Title: Geodesics with Unified Tangent-constrained Priors and Curvature Regularization

Abstract:

While curvature-penalized geodesic models have demonstrated significant efficacy in image segmentation by calculating globally optimal curves, they are prone to generating shortcuts when segmenting objects characterized by complex geometries and varying intensity distributions. This vulnerability stems from an absence of mechanisms to enforce shape-aware tangent constraints. To overcome this deficiency, we introduce a unified geodesic framework that combines tangent-constrained priors with curvature penalization. The core concept involves defining tangent admissibility directly within the orientation-lifted space, thereby restricting path tangents to spatially dependent angular sectors. These sectors are derived from intrinsic shape representatives (ISR), such as skeletons or interior landmarks. This approach generates a family of tangent-constrained Finslerian metrics, which extend traditional curvature-penalized geodesic models by imposing mandatory tangent constraints. The associated Hamilton-Jacobi-Bellman (HJB) partial differential equations (PDEs) can be solved efficiently using variants of the fast marching method, maintaining single-pass computational complexity. Evaluations on synthetic, natural, and medical imagery reveal that our proposed framework enhances robustness against topological shortcuts and weak boundaries, ultimately producing segmentation outcomes with superior shape fidelity relative to current geodesic models.

Source: arXiv Generated at: 2026-06-02 00:00:00 UTC