Homotopy relations for digital images


We introduce three generalizations of homotopy equivalence in digital images, to allow us to express whether a bounded and an unbounded digital image with standard adjacencies are similar with respect to homotopy. We show that these three generalizations are not equivalent to ordinary homotopy equivalence, and give several examples. We show that, like homotopy equivalence, our three generalizations imply isomorphism of fundamental groups, and are preserved under wedges and Cartesian products.

DOI Code: 10.1285/i15900932v37n1p99

Keywords: digital topology; digital image; homotopy; fundamental group

Full Text: PDF

Creative Commons License
This work is licensed under a Creative Commons Attribuzione - Non commerciale - Non opere derivate 3.0 Italia License.