TTKTopologicalSimplificationByPersistence not working for certain thresholds

[kamakshidasan]

I am trying to apply TTKTopologicalSimplificationByPersistence on a particular dataset. After a particular threshold, the filter seems to hang.

I have attached the dataset exhibiting this behaviour.

vtk_file = 'smooth_fire_clip_tv_2270.vtk'
file_path = os.path.join(input_directory, vtk_file)

vtk_reader = LegacyVTKReader(FileNames=[file_path])
clean_to_grid = CleantoGrid(Input=vtk_reader)
tetrahedralize_data = Tetrahedralize(Input=clean_to_grid)

topological_simplification = TTKTopologicalSimplificationByPersistence(Input=tetrahedralize_data)
topological_simplification.PersistenceThreshold = 3.8
topological_simplification.ThresholdIsAbsolute = 1
topological_simplification.InputArray = ['POINTS', 'Elevation']
topological_simplification.PairType = 'Extremum-Saddle'

On thresholds from [0.001, 3.7], the filter seems to work as expected. However, on 3.8 the filter seems to hang.

The same is seen on Paraview GUI also.

OS: MacOS 14.7 (23H124), Paraview 5.12.0 was downloaded directly from Paraview's website. TTK was installed from the plugins section.

I will be unable to build TTK from scratch or change Paraview's version or use another OS at the moment, and hence this issue has not been tested on other environments.

Also, which paper is in the backend of TTKTopologicalSimplificationByPersistence?

smooth_fire_clip_tv_2270.vtk.zip

[JonasLukasczyk]

Thank you for raising this issue. I investigated the problem and the root cause is the topology of the mesh. Specifically, the region that needs to be simplified and runs into an infinite loop belongs to this part of the mesh:

As you can see that region is connected only via the saddle (a single vertex) to the rest of the domain.
In short, this causes a problem in the current implementation of the LTS backend. As a quick solution you can do topological simplification before we had the LTS backend:

1. extract the maxima-saddle persistence pairs
2. threshold them
3. use topological simplification (not topological simplification by persistence) with the OLD backend

Now for the long technical explanation why this is happening. LTS is based on the concept that local regions can be simplified individually. The subprocedure responsible for this computes a local order in a region such that:

1. the only maximum according to the local order in the region is the saddle
2. all local minima that are created in this subprocedure are located at the boundary of the region (hence globally they are not minima).

The current implementation currently checks if the created minima are indeed on the boundary of the domain, and if not then the algorithm needs an additional iteration. With the topology of the current region it is impossible that the created minima are located at the boundary, since the only boundary vertex is the saddle which is a local maximum! So to solve this in the future we need to test for this special case to safely exit with the motto: we did the best we could with this topology. But I'm not sure when this will happen so I recommend the legacy simplification for now.

[JonasLukasczyk]

Turned out implementing this test was not so difficult after all: #1093. But for now I will still recommend going with the legacy simplification.