Recursive Implementation of Erosions and Dilations Along Discrete Lines At Arbitrary Angles

Van Herk has shown that the erosion/dilation operator with a linear structuring element of an arbitrary length can be implemented in only 3 min/max operations per pixel. In this paper, the algorithm is generalized to erosions and dilations along discrete lines at arbitrary angles. We also address the padding problem; so that the operation can be performed in place without copying the pixels to and from an intermediate buffer. Applications to image filtering and to radial decompositions of discs are presented. Keywords. Mathematical morphology, image filtering, algorithms, recursivity, line and periodic structuring elements, radial decompositions. Name and address of corresponding author: Dr. Pierre Soille LGI2P Ecole des Mines d'Al`es Parc scientifique Georges Besse F--30000 Nimes France Ph.: int+33- 66 38 70 22 Fax: int+33- 66 38 70 74 Email: soille@eerie.fr Pierre Soille is with the Laboratoire de G'enie Informatique et d'Ing'enierie de Production of the Ecole des Mines d'Al`es, Parc..