Persistence Clustering 4

Pipeline description

This pipeline is the same as the previous ones and performs a clustering by persistence on a 2D data set taken from the scikit-learn examples. Please check out the Karhunen-Love Digits 64-Dimensions example for an application of this pipeline on a real-life data set..

First, this example loads a point cloud from disk (top left view in the above screenshot), then it computes a mesh on which a density field is obtained with a Gaussian Resampling on the points (top right view in the above screenshot). This density field will be considered as the input scalar data.

Next, a PersistenceDiagram is computed and thresholds are applied base on persistence to maintain only the features with a persistence above a certain value. The result is a simplified persistence diagram (bottom left view in the above screenshot).

The simplified persistence diagram is then used as a constraint for the TopologicalSimplification of the input scalar data, giving us a simplified data.

From there a MorseSmaleComplex is computed (bottom right view in the above screenshot). Finally, by using the identifier of the 2-dimension cell of the Morse Smale complex where one point lands, a cluster identifier, encoded in the AscendingManifold field in the ouput, is given to it.

ParaView

To reproduce the above screenshot, go to your ttk-data directory and enter the following command:

paraview states/persistenceClustering4.pvsm

Python code

from paraview.simple import *

# create a new 'CSV Reader'
clusteringcsv = CSVReader(FileName=["clustering4.csv"])

# create a new 'Table To Points'
tableToPoints1 = TableToPoints(Input=clusteringcsv)
tableToPoints1.XColumn = "X"
tableToPoints1.YColumn = "Y"
tableToPoints1.a2DPoints = 1
tableToPoints1.KeepAllDataArrays = 1

# create a new 'Gaussian Resampling'
gaussianResampling1 = GaussianResampling(Input=tableToPoints1)
gaussianResampling1.ResampleField = ["POINTS", "ignore arrays"]
gaussianResampling1.ResamplingGrid = [256, 256, 3]
gaussianResampling1.SplatAccumulationMode = "Sum"

# create a new 'Slice'
slice1 = Slice(Input=gaussianResampling1)
slice1.SliceType = "Plane"

# init the 'Plane' selected for 'SliceType'
slice1.SliceType.Normal = [0.0, 0.0, 1.0]

# create a new 'TTK PersistenceDiagram'
tTKPersistenceDiagram1 = TTKPersistenceDiagram(Input=slice1)
tTKPersistenceDiagram1.ScalarField = ["POINTS", "SplatterValues"]

# create a new 'Threshold'
threshold1 = Threshold(Input=tTKPersistenceDiagram1)
threshold1.Scalars = ["CELLS", "PairIdentifier"]
threshold1.ThresholdMethod = "Between"
threshold1.LowerThreshold = -0.1
threshold1.UpperThreshold = 999999999

# create a new 'Threshold'
persistenceThreshold0 = Threshold(Input=threshold1)
persistenceThreshold0.Scalars = ["CELLS", "Persistence"]
persistenceThreshold0.ThresholdMethod = "Between"
persistenceThreshold0.LowerThreshold = 10.0
persistenceThreshold0.UpperThreshold = 999999999

# create a new 'TTK TopologicalSimplification'
tTKTopologicalSimplification1 = TTKTopologicalSimplification(
    Domain=slice1, Constraints=persistenceThreshold0
)
tTKTopologicalSimplification1.ScalarField = ["POINTS", "SplatterValues"]

# create a new 'TTK MorseSmaleComplex'
tTKMorseSmaleComplex1 = TTKMorseSmaleComplex(Input=tTKTopologicalSimplification1)
tTKMorseSmaleComplex1.ScalarField = ["POINTS", "SplatterValues"]

# create a new 'Resample With Dataset'
resampleWithDataset1 = ResampleWithDataset(
    SourceDataArrays=OutputPort(tTKMorseSmaleComplex1, 3),
    DestinationMesh=tableToPoints1,
)

# save the output(s)
SaveData("OutputClustering.csv", resampleWithDataset1)

To run the above Python script, go to your ttk-data directory and enter the following command:

pvpython python/persistenceClustering4.py

Inputs

• clustering4.csv: a table of 2 dimension points.

Outputs

• data4Resampled.csv: the output is the data resampled in CSV file format, the cluster identifier of a point is given in the AscendingManifold field.

C++/Python API

PersistenceDiagram

TopologicalSimplification

MorseSmaleComplex