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 so-called 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.