Threshold superposition in morphological image analysis systems

It is shown that four composite morphological systems, namely morphological edge detection, peak/valley extraction, skeletonization, and shape-size distributions obey a weak linear superposition, called threshold-linear superposition. The output image signal or measurement from each system is shown to be the sum of outputs due to input binary images that result from thresholding the input gray-level image at all levels. 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