Geodesics with Unified Tangent-constrained Priors and Curvature Regularization
Quick Take
A new unified geodesic framework integrates tangent-constrained priors with curvature penalization, enhancing image segmentation by improving robustness against weak boundaries and topological shortcuts. This approach utilizes Hamilton-Jacobi-Bellman PDEs for efficient numerical solutions, demonstrating superior shape fidelity in synthetic, natural, and medical images compared to existing models.
Key Points
- Integrates tangent-constrained priors with curvature penalization for better segmentation.
- Utilizes Hamilton-Jacobi-Bellman PDEs for efficient numerical solutions.
- Demonstrates improved robustness against weak boundaries in complex shapes.
- Achieves enhanced shape fidelity in synthetic, natural, and medical images.
- Extends classical geodesic models with mandatory tangent constraints.
Article Content
From source RSS / original summaryarXiv:2606. 00139v1 Announce Type: new Abstract: Curvature-penalized geodesic models have proven their effectiveness in image segmentation by computing globally optimal curves. Unfortunately, these models remain susceptible to shortcuts when delineating objects with complex shapes and image intensity distributions, as they lack mechanisms to enforce shape-aware tangent constraints.
To address this limitation, we propose a unified geodesic framework that integrates tangent-constrained priors with curvature penalization. The key idea is to formulate tangent admissibility directly within the orientation-lifted space, where path tangents are restricted to spatially varying angular sectors derived from intrinsic shape representatives (ISR) such as skeletons or interior landmarks.
This formulation gives rise to a family of tangent-constrained Finslerian metrics, extending the classical curvature-penalized geodesic models while enforcing mandatory tangent constraints. The resulting Hamilton-Jacobi-Bellman (HJB) partial differential equations (PDEs) admit efficient numerical solutions via variants of the fast marching method, preserving the single-pass computational complexity.
Experiments on synthetic, natural, and medical images demonstrate that the proposed geodesic framework indeed improves robustness against weak boundaries and topological shortcuts, yielding segmentation results with enhanced shape fidelity compared to existing geodesic models.
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