Persistent Homology Transform is produced and maintained by
Yossi Bokor and Katharine Turner
yossi.bokor@anu.edu.au and katharine.turner@anu.edu.au
This package provides an implementation of the Persistent Homology Transform, as defined in Persistent Homology Transform for Modeling Shapes and Surfaces.
Currently, the best way to install PersistentHomologyTransfer is to run the following in Julia:
using Pkg
Pkg.add(PersistentHomologyTransfer)PHT computes the Persistent Homology Transform of simple, closed curves in \(\mathbb{R}^2\) given an \(m \times 2\) CSV file of ordered points sample from the curve in either a clockwise or anti-clockwise direction. You can either specify the directions explicity as a \(n \times 2\) array (directions::Array{Float64}(n,2)), or specify an integer (directions::Int64) and then the directions used will be generated by
angles = [n*pi/(directions/2) for n in 1:directions]
directions = [[cos(x), sin(x)] for x in angles]To perform the Persistent Homology Transfer for the directions, run
PHT(points, directions)This outputs an array of Eirene Persistence Diagrams, one for each direction.
We will go through an example using a random shape and 20 directions. You can download the CSV file from here
To begin, load the CSV file into an array in Julia
Boundary = CSV.read("<path/to/file>")
Persistence_Diagrams = PHT(Boundary, 20)You can then access the persistence diagram corresponding to the \(i^{th}\) direction as
Persistence_Diagrams[i]