Closing and Opening based on discrete t-norms. Applications to natural Image Analysis

This paper delves deeply into the recently introduced mathematical morphology based on discrete t-norms. Closing and opening operators and the concepts of open and closed objects are introduced. All the properties satisfied by nilpotent t-norms, even the generalized idempotence, hold too. After that, some experimental results, using comparative measures, on edge detection are showed. Some experimental results concerning the Top-Hat transformations and the basic filters built from the opening and closing operators are presented. Top-Hat experiments are compared with those obtained with the umbra approach, nilpotent t-norms and uninorms, proving that the discrete approach provides notable results. Moreover, different objective measures are used in order to evaluate the filtered results depending on the amount of noise in the image.