Separable Paravector Orientation Tensors for Enhancing Retinal Vessels

Robust detection of retinal vessels remains an unsolved research problem, particularly in handling the intrinsic real-world challenges of highly imbalanced contrast between thick vessels and thin ones, inhomogeneous background regions, uneven illumination, and complex geometries of crossing/bifurcations. This paper presents a new separable paravector orientation tensor that addresses these difficulties by characterizing the enhancement of retinal vessels to be dependent on a nonlinear scale representation, invariant to changes in contrast and lighting, responsive for symmetric patterns, and fitted with elliptical cross-sections. The proposed method is built on projecting vessels as a 3D paravector valued function rotated in an alpha quarter domain, providing geometrical, structural, symmetric, and energetic features. We introduce an innovative symmetrical inhibitory scheme that incorporates paravector features for producing a set of directional contrast-independent elongated-like patterns reconstructing vessel tree in orientation tensors. By fitting constraint elliptical volumes via eigensystem analysis, the final vessel tree is produced with a strong and uniform response preserving various vessel features. The validation of proposed method on clinically relevant retinal images with high-quality results, shows its excellent performance compared to the state-of-the-art benchmarks and the second human observers.