An efficient recursive edge-aware filter

• A novel edge-aware filtering with constant time complexity.
• Recursive weighted summation yielding window size independency.
• Soft weighting via effective connected support regions
• Low number of operations per pixel per disparity (6 adds and 4 muls) during aggregation.
• Multi-directional support.

In this study, an efficient edge-aware filtering methodology, namely permeability filter, that exploits recursive updates among horizontal and vertical axes, is extended for common image filtering applications, including denoising, segmentation and depth up-scaling. Besides, an 8-neighbor update methodology, that is applicable for all type of recursive filters, is proposed extending orthogonally generated supporting regions into multi-directional support. This extension provides fine smoothing, especially at object boundaries, and yields crisp aggregation regions for each pixel. Since it provides geometrically stable connected support regions for each pixel, the recursive filters remove the dependency on pre-defined windows that is common among the state-of-the-art edge-aware filters, and also provide complete content adaptability. Based on extensive experiments against popular edge-aware filters, it can be concluded that the permeability filter outperforms most of the state-of-the-art techniques in terms of both speed and precision, especially for geometry dependent applications, such as depth data up-scaling and stereo matching; while providing a competitive segmentation and de-nosing capability. Besides, the proposed multi-direction extension methodology significantly improves the performances of recursive filters in almost each application with up to three times increase in computation time. This remarkable performance is due to the unification of connected support regions by soft weights, while preventing over smoothing and enabling crisp models that improve performance on the specified applications. In conclusion, permeability filter and its proposed 8-neighbor recursion methodology is an efficient alternative to edge-aware filters in many application areas by the proposed multi-directional support with window size independency and providing high performance with quite low computational complexity.