Statistics Measures

Except for the Pixel Dump and Texture different levels of statistics can be collected:

Selected Statistics: Configured statistics measures.
Statistics: Standard descriptive statistics measures.
Statistics + Surface + Sphericity: Standard descriptive statistics measures, a VOI surface estimate and an index of how sphere-shaped the VOI is.
Statistics + Surface + Sphericity + Diameter + Fractal dimension: As above, plus the maximum VOI diameter and the fractal dimension.

The selected statistic type is calculated for each VOI.

Statistics Measures

The following basic descriptive statistics are calculated using the values of all pixel classified for a VOI. With binary classifications each included pixel contributes equally. Pixels with NaN value are excluded from statistics. Correspondingly, they don't contribute to Volume or NumberOfPixels.

With the Fraction mode classification, however the contribution of a pixel is proportional to the fractional area f_i included in the contour (f_i=1 fully included, f_i=0.5 50% included). This weighting applies for the Average, the Standard Deviation, the Volume, the Total and the AUC. For the other measures, which don't support fractional contributions, only the pixels with f_i>0.5 are used.

The statistics calculation using a probabilistic atlas is similar to the fraction mode. The contribution of a pixel is proportional to its probability p_i for belonging to the VOI (p_i=1 certainly included, p_i=0.5 included with 50% probability). For measures, which don't support fractional contributions, only the pixels with probability above a user-defined threshold (p_i>p_t) are used.

Notes:
1. Due to calculation of the fractional area, statistics using the Fraction mode is substantially more time-consuming.
2. The fraction mode is not effective for automatically generated VOIs (iso-contouring, atlases), because the contours follow the pixel boundaries.

Averaged	Average of the pixel values. Fraction mode: Sum(f_iv_i)/Sum(f_i). v_ivalue of pixel i. Probabilistic atlas: Sum(f_ip_i)/Sum(p_i). p_iprobability of pixel i for belonging to VOI_i.
Sd	Population standard deviation of the pixel values. Fraction mode: a weighted standard deviation is calculated accounting for the pixel area included in the contour. Probabilistic atlas: a weighted standard deviation is calculated accounting for the probability of pixel i for belonging to VOI_i.
Stdv	Sample standard deviation of the pixel values. Fraction mode, Probabilistic atlas: analogous to Sd.
Volume	Volume of the VOI pixels. It is based on the pixel size in x and y and the slice thickness in z. Fraction mode: Sum(f_i)pixel-volume. Probabilistic atlas: NumberOfPixels**pixel-volume.
Total(SUM)	Sum of the pixel values. The interpretation depends on the image contents. In the case of activity units the result will be total activity in the VOI. Fraction mode: Sum(f_iv_i), Probabilistic atlas: Sum(p_iv_i).
*Total(AVRVOL)**	Average of the pixel values multiplied by the VOI volume. The interpretation depends on the image contents. In the case of activity concentration units, the result represents total activity in the VOI. Fraction mode: Sum(f_iv_i)pixel-volume, Probabilistic atlas: Average*Volume. In the case of SUV units, the result is called Total Lesion Glycolysis (TLG). The TLG is usually calculated in combination with a lower range.
Min	Minimum pixel value. Fraction mode: Considers pixels with f_i>0.5. Probabilistic atlas: Considers pixels with p_i>p_t.
Max	Maximum pixel value. Fraction mode: Considers pixels with f_i>0.5. Probabilistic atlas: Considers pixels with f_i>p_t.
NumberOfPixels	Number of pixels included in the VOI. Fraction mode: Considers pixels with f_i>0.5, Probabilistic atlas: Considers pixels with p_i>p_t.
NumberOfEffectivePixels	Fraction mode: Sum(f_i). Probabilistic atlas: Sum(p_i). Otherwise equal to NumberOfPixels.
HotAveraged	The highest pixel values averaged. The default Number of Hottest Pixels values to be averaged can be set in the User configuration, and can be changed in the upper part of the statistics window. Fraction mode: Considers pixels with f_i>0.5. Probabilistic atlas: Considers pixels with p_i>p_t.
Q1	First quartile of the VOI pixel values. Fraction mode: Considers pixels with f_i>0.5. Probabilistic atlas: Considers pixels with p_i>p_t.
Median	Median value of the VOI pixel values. Fraction mode: Considers pixels with f_i>0.5. Probabilistic atlas: Considers pixels with p_i>p_t.
Q3	Third quartile of the VOI pixel values. Fraction mode: Considers pixels with f_i>0.5. Probabilistic atlas: Considers pixels with p_i>p_t.
AreaUnderCurve	Static data: Averaged times frame duration. Fraction mode: Sum(f_iv_it)/Sum(f_i) (t = acquisition duration). Probabilistic atlas: Sum(p_iv_it)/Sum(p_i). Dynamic data: Integral of the Averaged curve.
HypoxiaIndex	Fraction of pixels in the VOI which have a value above the threshold in the Hypoxia Threshold field. Fraction mode: Considers pixels with f_i>0.5. Probabilistic atlas: Considers pixels with p_i>p_t.
HypoxicVolume	Represents the number of voxels inside a VOIs with value greater than the hypoxia threshold multiplied by the volume of the pixel size. Fraction and the Binary mode - consider only the voxels with f_i > 0.5 .
NumberOfNaNs	Represents the number of voxel with NaN value inside the VOI
VolumeWithoutNaNs	Volume of the VOI pixels which value is different from NaN. It is based on the pixel size in x and y and the slice thickness in z. Fraction mode: Sum(f_i)*pixel-volume.

Additional Measures

The following additional VOI measures can be obtained with the corresponding statistics button:

SurfaceArea	Estimate of the VOI surface which is obtained by triangulating the contours and accumulating the triangle areas. Fraction mode: Considers pixels with f_i>0.5.
Sphericity	Index of how spherical a VOI is. The values range between 0 and 1 (perfect sphere). Wikipedia. Fraction mode: Considers pixels with f_i>0.5.
DiameterMax	Maximal distance between any two pixels in the VOI. The calculation can take substantial time and is restricted to VOIs enclosing less than 100'000 pixels. Fraction mode: Considers pixels with f_i>0.5.
Fractal Dimension (FD)	Measures the complexity of a 3-dimensional structure, approximated by a sphere, by calculating its box-counting dimension. Is an index for characterizing fractal patterns or sets by quantifying their complexity as a ratio of the change in detail to the change in scale. Wikipedia. It does not provide an absolute quantification and it is a real value between 0 and 3. Small values of FD in 3D VOIs indicate a complex structure. Fraction mode: considers pixel with f_i>0. For 2-dimensional ROIs (ROIs on one slice) the FD value is between 0 and 2. A convenient tool, the fractal generator, is available in Pmod. It is accessible with the Load button configured on Generated: The tool allows creating data with well known fractals like Menger Sponge, Jerusalem Cube, Cantor Dust 3D. The FD value calculated with PMOD for a known fractal structure is very similar to the theoretical value. Wikipedia. The difference is due to the limited sample size.
FD_LConfidence Interval	Low confidence interval of the FD. Fraction mode: considers pixel with f_i>0.
FD_HConfidence Interval	High confidence interval of the FD. Fraction mode: considers pixel with f_i>0.