Interchangeable pairs of pixels in two-valued digital images

摘要

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. We give a local characterization of such pairs, and also prove that any isolated simply connected component of 1's has at least one pixel that is interchangeable with one of its neighbors. Finally, we give conditions under which two images whose sets of 1's are simply connected and have the same number of pixels can be transformed into one another by a sequence of interchanges. In particular, we show that any two digital arcs that have the same length can be transformed into one another by interchanges.