Finslerian-type GAF extensions of the Riemannian framework in digital image processing

Abstract

Digital image processing was recently proved to be successfully approached by variational tools, which extend the Casseles-Kimmel-Sapiro weighted length problem. Such tools essentially lead to the socalled Geodesic Active Flow (GAF) process, which relies on the derived mean curvature flow PDE. This prolific process is valuable due to both the provided numeric mathematical insight, which requires specific nontrivial choices for implementing the related algorithms, and the variety of possible underlying specific geometric structures. A natural Finsler extension of Randers type was recently developed by the authors, which emphasizes the anisotropy given by the straightforward gradient, while considering a particular scaling of the Lagrangian. The present work develops to its full extent the GAF process to the Randers Finslerian framework: the evolution equations of the model are determined in detail, Matlab simulations illustrate the obtained theoretic results and conclusive remarks are drawn. Finally, open problems regarding the theoretic model and its applicative efficiency are stated.