✍ Scribed by Azriel Rosenfeld; Akira Nakamura
No coin nor oath required. For personal study only.
A pair of neighboring, opposite-valued pixels in a two-valued digital image is called interchangeable if reversing their values preserves the topology of the image. It was conjectured in Rosenfeld, Saha, Nakamula, Pattern Recognition 34 ( 2001) 1853-1865 that if two digital images have the same number of 1's, and their sets of 1's S; T are simply connected, then S can be transformed into T by a sequence of interchanges. In that paper this conjecture was proved only for certain special cases-for example, if S and T are arcs. This paper proves the conjecture for arbitrary simply connected sets.
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