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Comments on "On the invertibility of morphological representation of binary images" [with reply]

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4 Author(s)
B. E. Jang ; Adv. Imaging Res. Lab., Kodak Health Imaging Syst. Inc., Rochester, NY, USA ; R. T. Chin ; M. Charif-Chefchaouni ; D. Schonfeld

The authors comments that Charif-Chefchaouni and Schonfeld (see ibid., vol.3, no.6, p.847, 1994) investigated the invertibility of a morphological representation of binary images and determined the necessary and sufficient conditions for its inverse. The authors show that one of the derived necessary conditions is not valid. A counterexample is given to illustrate our observations. Charif-Chefchaouni and Schonfeld reply that the new sufficient condition is proposed for the invertibility of the morphological image representation. A modification of its inverse is subsequently used to derive a new necessary condition for the invertibility of the morphological image representation. A composition of these conditions is finally used to provide a new necessary and sufficient condition under some restrictions for the invertibility of the morphological image representation. These necessary and sufficient conditions form a revision of one of the necessary conditions for the invertibility of the morphological image representation stated in the original paper.

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IEEE Transactions on Image Processing  (Volume:5 ,  Issue: 3 )