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About this paper
Petar Hristov, Ingrid Hotz, Talha Bin Masood
A method is presented for the exact computation of Trait-Induced Merge Trees (TIMTs) for bivariate fields, overcoming inaccuracies in prior approximations by leveraging the simplex-wise convexity of the distance-to-trait function. The approach constructs a graph provably isomorphic to the true TIMT, enhancing the reliability of topological feature extraction for multivariate data.
Key insights
- Simplex-wise convexity of the distance-to-trait function implies that all topological events for TIMTs must occur at shared boundaries between simplices, not strictly inside them.
- Positive-valued interior edge minima that act as critical events for the TIMT are necessarily located on Jacobi edges of the underlying bivariate map.
- A theoretical error bound demonstrates that the exact and vertex-sampled approximate sublevel set filtrations are ε-interleaved, quantifying the approximation's limitations.
Summary by alphaXiv.
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