PARABOLIC NONLINEAR LAPLACIAN: MORPHOLOGICAL COUNTERPART OF LAPLACIAN OF GAUSSIAN

摘要

The Laplacian of Gaussian (LoG) is the second spatial derivative of an image that has first been smoothed with a Gaussian kernel.The LoG is a simple but very useful transformation for edge detection and feature extraction.In the classical literature of mathematical morphology,the morphological Laplacian is exclusively defined for flat operators as the difference between the gradient by dilation and the gradient by erosion.Using the counter-harmonic paradigm as a nonlinearization framework,the aim of this paper is to propose the morphological counterpart of the LoG,named the parabolic nonlinear laplacian (NLoG) and to study its behaviour with respect to the linear LoG.We show that the NLoG involves derivatives of dilation and erosion using a particular pair of nonflat structuring functions.