How it works
Step 01
Locally Aligned Ant Technique (LAAT)
Virtual ants explore the neighbourhood, and prefer to move along the direction of 1-dimensional structures, identified using a principal componente analysis. Their decaying pheromone trails, attract more ants that tend to reinforce the detection of weak 1-Dimensional structures. After the pheromone map has been built, a pheromone threshold is applied, effectively denoising the 1 Dimensional structures that were uncovered by the ants.
Step 02
Evolutionary Manifold Alignment Aware Agents (EM3A):
Moves the particles towards the backbone of the filamentary structure (Paper)
After denoising with LAAT, the remaining data points are passed to the MBMS algorithm. This shifts their positions towards the local density peak using a diffusion algorithm. The result is that all the points finish in a highly concentrated 1-D spine at the centres of the original 1D structures. This spine can then be used as a 'centre' of the 1D structures, in order to measure distances of other objects from them.
Step 03
Dimensionality Index (DimIndex)
Assign to the particles their intrinsic dimension (Paper)
In a 3D data set, some objects are primarily 3D (like spherical objects), some are 2D (like walls or planes), and some are 1D (like filaments or streams). The DimIndex tool provides a means to separate the structures according to their dimensionality. This can be valuable if the goal is to identify a specific type of structure (e.g. 1D filaments) for further analysis.
Step 04
Multi-Manifold Crawling (Crawling)
Operates on the one-dimensional partition. Discover the filaments and constructs their corresponding skeletons (Paper)
The crawling algorithm allows us to convert the concentrated spine of data points from the MBMS algorithm into a convenient set of continuously linked vectors, connecting pairs of points (i.e. segments that trace out the spine of the 1D structures). In this way, there is a single point at any position along the 1D structure that marks out the structures centre. Segments are grouped together into continuous sets so as individual 1D structures can be uniquely identified.
Step 05
Stream Generative Topographic Mapping (SGTM)
Builds a probabilistic model for each extracted sub-structure, describing the transverse noise distribution along the manifold itself as a constrained Gaussian mixture model (Paper)
Using constrained gaussian mixture models, the probability that objects belong to specific 1-D structures is quantified by building a probabilistic model for each individual structure. This is a powerful approach to assigning membership for individual objects in complex structures.