Edge-preserving smoothing using a similarity measure in adaptive geodesic neighbourhoods

This paper introduces a novel image-dependent filtering approach derived from concepts known in mathematical morphology and aiming at edge-preserving smoothing of natural images. Like other adaptive methods, it assumes that the neighbourhood of a pixel contains the essential information required for the estimation of local features in the image. The proposed strategy essentially consists in a weighted averaging combining both spatial and tonal information. For that purpose, a twofold similarity measure is calculated from local geodesic time functions. This way, no prior operator definition is required since a weighting neighbourhood and a weighting kernel are determined automatically from the unfiltered input data for each pixel location. By designing relevant geodesic masks, two adaptive filtering algorithms are derived that are particularly efficient at smoothing heterogeneous areas while preserving relevant structures in greyscale and multichannel images.