A modified gray level morphological gradient with accurate orientation estimates and reduced noise sensitivity

A new gray level morphological gradient method is proposed which uses gradient projections to both provide orientation information and also to reduce sensitivity to added noise. This results in a substantial performance improvement for both the blur minimum operator (BMO) and the well known morphological gradient defined as the difference between a dilated and eroded image using a symmetric structuring element. This new method is particularly attractive for applications which use morphological filtering at higher levels of processing, since complex structuring elements may often be decomposed into smaller structuring elements suitable for gradient operations. The performance is analyzed with respect to edge segment orientation accuracy using an image content model of an ideal sharp edge blurred by a square or circular aperture function with no preferential relationship between the orientation and displacement of the edge and the pixel grid. Sensitivity to noise can be evaluated in terms of the probability of false edge detection for a variety of noise sources. The theoretical results are supported with simulations designed to demonstrate performance expectations.