Geodesics with Unified Tangent-constrained Priors and Curvature Regularization

Researchers propose a unified geodesic framework that combines tangent-constrained priors with curvature regularization to improve image segmentation accuracy. The method addresses limitations in existing models by enforcing shape-aware constraints through orientation-lifted spaces, achieving robust segmentation with enhanced shape fidelity on medical and natural images.

This paper presents a significant advancement in computational geometry applied to image segmentation, tackling a fundamental challenge in computer vision: preventing algorithm shortcuts when delineating complex object shapes. Traditional curvature-penalized geodesic models optimize globally but lack mechanisms to respect inherent shape characteristics, leading to topologically incorrect results when boundaries are weak or ambiguous. The researchers address this by integrating tangent-constrained priors directly into the geodesic framework, forcing solution paths to respect angular sectors derived from intrinsic shape representatives like skeletons. The theoretical contribution lies in formulating tangent admissibility within orientation-lifted spaces and extending classical Finslerian metrics with mandatory constraints, creating a mathematically elegant unified framework. Computationally, the approach maintains single-pass efficiency through Hamilton-Jacobi-Bellman PDE solutions via fast marching variants, making it practically viable for real-world applications. The method demonstrates particular value in medical imaging, where segmentation accuracy directly impacts diagnostic accuracy and treatment planning. Experimental validation across synthetic, natural, and medical datasets shows consistent improvements in robustness against weak boundaries and topological shortcuts compared to existing geodesic models. This work bridges pure mathematics (differential geometry) with applied computer vision, offering practitioners a more reliable tool for automated segmentation tasks. The framework's extensibility suggests potential applications in 3D medical imaging, autonomous navigation, and other domains requiring robust shape-aware path optimization.

• →Unified geodesic framework integrates tangent constraints with curvature penalization to improve image segmentation robustness.
• →Method formulates shape-aware constraints in orientation-lifted spaces using intrinsic shape representatives like skeletons.
• →Hamilton-Jacobi-Bellman PDE solutions preserve computational efficiency with single-pass fast marching algorithms.
• →Experimental results demonstrate enhanced shape fidelity and resistance to weak boundaries in medical imaging applications.
• →Approach extends classical Finslerian metrics with mandatory tangent constraints for improved topological correctness.