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# Quantities

Fri, 23/10/2015 - 15:29 -- Montevil

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.

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**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.

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**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

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**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

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**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

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**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.).