Some enumerations of binary digital images
This work addresses a gap in digital topology by providing foundational enumerations for small binary images, though it is incremental as it builds on existing studies without introducing new methods.
The paper tackled the problem of cataloging binary digital images of small sizes by enumerating classes up to isomorphism and determining homotopy equivalences, resulting in patterns that led to conjectures about irreducible but non-rigid images.
The topology of digital images has been studied much in recent years, but no attempt has been made to exhaustively catalog the structure of binary images of small numbers of points. We produce enumerations of several classes of digital images up to isomorphism and decide which among them are homotopy equivalent to one another. Noting some patterns in the results, we make some conjectures about digital images which are irreducible but not rigid.