Mathematical morphology and convolutions

Abstract

SUMMARYThe transforms of mathematical morphology may be generated by convolutions followed by thresholdings. Furthermore, the convolution‐thresholding pair may generalize mathematical morphology in three directions thanks to adjustments of the thresholding level, weighting of the coefficients of the convolution matrix and iterations. This leads to a wide set of non‐linear operators and structuring elements, including powerful directional transforms and an accurate iterative approach of a circular structuring element of any size and thus to a good approximation of the Euclidean distance.