Automatic selection of the cut-locus detection threshold

Develop an automatic strategy for selecting the threshold parameter used to detect the cut locus in the iLogMap-with-cut-locus-removal algorithm, replacing the fixed value t = π/4.

Background

The iLogMap variant with cut-locus removal detects an estimated cut locus from the geodesic distance field using a threshold parameter t, and then solves the magnetic synchronization eigenproblem on the domain with the detected cut locus removed. The paper fixes this threshold at t = π/4 in its experiments.

Although the authors report that the method is relatively insensitive to the threshold over a broad range of values, the choice is currently manual. An automatic selection procedure would improve the method’s robustness and usability, particularly across geometries and source points with different cut-locus structures.

References

Although the method is relatively insensitive to the choice of $t$ over a broad range of values, an automatic selection strategy remains an open problem , and one from which our method would directly benefit.

— iLogMap: Geodesic Polar Coordinates Parameterization with the Magnetic Laplacian  (2609.10503 - Banduc et al., 9 Sep 2026) in Section 4, Discussion, subsection “Limitations”