## Expand description

Implementation of the NBLAST algorithm for quantifying neurons’ morphological similarity. Originally published in Costa et al. (2016) and implemented as part of the NeuroAnatomy Toolbox.

## Algorithm

Each neuron is passed in as a point cloud sample (the links between the points are not required).
A tangent vector is calculated for each point, based on its location and that of its nearest neighbors.
Additionally, an `alpha`

value is calculated, which describes how colinear the neighbors are,
between 0 and 1.

To query the similarity of neuron `Q`

to neuron `T`

:

- Take a point and its associated tangent in
`Q`

- Find the nearest point in
`T`

, and its associated tangent - Compute the distance between the two points
- Compute the absolute dot product of the two tangents
- Apply some empirically-derived function to the (distance, dot_product) tuple
- As published, this is the log probabity ratio of any pair belonging to closely related or unrelated neurons

- Find the nearest point in
- Repeat for all points, summing the results

The result is not easily comparable:
it is highly dependent on the size of the point cloud
and is not commutative, i.e. `f(Q, T) != f(T, Q)`

.

To make queries between two pairs of neurons comparable,
the result can be normalized by the “self-hit” score of the query, i.e. `f(Q, Q)`

.

To make the result commutative, the forward `f(Q, T)`

and backward `f(T, Q)`

scores can be combined in some way.
This library supports several means (arithmetic, harmonic, and geometric), the minimum, and the maximum.
The choice will depend on the application.
This can be applied after the scores are normalized.

The backbone of the neuron is the most easily sampled and most stereotyped part of its morphology, and therefore should be focused on for comparisons. However, a lot of cable is in dendrites, which can cause problems when reconstructed in high resolution. Queries can be weighted towards straighter, less branched regions by multiplying the absolute dot product for each point match by the geometric mean of the two alpha values.

More information on the algorithm can be found here.

## Usage

The QueryNeuron and TargetNeuron traits
define types which can be compared with NBLAST.
All `TargetNeuron`

s are also `QueryNeuron`

s.
Both are Neurons.

PointsTangentsAlphas and RStarTangentsAlphas implement these, respectively. Both can be created with pre-calculated tangents and alphas, or calculate them on instantiation.

The NblastArena contains a collection of `TargetNeuron`

s
and a function to apply to pointwise DistDots to generate
a score for that point match, for convenient many-to-many comparisons.
A pre-calculated table of point match scores can be converted into a function with table_to_fn.

## Re-exports

`pub use nalgebra;`

## Structs

- The result of comparing two (point, tangent) tuples. Contains the Euclidean distance between the points, and the absolute dot product of the (unit) tangents, i.e. the absolute cosine of the angle between them (possibly scaled by the geometric mean of the alphas).
- Struct for caching a number of neurons for multiple comparable NBLAST queries.
- Minimal struct to use as the query (not the target) of an NBLAST comparison. Equivalent to “dotprops” in the reference implementation.
- Target neuron using an R*-tree for spatial queries.
- Calculate a score matrix (lookup table for converting point matches into NBLAST scores) from real data using some sets of matching and non-matching neurons.
- A tangent, alpha pair associated with a point.

## Enums

- Enumeration of methods to ensure that queries are symmetric/ commutative (i.e.
`f(q, t) = f(t, q)`

). Specific applications will require different methods. Geometric and harmonic means bound the output to be >= 0.0. Geometric mean may work best with non-normalized queries. Max may work if an unknown one of the query and target is incomplete.

## Traits

- Trait describing a point cloud representing a neuron.
- Trait for objects which can be used as queries (not necessarily as targets) with NBLAST. See TargetNeuron.
- Trait describing a neuron which can be the target (or the query) of an NBLAST match.

## Functions

- Convert an empirically-derived table mapping pointwise distance and tangent absolute dot products to pointwise scores into a function which can be passed to neuron queries. These scores are then summed across all points in the query to give the raw NBLAST score.

## Type Definitions

- 3D unit-length vector type used internally
- 3D point type used internally
- Floating point precision type used internally