GENERALIZED \(H^h\)-RECURRENT FINSLER GEOMETRY WITH APPLICATIONS TO ANISOTROPIC IMAGE PROCESSING

Abstract

In this paper, we investigate the structure of generalized H^h-recurrent Finsler spaces (G-H^h-R-F_n) and establish several recurrence relations for Cartan’s h-curvature tensor and its associated geometric invariants. In particular, Theorems 3.1, 3.2, and 4a.3 provide novel conditions characterizing the stability and recurrence of curvature under horizontal covariant differentiation. To demonstrate the practical significance of these results, we extend the theoretical framework to the domain of digital image processing. A Finslerian metric derived from image gradients is constructed to model anisotropic features, and the recurrence conditions are shown to enhance edge preservation during anisotropic diffusion filtering. Simulation steps are outlined, illustrating how the recurrence properties of curvature tensors improve noise suppression and directional stability compared to standard Euclidean methods. The proposed approach highlights the dual role of generalized Finsler recurrence: as a fundamental extension in differential geometry and as a powerful tool for advanced computer vision applications such as denoising, segmentation, and texture analysis.