Recognition of Isothetic Arc Using Number Theoretic Properties

Abstract

In this paper, we propose an arc recognition method based on the number theoretic properties of isothetic covers. A definition of digital circles is given based on the dilation of Euclidean circles with unit squares. We show that a variant of the digital circle is equivalent to the grid centers between the isothetic covers of disks. Number theoretic properties of the isothetic covers of disks are explored and show that the distribution of square numbers can be used to find the run lengths of the isothetic covers. Arc recognition algorithms are developed based on the number theoretic properties.