Determine convergence under the tighter stopping tolerance

Determine whether the checkerboard-, disk-, and Otsu-initialized Chan–Vese segmentation runs achieve full convergence when evaluated with stopping tolerance ε = 10⁻⁵ and a maximum budget of 500 iterations, rather than merely reaching the iteration ceiling.

Background

The study evaluates the scikit-image Chan–Vese solver with three initial level-set fields—checkerboard, disk, and Otsu-based initialization—under default and tighter stopping tolerances. With ε = 10⁻⁵, all three configurations have a median of 500 iterations, and nearly all or all runs reach the maximum iteration budget. Consequently, the reported sensitivity results cannot establish how the methods would compare after genuine numerical convergence. The unresolved issue is whether additional iterations would materially change the segmentation outputs or the relative performance of the initializers.

References

At $\epsilon=10{-5}$, mean Dice is 0.6404 for checkerboard, 0.4069 for disk, and 0.6601 for Otsu initialization. All three have a median of 500 iterations. The limit is reached by 551 checkerboard runs and all 600 runs for each other initializer, leaving full convergence unresolved.

— Initialization and Stopping Tolerance in CPU Dermoscopic Segmentation  (2609.25685 - Xu et al., 22 Sep 2026) in Section 5.2, “Stopping-Criterion Sensitivity”