THRESHOLD SUPERPOSITION IN MORPHOLOGICAL IMAGE-ANALYSIS SYSTEMS

In this correspondence it is shown that many composite morphological systems, such as morphological edge detection, peak/ valley extraction, skeletonization, and shape-size distributions obey a weak linear superposition, called threshold-linear superposition. Namely, the output image signal or measurement from each system is the sum of outputs due to input binary images that result from thresholding the input gray-level image at all levels. Then these results are generalized to a vector space formulation, e.g., to any finite linear combination of simple morphological systems. Thus many such systems processing gray-level images are reduced to corresponding binary image processing systems, which are easier to analyze and implement. © 1990 IEEE