Edge Preserving Filters using Geodesic Distances on Weighted Orthogonal Domains

We introduce a framework for image enhancement, which smooths images while preserving edge information. Domain (spatial) and range (feature) information are combined in one single measure in a principled way. This measure turns out to be the geodesic distance between pixels, calculated on weighted orthogonal domains. The weight function is computed to capture the underlying structure of the image manifold, but allowing at the same time to efficiently solve, using the Fast Marching algorithm on orthogonal domains, the eikonal equation to obtain the geodesic distances. We show promising results in edge-preserving denoising of gray scale, color and texture images.