# SAMA documentation - Quantities

Documentation for Software for Automated Morphological Analysis : quantities evaluated and their interpretation.

## SAMA documentation - Quantities

Summary of the relevant quantities, by order of appearance in the pdf produced.

### Basic morphometrics

Note: axis refers to the axis when fitting the structure to an ellipsoid.

• "Quality" Elon1-Elon2 without lumen analysis. Elon1-Elon2+5*lumenosity with lumen analysis.

Proportions of the structure:

• "Elon1" elongation: length of the main axis of the structure/length of the second axis of the structure
• "logElon1" Logarithm of Elon1-1 .
• "Elon2" flatness: length of the second axis of the structure/length of the third axis of the structure
• "logElon2" Logarithm of Elon2 -1.

Sizes

• "logvol" Logarithm of the volume of the structure, in units (ex: µm³).
• "logEll_MajRad" logarithm of the length of the largest axis of the structure.
• "logFerret" logarithm of the largest distance between two points of the structure.

Comparison with other shapes

• "Sphericity" ratio of volume to area set to 1 for spheres (and smaller for any other shape). That is S³=36 pi V²/A³.
• "RatioVolEllipsoid" volume of the structure / volume of the embeding ellipsoid. Describes how convoluted the structure is that is to say how different from en ellipsoid it is.
• "logRatioVolEllipsoid" Logarithm of 1-RatioVolEllipsoid.
• "RatioVolbox" Volume of the structure/ Volume of its bounding box.
• "logRatioVolbox" Logarithm 1-RatioVolbox.
• "logMoment1" "logMoment2" "logMoment3" logarithms of the three moments invariant by rotation and translation discussed in Sadjadi, Firooz A.; Hall, Ernest L., "Three-Dimensional Moment Invariants," in Pattern Analysis and Machine Intelligence, IEEE Transactions on , vol.PAMI-2, no.2, pp.127-136, March 1980 doi: 10.1109/TPAMI.1980.4766990
http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4766990&isnumber=4766983
• "logMoment4" "logMoment5" Moments also invariant by scaling.

### Thickness measures (from bonej)

Thickness is a quantity that can be computed for every point inside a structure: it is the radius of the largest ball which contains this point and that fit inside the structure.

• "Thickness_Mean" Each structure is represented by its mean thickness.
• "Thickness_SD" Each structure is represented by the standard deviation of its thickness.
• "Thickness_Max" Each structure is represented by the thickness of its thickest point.
• "logThickness_Mean", "logThickness_SD", "logThickness_Max" Logarithm of the above.
• "rThickness_Mean" reduced thickness: Mean Thickness / volume of the structure (power 1/3, to compare a length with a length)
• "rThickness_SD" same for standard deviation.
• "rThickness_Max" same for maximum.
• "rbThickness_SD" standard deviation / mean
• "rbThickness_Max" max/ mean

### Lumen analysis

• "lumenosity" volume of lumen / volume of the structure
• "lumen" 1 if there is a lumen 0 otherwise. (when the mean is applied, it is the proportion of structures with lumena).

### Branching analysis

• "complexity" logarithm of the number of branches of the skeleton.
• "complexity2" 0 if there is one branch and 1 if there is 2 branches or more.
• "complexity3" logarithm of the cumulative length of branches.
• "complexity4" "entropy" of the branches (sum -p log(p) with p=length of the branch/ cumulative length of branches).

### PCA analysis

• "Dim.1" "Dim.2" "Dim.3" "Dim.4" "Dim.5" The first 5 dimension from pca analysis. The variable taken into account depend on the analysis options (with or without lumen analysis, branching analysis, etc.).