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Persistence Clustering Gallery

Persistence Clustering Gallery Image

The Persistence Clustering Gallery is composed of the following examples (from left to right):

Each example is explained in more details in its own documentation and is shown in the above screenshot in a pair of images, one showing the dataset (upper half), the other showing the results of the pipeline (bottom half).

Pipeline description

All examples of the Gallery have a similar pipeline.

First, it loads a point cloud from disk, then it computes a mesh on which a density field is obtained with a Gaussian Resampling on the points (top 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.

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 view in the above screenshot) then smoothed. Finally, by using the identifier of the 2-dimension cell of the Morse Smale complex where one point lands, a cluster is given to it.

ParaView

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

$ paraview --state=states/persistenceClusteringGallery.pvsm

Python code

Persistence clusering 0

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#!/usr/bin/env python

from paraview.simple import *

# paraview 5.9 VS 5.10 compatibility ===========================================
def ThresholdBetween(threshold, lower, upper):
    try:
        # paraview 5.9
        threshold.ThresholdRange = [lower, upper]
    except:
        # paraview 5.10
        threshold.ThresholdMethod = "Between"
        threshold.LowerThreshold = lower
        threshold.UpperThreshold = upper
# end of comphatibility ========================================================

# create a new 'CSV Reader'
clustering0csv = CSVReader(FileName=['clustering0.csv'])

# create a new 'Table To Points'
tableToPoints1 = TableToPoints(Input=clustering0csv)
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'
persistenceThreshold0 = Threshold(Input=tTKPersistenceDiagram1)
persistenceThreshold0.Scalars = ['CELLS', 'Persistence']
ThresholdBetween(persistenceThreshold0, 10.0, 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)
resampleWithDataset1.CellLocator = 'Static Cell Locator'

SaveData("OutputClustering.csv", resampleWithDataset1)

Persistence clusering 1

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from paraview.simple import *

# paraview 5.9 VS 5.10 compatibility ===========================================
def ThresholdBetween(threshold, lower, upper):
    try:
        # paraview 5.9
        threshold.ThresholdRange = [lower, upper]
    except:
        # paraview 5.10
        threshold.ThresholdMethod = "Between"
        threshold.LowerThreshold = lower
        threshold.UpperThreshold = upper
# end of comphatibility ========================================================

# create a new 'CSV Reader'
clusteringcsv = CSVReader(FileName=["clustering1.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"]
ThresholdBetween(threshold1, -0.1, 999999999)

# create a new 'Threshold'
persistenceThreshold0 = Threshold(Input=threshold1)
persistenceThreshold0.Scalars = ["CELLS", "Persistence"]
ThresholdBetween(persistenceThreshold0, 10.0, 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)

Persistence clusering 2

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from paraview.simple import *

# paraview 5.9 VS 5.10 compatibility ===========================================
def ThresholdBetween(threshold, lower, upper):
    try:
        # paraview 5.9
        threshold.ThresholdRange = [lower, upper]
    except:
        # paraview 5.10
        threshold.ThresholdMethod = "Between"
        threshold.LowerThreshold = lower
        threshold.UpperThreshold = upper
# end of comphatibility ========================================================

# create a new 'CSV Reader'
clusteringcsv = CSVReader(FileName=['clustering2.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.GaussianSplatRadius = 0.05
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']
ThresholdBetween(threshold1, -0.1, 999999999)

# create a new 'Threshold'
persistenceThreshold0 = Threshold(Input=threshold1)
persistenceThreshold0.Scalars = ['CELLS', 'Persistence']
ThresholdBetween(persistenceThreshold0, 5.0, 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)

Persistence clusering 3

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from paraview.simple import *

# paraview 5.9 VS 5.10 compatibility ===========================================
def ThresholdBetween(threshold, lower, upper):
    try:
        # paraview 5.9
        threshold.ThresholdRange = [lower, upper]
    except:
        # paraview 5.10
        threshold.ThresholdMethod = "Between"
        threshold.LowerThreshold = lower
        threshold.UpperThreshold = upper
# end of comphatibility ========================================================

# create a new 'CSV Reader'
clusteringcsv = CSVReader(FileName=['clustering3.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']
ThresholdBetween(threshold1, -0.1, 999999999)

# create a new 'Threshold'
persistenceThreshold0 = Threshold(Input=threshold1)
persistenceThreshold0.Scalars = ['CELLS', 'Persistence']
ThresholdBetween(persistenceThreshold0, 10.0, 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)

Persistence clusering 4

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from paraview.simple import *

# paraview 5.9 VS 5.10 compatibility ===========================================
def ThresholdBetween(threshold, lower, upper):
    try:
        # paraview 5.9
        threshold.ThresholdRange = [lower, upper]
    except:
        # paraview 5.10
        threshold.ThresholdMethod = "Between"
        threshold.LowerThreshold = lower
        threshold.UpperThreshold = upper
# end of comphatibility ========================================================

# 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']
ThresholdBetween(threshold1, -0.1, 999999999)

# create a new 'Threshold'
persistenceThreshold0 = Threshold(Input=threshold1)
persistenceThreshold0.Scalars = ['CELLS', 'Persistence']
ThresholdBetween(persistenceThreshold0, 10.0, 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)

C++/Python API

GeometrySmoother

PersistenceDiagram

TopologicalSimplification

MorseSmaleComplex