Abstract
This paper explores proofs of the isoperimetric inequality for 4-connected shapes on the integer grid ℤ2, and its geometric meaning. Pictorially, we discuss ways to place a maximal number unit square tiles on a chess board so that the shape they form has a minimal number of unit square neighbors. Previous works have shown that "digital spheres" have a minimum of neighbors for their area. We here characterize all shapes that are optimal and show that they are all close to being digital spheres. In addition, we show a similar result when the 8-connectivity metric is assumed (i.e. connectivity through vertices or edges, instead of edge connectivity as in 4-connectivity). © Springer-Verlag Berlin Heidelberg 2006.
Cite
CITATION STYLE
Altshuler, Y., Yanovsky, V., Vainsencher, D., Wagner, I. A., & Bruckstein, A. M. (2006). On minimal perimeter polyminoes. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 4245 LNCS, pp. 17–28). Springer Verlag. https://doi.org/10.1007/11907350_2
Register to see more suggestions
Mendeley helps you to discover research relevant for your work.
