Approximation of Digital Circles by Regular Polygons

In this paper, we show that an ideal regular (convex) polygon corresponding to a digital circle is possible for some of the digital circles, especially for the ones having smaller radii. For a circle whose ideal regular polygon is not possible, an approximate polygon, tending to the ideal one, is possible, in which the error of approximation can be controlled by the number of vertices of the approximate polygon. These (ideal or approximate) polygonal enclosures of digital circles have several applications in approximate point set pattern matching. We have reported the conditions under which an ideal regular polygon definitely exists corresponding to a digital circle, and the conditions under which the existence of an ideal regular polygon becomes uncertain. Experimental results have been given to exhibit the possibilities of approximation and the tradeoff in terms of error versus approximation.

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