An explicit formula for the number of tunnels in digital objects
<|reference_start|>An explicit formula for the number of tunnels in digital objects: An important concept in digital geometry for computer imagery is that of tunnel. In this paper we obtain a formula for the number of tunnels as a function of the number of the object vertices, pixels, holes, connected components, and 2x2 grid squares. It can be used to test for tunnel-freedom a digital object, in particular a digital curve.<|reference_end|>
@article{brimkov2005an,
    title={An explicit formula for the number of tunnels in digital objects},
    author={Valentin Brimkov, Angelo Maimone, Giorgio Nordo},
    journal={arXiv preprint arXiv:cs/0505084},
    year={2005},
    archivePrefix={arXiv},
    eprint={cs/0505084},
    primaryClass={cs.DM cs.CG cs.CV}
}