Adaptive morphological filtering using similarities based on geodesic time

Abstract

In this paper, we introduce a novel image-dependent filtering approach derived from concepts known in mathematical morphology. Like other adaptive methods, it assumes that the local neighbourhood of a pixel contains the essential process required for the estimation of local properties. Indeed, it performs a local weighted averaging by combining both spatial and tonal information in a single similarity measure based on the local calculation of discrete geodesic time functions. Therefore, the proposed approach does not require the definition of any initial spatial window but determines adaptively, directly from the input data, the neighbouring sample points and the associated weights. The resulting adaptive filters are consistent with the content of the image and, therefore, they are particularly designed for the purpose of denoising and smoothing of digital images. © 2008 Springer-Verlag Berlin Heidelberg.