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A novel algorithm to derive an approximate cellular envelope of an arbitrarily thick digital curve on a 2D grid is proposed in this paper. The concept of “cellular envelope” is newly introduced in this paper, which is defined as the smallest set of cells containing the given curve, and hence bounded by two tightest (inner and outer) isothetic polygons on the grid. Contrary to the existing algorithms that use thinning as preprocessing for a digital curve with changing thickness, in our work, an optimal cellular envelope (smallest in the number of constituent cells) that entirely contains the given curve is constructed based on a combinatorial technique. The envelope, in turn, is further analyzed to determine polygonal approximation of the curve as a sequence of cells using certain attributes of digital straightness. Since a real-world curve/curve-shaped object with varying thickness and unexpected disconnectedness is unsuitable for the existing algorithms on polygonal approximation, the curve is encapsulated by the cellular envelope to enable the polygonal approximation. Owing to the implicit Euclidean-free metrics and combinatorial properties prevailing in the cellular plane, implementation of the proposed algorithm involves primitive integer operations only, leading to fast execution of the algorithm. Experimental results including CPU time reinforce the elegance and efficacy of the proposed algorithm.

PACE: Polygonal Approximation of Thick Digital Curves Using Cellular Envelope