imean\) by \(Volume\) in mL. [LARSON 1999]

\begin{equation}

INTENSITY-HISTOGRAM\_mean=V \cdot \frac{1}{N}\sum_{i}I_i

\end{equation}

**INTENSITY-HISTOGRAM_Skewness** is the asymmetry of the grey-level distribution.

\begin{equation}

INTENSITY-HISTOGRAM\_Skewness=\frac{\frac{1}{N}\sum_{i}(I(i)-\overline{I})^{3}}{\left(\sqrt{\frac{1}{N}\sum_{i}(I(i)-\overline{I})^{2}}\right)^{3}}\end{equation}

where \(I(i)\) corresponds to the number of voxels with intensity \(i\), \(N\) the total number of voxels in the Volume of Interest and \(\overline{I}\) the average of grey-levels.

**INTENSITY-HISTOGRAM_Kurtosis** reflects the shape of the grey-level distribution (peaked or flat) relative to a normal distribution.

\begin{equation}

INTENSITY-HISTOGRAM\_Kurtosis=\frac{\frac{1}{N}\sum_{i}(I(i)-\overline{I})^{4}}{\left(\frac{1}{N}\sum_{i}(I(i)-\overline{I})^{2}\right)^{2}}\end{equation}

where \(I(i)\) corresponds to the number of voxels with intensity \(i\), \(N\) the total number of voxels in the Volume of Interest and \(\overline{I}\) the average of grey-levels.

**INTENSITY-HISTOGRAM_RIM**

is the envelope Intensity Mean CONVENTIONAL_RIM_* of successive layers of voxels from the outside of the region to the inside. Each layer is 1 voxel thick. These envelopes are getting smaller and smaller (3D erosion of 1 voxel) up to the center of the ROI.

Other statistics are extracted from these envelopes, in particular:

- INTENSITY-HISTOGRAM_RIM_min: minimum value of voxel values from the envelopes
- INTENSITY-HISTOGRAM_RIM_stdev: standard deviation value of voxel values from the envelopes
- INTENSITY-HISTOGRAM_RIM_max: maximum value of voxel values from the envelopes
- INTENSITY-HISTOGRAM_RIM_Volume (mL): volume in millilitre unit of all voxels from the envelopes
- INTENSITY-HISTOGRAM_RIM_Volume (vx): volume in voxel unit of all voxels from the envelopes
- INTENSITY-HISTOGRAM_RIM_sum: sum of voxel values from the envelopes

Example of results for 6 envelopes:

- INTENSITY-HISTOGRAM_RIM_mean = 1.2684131|1.2192162|1.2974288|1.3191646|1.271777|1.226076|

The first value 1.2684131 is SUV_mean (if SUV is unit of voxel value), of the 1-voxel thick envelope of the ROI, 1.2192162 the mean of the envelope after an erosion of 1 voxel, 1.226076 the mean of the smallest envelope (center of ROI).