  Distance measuring is a very important task in digital geometry and digital
image processing. Due to our natural approach to geometry we think of the set
of points that are equally far from a given point as a Euclidean circle. Using
the classical neighbourhood relations on digital grids, we get circles that
greatly differ from the Euclidean circle. In this paper we examine different
methods of approximating the Euclidean circle in the square grid, considering
the possible motivations as well. We compare the perimeter-, area-, curve- and
noncompactness-based approximations and examine their realization using
neighbourhood sequences. We also provide a table which summarizes our results,
and can be used when developing applications that support neighbourhood
sequences.
