Determining Digital Circularity Using Integer Intervals
Digital circularity is a well-researched topic for its real-world practicality to circularity measure, estimation of discrete curvature, circular arc segmentation, etc. The proposed work reveals a novel technique to determine whether a digital curve segment is digitally circular using the correspondence of its constituent runs with the square numbers in integer intervals. The notion of radii nesting is used to successively analyze these runs of digital points. Two algorithms have been proposed along with their demonstrations and detailed analysis, and a simple-yet-effective solution has been provided to expedite them using infimum circle and supremum circles that bound the initial range of radii. We have also shown how the proposed technique can be used for segmentation of an arbitrary digital curve segment into a sequence of circular arcs. Experimental results have been given to demonstrate the efficiency and elegance of the proposed technique.
digital circularity digital circles digital geometry number theory vectorization