Alternating Direction Implicit (ADI) schemes for a PDE-based image osmosis model
For researchers in image processing, this work provides a computationally efficient numerical method for the osmosis model, though it is an incremental improvement over existing implicit techniques.
The authors developed ADI splitting schemes for a PDE-based image osmosis model, achieving efficient numerical solutions that preserve continuous model properties. The method outperforms classical implicit methods, even with large time steps, as demonstrated in shadow removal applications.
We consider \emph{Alternating Direction Implicit} (ADI) splitting schemes to compute efficiently the numerical solution of the PDE osmosis model considered by Weickert et al. for several imaging applications. The discretised scheme is shown to preserve analogous properties to the continuous model. The dimensional splitting strategy traduces numerically into the solution of simple tridiagonal systems for which standard matrix factorisation techniques can be used to improve upon the performance of classical implicit methods, even for large time steps. Applications to the shadow removal problem are presented.