## Metrics

**This list reflects only default measurements and is not exhaustive. For each metric SNT retrieves the descriptive statistics Mix, Max, Mean, Standard Deviation (SD), Sum and N**, which may lead to inevitable redundancy between measurements.

E.g., when measuring Branch length for a particular cell, it is possible to retrieve the length of the smallest branch (

*Min*), the longest (

*Max*), the average and standard deviation of all branch lengths (

*Mean*and

*SD*), their total length (

*Sum*), and number (

*N*).

Also, please note that some of the metrics described here have been ported from L-measure: doi:10.1038/nprot.2008.51

###### Branch contraction

A measure of *straightness*. The ratio between the Euclidean distance of a branch (i.e., Euclidean distance between the first and last node of the branch) and its path length. Range of values: ]0–1] (unitless)

###### Branch fractal dimension

Also known has Hausdorff dimension. Defined as the slope obtained from the log-log plot of *Path distance vs Euclidean distance*, as implemented by L-measure following the definition of Marks & Burke (2007). It is only computed for branches defined by at least five nodes. Described in: doi:10.1002/cne.21418

###### Branch length

The path length of a branch (i.e., the sum of all its internode distances)

###### Branch mean radius

The average of the radii of the nodes defining a branch

###### Branch surface area

*Estimated* surface area^{1} of a branch computed from treating each internode segment as a conical frustum and summing the surface area of all frusta

###### Branch volume

*Estimated* volume^{1} of a branch computed from treating each internode segment as a conical frustum and summing the volume of all frusta

###### Cable length

The total path length of a structure, i.e., the sum of all internode distances of its paths

###### Complexity index

Also known as “Dendritic Complexity Index”. An index based on the number of primary neurites, total arbor length, and the number and Strahler-order of terminal branches. Described in: doi:10.1523/JNEUROSCI.19-22-09928.1999

###### Convex hull: Boundary size

The perimeter of the 2D polygon or the surface area of the 3D polyhedron of the convex hull

###### Convex hull: Boxivity

The extent to which the convex hull approaches a rectangle (2D) or a cuboid (3D). Range of values: 0–1 (unitless)

###### Convex hull: Centroid-root distance

The distance between the root of a neuronal arbor and the centroid of its convex hull

###### Convex hull: Elongation

The caliper (also known as Feret) diameter of the convex hull

###### Convex hull: Roundness

The extent to which the convex hull approaches a circle (2D) or a sphere (3D). Range of values: 0–1 (unitless)

###### Convex hull: Size

Either the area of the 2D polygon, or the volume of the 3D polyhedron defining the convex hull

###### Depth

The depth of the bounding box embedding the structure being measured

###### Height

The height of the bounding box embedding the structure being measured

###### Horton-Strahler bifurcation ratio

The average bifurcation ratio of Strahler bifurcation ratios

###### Horton-Strahler number

The highest Horton-Strahler number of a tree, i.e., the Horton-Strahler number of its root node

###### Internode distance

The distance between nodes defining a branch or a Path

###### Internode distance (squared)

The squared distance between nodes defining a branch or a Path. Alternative to *Internode distance* when faster computations are required.

###### Length of inner branches

The sum of branch lengths of branches of highest Strahler order. Typically, these correspond to the most ‘internal’ branches of an arbor, in direct sequence from the root. Note that_Primary branches_ are *inner branches* starting at the tree’s root.

###### Length of longest shortest path

Considering a graph-theory tree, the *Length of longest shortest path* corresponds to the graph diameter. Note that this metric can only be computed for structures that are valid mathematical trees.

###### Length of primary branches

The sum of branch lengths of primary (or root-associated) branches. Primary branches have origin in a tree’s root, extending to the closest branch point or end-point, i.e., they are *inner branches* starting at the root. Note that a primary branch can also be terminal.

###### Length of terminal branches

The sum of branch lengths of branches ending at terminal endpoints (tips)

###### No. of branch nodes (branch fragmentation)

The total number of nodes (and thus *compartments*) in a branch

###### No. of branch points

The total number (count) of branch points (also known as fork points)

###### No. of branches

The total number (count) of branches

###### No. of fitted paths

The total number (count) of fitted paths

###### No. of inner branches

The number of branches of highest Strahler order. Typically, these correspond to the most ‘internal’ branches of an arbor, in direct sequence from the root

###### No. of path nodes (path fragmentation)

The total number of nodes (and thus *compartments*) in a path

###### No. of paths

The total number (count) of paths defining a structure

###### No. of primary branches

The total number (count) of primary (or root-associated) branches. Primary branches have origin in a tree’s root, extending to the closest branch point or end-point, i.e., they are *inner branches* starting at the root. Note that a primary branch can also be terminal.

###### No. of spines/varicosities

Sum of all spine/varicosity markers in a structure

###### No. of spines/varicosities per path

Number of spines/varicosities associated with a path

###### No. of terminal branches

The total number (count) of branches ending at terminal endpoints (tips)

###### No. of tips

The total number (count) of terminal endpoints in a structure

###### No. of total nodes

The total number (count) of nodes in a structure

###### Node intensity values

The pixel intensity at each node location

###### Node radius

The radius at each node, typically obtained from fitting procedures

###### Partition asymmetry

L-measure metric. Computed at each bifurcation point of the structure being measured. Note that branch points with more than 2 children are ignored. Given \(n1, n2\) the number of tips on each side of a bifurcation point, Partition asymmetry is defined as: \(\frac{abs(n1-n2)}{(n1+n2-2)}\).

###### Path channel

The color channel associated with a path (multidimensional image)

###### Path contraction

The ratio between the Euclidean distance of a path (i.e., Euclidean distance between the first and last node of the path) and its path length. Range of values: ]0–1[ (unitless)

###### Path frame

The time-lapse frane associated with a path (multidimensional image)

###### Path length

The sum of all internode distances in a path

###### Path mean radius

The average of the radii of the nodes defining a path

###### Path order

###### Path spine/varicosity density

The number (count) of spine/varicosity markers associated with a path, divided by its path length

###### Path surface area

*Estimated* surface area^{1} of a path computed from treating each internode segment as a conical frustum and summing the surface area of all frusta

###### Path volume

*Estimated* volume^{1} of a path computed from treating each internode segment as a conical frustum and summing the volume of all frusta

###### Remote bif. angles

The angle between each bifurcation point and its children in the simplified graph, which comprise either branch points or terminal nodes. Note that branch points with more than 2 children are ignored.

###### Sholl: Decay

The Sholl regression coefficient

###### Sholl: Degree of Polynomial fit

The polynomial degree used to fit the Sholl profile. See Sholl › Fitting functions

###### Sholl: Kurtosis

See Kurtosis in Sholl › Metrics based on sampled data

###### Sholl: Max

See Max inters. in Sholl › Metrics based on sampled data

###### Sholl: Max (fitted)

See Critical value in Sholl › Metrics based on fitted data

###### Sholl: Max (fitted) radius

See Critical radius in Sholl › Metrics based on fitted data

###### Sholl: Mean

See Mean inters. in Sholl › Metrics based on sampled data

###### Sholl: No. maxima

The number of times *Max inters.* occurs in a Sholl profile. See Max inters. in Sholl › Metrics based on sampled data

###### Sholl: No. secondary maxima

The number of times a secondary peak occurs in a Sholl profile. See Max inters. in Sholl › Metrics based on sampled data

###### Sholl: Ramification index

See Schoenen Ramification index in Sholl › Metrics based on sampled data

###### Sholl: Skeweness

See Skeweness in Sholl › Metrics based on sampled data

###### Sholl: Sum

See Sum inters. in Sholl › Metrics based on sampled data

###### Surface area

Treating each internode segment as a conical frustum, the sum of the surface areas^{1} of all frusta

###### Volume

Treating each internode segment as a conical frustum, the sum of the volume^{1} of all frusta

###### Width

The width of the bounding box embedding the structure being measured

###### X,Y,Z coordinates

Cartesian coordinates in the three-dimensional space

##### Notes

- This list does not include specialized metrics provided by dedicated SNT plugins, such as Strahler or Sholl
- Some combinations of metrics/statistics may not be meaningful: e.g., if you are only measuring a single cell, pairing cable length to
*SD*will not be useful, since only one value has been computed. In this case, the Measurements table will append ‘[Single metric]’ to such data - Each of the 60+ metrics is represented by five statistical properties: minimum, maximum, mean, standard deviation and sum, resulting in a total of at least \(60\times 5\) features. Note that there is an intrinsic redundancy between these features: E.g., for a given cell, retrieving Branch length’s
*N*is effectively the same as retrieving No. of branches *NaN*values for a reported metric typically reflect undefined operations (e.g., division by zero), or the fact that the reconstruction being parsed is not a valid mathematical tree- Currently, volume-related metrics do not take into account path fillings

## Group Statistics

SNT assembles comparison reports and simple statistical reports (two-sample t-test/one-way ANOVA) for up to six groups of cells. This is described in Comparing Reconstructions. Descriptive statistics of measurements can be obtained by running *Summarize Existing Results* in the Measurements dialog or by running Frequency/Distribution Analysis commands.

## Glossary

###### Mesh

A polygon mesh defines the shape of a three-dimensional polyhedral object. In neuronal anatomy, meshes define neuropil annotations, typically compartments of a reference brain atlas (e.g., the hippocampal formation in mammals, or mushroom bodies in insects)

###### Multi-dimensional image

An image with more than 3 dimensions (3D). Examples include fluorescent images associated with multiple fluorophores (multi-channel) and images with a time-dimension (time-lapse videos). A 3D multi-channel timelapse has 5 dimensions

###### Neurite

Same as neuronal process. Either an axon or a dendrite

###### Path

Can be defined as a sequence of branches, starting from soma or a branch point until a termination. In manual and assisted (semi-automated) tracing, neuronal arbors are traced using paths, not branches. Fitting algorithms that take into account voxel intensities can be used to refine the center-line coordinates of a path, typically to obtain more accurate curvatures. Fitting procedures can also be used to estimate the volume of the neurite(s) associated with a path

###### (Neuronal) morphometry

Quantification of neuronal morphology

###### Neuropil

Any area in the nervous system. The cellular tissue around neuronal processes

###### Out-of-core

Software with out-of-core capabilities is able to process data that is too large to fit into a computer’s main memory

###### Reconstruction

See Tracing

###### ROI

Region of Interest. Define specific parts of an image to be processed in image processing routines

###### Skeleton

A thinned version of a digitize shape (such as a neuronal reconstruction) or of a binary image

###### Tracing

A digital reconstruction of a neuron or neurite. The term predates computational neuroscience and reflects the manual ‘tracing’ on paper performed with camera lucida devices by early neuroanatomists

###### Volume rendering

A visualization technique for displaying image volumes (3D images) directly as 3D objects

This glossary was assembled from the supplementary note of SNT’s publication: doi:10.1038/s41592-021-01105-7