Fast gray-level morphological transforms with any structuring element

This paper presents efficient algorithms to perform standard morphological operations on gray-level images such as erosions and dilations with any structuring elements . In a first section the general case is studied. A solution taking advantage of overlapping areas of the structuring elements and involving either a hiearchical approach or a simple sort of the pixels of the image is described, along with a comparison of this algorithm with existing methods. The proposed method shows significant improvement over these methods. Some mean of accelerating the algorithm further are also indicated. In a second section, the particular case of the line segment as structuring element is studied and a new method for dealing with these structuring elements, oriented in any direction, is proposed, which features a constant, optimal computing time with respect to the length of these structuring elements. Extensions to other types of structuring elements using the described technique are also proposed.