Widest-Path Reachability Fields for Connectivity-Preserving Slender Structure Segmentation

What the math gives to ML

The paper introduces a transferable connectivity objective based on widest-path, or Max-Min, reachability: the strength of a connection is the maximum over paths of the weakest predicted pixel on each path. This complements pixel losses because its gradient is concentrated on bottleneck pixels rather than diluted over thick foreground regions and background. The direct neural-network integration is a differentiable reachability loss over local image-grid graphs, using soft minimum and soft maximum operators during training while retaining ordinary segmentation logits at inference. A small-scale experiment can test whether this improves connected-component statistics and clDice at equal architecture, FLOPs, and pixel-loss budget.