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  "body": "\n## Summary\n\nDigital topology studies notions such as connectedness, boundaries and curves for sets of points of the integer lattice $\\Z^2$ or $\\Z^3$.\nSuch sets model the pixels or voxels of digital images.\nIts basic tools are adjacency relations between lattice points and the paths and connected components they define.\nOne also uses genuine topologies on $\\Z^n$, such as the Khalimsky topology.\nThese notions underlie image processing tasks such as counting objects, tracing borders and thinning shapes.\n\n## Explanations\n\n### L1 human\n\nA black-and-white picture on a screen is a set of black squares on a grid.\nTo say that a shape in the picture is \"in one piece\" or \"has a hole\", one must decide when two squares touch.\nThey may touch only along an edge, or also at a corner.\nFor example, two black squares that meet only at a corner form one piece under the corner rule but two pieces under the edge rule.\nDigital topology makes such choices precise and checks that familiar facts, such as \"a closed curve separates the inside from the outside\", still hold.\n",
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