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Topology�for Compression Evaluation

Congrong Ren (Presenter)

Lin Yan

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Topological descriptors (TDs)

persistence diagram

sublevel set filtrations with rising threshold

height function

Reeb graph

embedded Reeb graph

[Yan et al., EuroVis 2021]

2D Morse function

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Applications of Topology

Symmetry detection

[Thomas and Natarajan, IEEE VIS 2011]

Feature correspondence

[Feng et al., The Visual Computer 29]

Feature tracking

[Saikia and Weinkauf, EuroVis 2017]

Global structure changes

[Sridharamurthy et al., IEEE TVCG 2020]

Clustering & Classification

[Favelier et al, IEEE VIS 2018]

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Topology-preserving compression evaluation

  • Compression ratio
  • PSNR, MSE, SSIM, etc.
  • Runtime
  • Bottleneck distance
  • p-Wasserstein distance
  • Distance between TDs of f & decompressed f’
  • False Positive (FP), False Negative (FN), False Type (FT)

[Soler et al., PacificVis 2018]

original contour tree

FP

FN

FT

[Yan et al., VIS 2023]

scalar

field

vector

field

Critical point in cell?

No critical point, but detected

Has critical point, but missed

Wrong type:

Attracting / repelling?

FP

FN

FT

[Liang et al., TVCG 2022]