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P. Maragos, R.D. Ziff, "Threshold Superposition in Morphological Image Analysis Systems," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 12, no. 5, pp. 498504, May, 1990.  
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@article{ 10.1109/34.55110, author = {P. Maragos and R.D. Ziff}, title = {Threshold Superposition in Morphological Image Analysis Systems}, journal ={IEEE Transactions on Pattern Analysis and Machine Intelligence}, volume = {12}, number = {5}, issn = {01628828}, year = {1990}, pages = {498504}, doi = {http://doi.ieeecomputersociety.org/10.1109/34.55110}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, }  
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TY  JOUR JO  IEEE Transactions on Pattern Analysis and Machine Intelligence TI  Threshold Superposition in Morphological Image Analysis Systems IS  5 SN  01628828 SP498 EP504 EPD  498504 A1  P. Maragos, A1  R.D. Ziff, PY  1990 KW  morphological image analysis; edge detection; peak/valley extraction; skeletonization; shapesize distributions; thresholdlinear superposition; graylevel image; vector space; binary image processing; picture processing; vectors VL  12 JA  IEEE Transactions on Pattern Analysis and Machine Intelligence ER   
It is shown that four composite morphological systems, namely morphological edge detection, peak/valley extraction, skeletonization, and shapesize distributions obey a weak linear superposition, called thresholdlinear 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 graylevel 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 graylevel images are reduced to corresponding binary image processing systems, which are easier to analyze and implement.
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