Remarks on pointed digital homotopy

We show that homotopy equivalent digital images have isomorphic fundamental groups, even when the homotopy equivalence does not preserve the basepoint. This assertion appeared in [3], but there was an error in the proof; here, we correct the error. We present and explore in detail a pair of digital images with cu-adjacencies that are homotopic but not pointed homotopic. For two digital loops f, g : [0,m]Z → X with the same basepoint, we introduce the notion of tight at the basepoint (TAB) pointed homotopy, which is more restrictive than ordinary pointed homotopy and yields some different results.