Morphological Bilateral Filtering
A current challenging topic in mathematical morphology is the construction of locally adaptive operators, i.e., structuring functions that are dependent on the input image itself at each position. Development of spatially variant filtering is well established in the theory and practice of Gaussian filtering. The aim of the first part (second and third sections) of the paper is to study how to generalize these convolution-based approaches in order to introduce adaptive nonlinear filters that asymptotically correspond to spatially variant morphological dilation and erosion. In particular, starting from the bilateral filtering framework and using the notion of counter-harmonic mean, our goal is to propose a new low complexity approach to defining spatially variant bilateral structuring functions. Then, in the second part (fourth section) of the paper, an original formulation of spatially variant flat morphological filters is proposed, where the adaptive structuring elements are obtained by thresholding the bilateral structuring functions. The methodological results of the paper are illustrated with various comparative examples.
bilateral filtering counter-harmonic mean adaptive mathematical morphology spatially variant structuring functions