Abstract

Morphological image processing based on binary set representation of an image has been receiving increasing attention as a viable alternative to the linear image processing based on Fourier domain filtering [1], The fundamental morphological filtering operations of erosion and dilation are nonlinear operations from which more complex operations (opening, closing, pattern spectra) suitable for shape extraction and analysis can be synthesized. The morphological operations are defined between a working image and a much smaller image called the structuring element. In most cases the structuring element is binary while the working image can be binary, analog with binary threshold decomposition representation or analog with weighted binary representation. For the first two representations, the dilation and erosion operations consist of a superposition of several shifted replicas of the working image followed by a point-wise threshold operation at different levels; 1 for dilation and (m-1) for erosion, where "m" is the number of images superposed. With the third representation, the minimum/maximum value (for dilation/erosion, respectively) for the superposed pixels is detected and assigned as the pixel value in the output image. In either case, the processing operations are of low complexity. The number of shifted replicas of the working image and the amount of shift corresponds to the number and position, respectively, of bright pixels in the structuring element. For large and irregularly shaped structuring elements the morphological processing operation complexity is dominated by data communication.

© 1991 Optical Society of America