Connectivity-preserving transformations of binary images
A binary image I is B(a), W(b)-connected, where a, b is an element of {4, 8}, if its foreground is a-connected and its background is b-connected. We consider a local modification of a B(a), W(b)-connected image I in which a black pixel can be interchanged with an adjacent white pixel provided that this preserves the connectivity of both the foreground and the background of I. We have shown that for any (a, b) is an element of {(4, 8), (8, 4), ( 8, 8)}, any two B(a), W(b)-connected images I and J each with n black pixels differ by a sequence of Theta(n(2)) interchanges. We have also shown that any two B(4), W(4)-connected images I and J each with n black pixels differ by a sequence of O(n(4)) interchanges. (C) 2007 Elsevier Inc. All rights reserved.
connectivity binary images interchanges digital topology transforming images ip-equivalence