Threshold Parallelism in Morphological Feature Extraction, Skeletonization, and Pattern Spectrum

In this paper 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 thresholdlinear superposition: Namely, the output graytone image is the sum of outputs due to input binary images, which result from thresholding the input graytone image at all levels. Then these results are generalized to a vector space formulation, e.g., to any linear combination of simple morphological systems such as erosion, dilation, rank -order filters, and their cascade or max /min combinations. Thus many such systems processing graytone images are reduced to corresponding binary image processing systems, which are easier to analyze and implement.