Speeding-up successive Minkowski operations with bit-plane computers

Performing successive Minkowski operations on binary images is a well known and widely used task in image processing. In bit-serial parallel computers (so called bit-plane computers) the time necessary to perform such operations depends to a great extent on the complexity of the particular structuring element T. As it is well known, this computation time can be reduced if T is decomposed into the (set theoretical) sum of simpler structuring elements. Such decompositions, however, are known only for a very narrow class of structuring elements. In this paper, a modification of that decomposition method is presented which results in speeding up the Minkowski operations for a broader class. It is shown that, after a certain number of steps, just the ‘extreme points’ of the structuring element are important. So, unlike the convenient methods, it is successfully applied only if sequences of Minkowski operations are applied. This is the case in particular in mathematical morphology when erosion, dilatation, opening (ouverture), and closing (fermeture) are performed repeatedly.