Properties of Morphological Dilation in Max-Plus and Plus-Prod Algebra in Connection with the Fourier Transformation

Abstract The basic filters in mathematical morphology are dilation and erosion. They defined by a structuring element that is usually shifted pixel-wise over an image, together with comparison process takes place within the corresponding mask. This made grey value case means of maximum or minimum formation. Hence, there easy access to max-plus algebra and, change, also theory linear algebra. We show approximation function forms commutative semifield (with respect multiplication) corresponds again limit case. In this way, we demonstrate novel logarithmic connection between Fourier transform slope transformation. addition, prove fast depends only on size used. Moreover, derive bound above which yields results exact terms quantisation.