An algorithmic comparison between square- and hexagonal-based grids
CVGIP: Graphical Models and Image Processing
Pentagon--hexagon-patches with short boundaries
European Journal of Combinatorics
Digital Geometry: Geometric Methods for Digital Picture Analysis
Digital Geometry: Geometric Methods for Digital Picture Analysis
Characterization of digital circles in triangular grid
Pattern Recognition Letters
IEEE Transactions on Computers
On isoperimetrically optimal polyforms
Theoretical Computer Science
Digital Circularity and Its Applications
IWCIA '09 Proceedings of the 13th International Workshop on Combinatorial Image Analysis
On minimal perimeter polyminoes
DGCI'06 Proceedings of the 13th international conference on Discrete Geometry for Computer Imagery
Geometric transformations on the hexagonal grid
IEEE Transactions on Image Processing
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It is well known that a digitized circle doesn't have the smallest (digital arc length) perimeter of all objects having a given area. There are various measures of perimeter and area in digital geometry, and so there can be various definitions of digital circles using the isoperimetric inequality (or its digital form). Usually the square grid is used as digital plane. In this paper we use the triangular grid and search for those (digital) objects that have optimal measures. We show that special hexagons are Pareto optimal, i.e., they fulfill both versions of the isoperimetric inequality: they have maximal area among objects that have the same perimeter; and they have minimal perimeter among objects that have the same area.