Digital topology

Summary

Digital topology studies notions such as connectedness, boundaries and curves for sets of points of the integer lattice $\Z^2$ or $\Z^3$. Such sets model the pixels or voxels of digital images. Its basic tools are adjacency relations between lattice points and the paths and connected components they define. One also uses genuine topologies on $\Z^n$, such as the Khalimsky topology. These notions underlie image processing tasks such as counting objects, tracing borders and thinning shapes.