Fast implementation of gray-scale morphological image operations by a hybrid decomposition of structural function

This paper presents research on decomposition of morphological grayscale structural functions so that grayscale morphological transforms can be implemented quickly. An investigation into some theoretical and methodological issues about decomposition of structural function is conducted based on the results of decomposition of binary structure element in our previous work. Then a hybrid decomposition into neighborhood configurations for a large class of structural functions, which includes almost all useful structural functions especially some nonconvex ones, is proposed by use of the decomposing techniques for structure element in binary morphology. This hybrid decomposition can be calculated efficiently. From this decomposition, a fast implementing algorithm for grayscale morphological transforms is provided. It matches the common parallel image processors directly and so does not need support from complicated and special hardware.EI