Triangular covers of a digital object

Article Type

Research Article

Publication Title

Journal of Applied Mathematics and Computing


An optimal geometric representation of a digital object in the form of minimum-area cover is important in image analysis and computer vision. The first algorithm, to the best of our knowledge, for constructing the minimum-area polygonal cover of a 2D digital object as perceived on a uniform triangular grid, is proposed here. The polygonal cover is triangular in the sense that its boundary consists of a sequence of edges on the underlying grid. The proposed algorithm is based on certain combinatorial properties of a digital object on a grid, and it computes the tightest cover in time linear in the perimeter of the object. Experimental results are presented to demonstrate the efficacy, robustness, and versatility of the algorithm, and they indicate that the runtime varies inversely with the grid size. The proposed study on triangular covers of digital objects will find many applications to pattern analysis and shape matching.

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