Space-Efficient Outlines from Image Data via Vertex Minimization and Grid Constraints

When processing shape information derived from a noisy source such as a digital scanner, it is often useful to construct polygonal or curved outlines that match the input to within a specified tolerance and maximize some intuitive notions of smoothness, simplicity, and best fit. The outline description should also be concise enough to be competitive with binary image compression schemes. Otherwise, there will be a strong temptation to lose the advantages of the outline representation by converting back to a binary image format. This paper proposes a two-stage pipeline that provides separate control over the twin goals of smoothness and conciseness: the first stage produces a specification for a set of closed curves that minimize the number of inflections subject to a specified error bound; the second stage produces polygonal outlines that obey the specifications, have vertices on a given grid, and have nearly the minimum possible number of vertices. Both algorithms are reasonably fast in practice, and can be implemented largely with low-precision integer arithmetic.