Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Approximating the Euclidean circle in the square grid using
  neighbourhood sequences   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.

13
The categories of this paper are: quant-ph
32
The categories of this paper are: atom-ph
27
The categories of this paper are: comp-gas
30
The categories of this paper are: q-alg
11
The categories of this paper are: hep-lat
23
The categories of this paper are: solv-int
25
The categories of this paper are: patt-sol
9
The categories of this paper are: nlin
26
The categories of this paper are: bayes-an
15
The categories of this paper are: nucl-ex
35
The categories of this paper are: mtrl-th
6
The categories of this paper are: astro-ph
37
The categories of this paper are: supr-con
10
The categories of this paper are: q-bio
29
The categories of this paper are: funct-an
21
The categories of this paper are: adap-org