id author title date pages extension mime words sentence flesch summary cache txt np193774991 Brandon Rowekamp Planar Pixelations and Shape Reconstruction 2012 .txt text/plain 101 4 42 This approximation converges to the original shape in a very strong sense: as the size of the pixels goes to zero we can recover important geometric and topological invariants of the original shape such as Betti numbers, area, perimeter and curvature measures. Any subset of the plane can be approximated by a set of square pixels. cache/np193774991.txt txt/np193774991.txt