A Constant-time Algorithm for Erosions/Dilations with Applications to Morphological Texture Feature Computation

A computationally ecient algorithm for computing erosions and dilations by onedimensional grayscale structuring elements with constant slope is proposed. The computational complexity of this algorithm is independent of the size of the support of the structuring function. This is a generalization of the method proposed by Van Herk for the case of erosion and dilation by ̄at one-dimensional structuring elements. By appropriate combinations of these structuring elements, it is possible to approximate many useful structuring elements. This enables ecient computation of granulometries where the number of operations depends linearly on the number of openings. Theoretical and experimental results comparing the complexity of this algorithm with other standard techniques is presented. Two memory ecient algorithms are then presented. Several implementation issues in computing a granulometry and moments of the associated morphological pattern spectrum are then addressed. An ecient implementation of granulometries for large images on machines with limited memory, by dividing the image into smaller rectangular patches is then discussed. The optimum size of these patches is a function of the speci®c hardware and has been obtained experimentally for three di€erent hardware platforms. Finally, parallel implementation of the di€erent algorithms on two multiprocessor machines is discussed.