On minimal perimeter polyminoes

Authors:
Yaniv Altshuler;Vladimir Yanovsky;Daniel Vainsencher;Israel A. Wagner;Alfred M. Bruckstein
Affiliations:
Computer Science Department, Technion, Haifa, Israel;Computer Science Department, Technion, Haifa, Israel;Computer Science Department, Technion, Haifa, Israel;Computer Science Department, Technion, Haifa, Israel;Computer Science Department, Technion, Haifa, Israel
Venue:
DGCI'06 Proceedings of the 13th international conference on Discrete Geometry for Computer Imagery
Year:
2006

Citing 0
Cited 5

Discrete sets with minimal moment of inertia

Theoretical Computer Science
On isoperimetrically optimal polyforms

Theoretical Computer Science
On minimal moment of inertia polyominoes

DGCI'08 Proceedings of the 14th IAPR international conference on Discrete geometry for computer imagery
Isoperimetrically optimal polygons in the triangular grid

IWCIA'11 Proceedings of the 14th international conference on Combinatorial image analysis
Multi-agent Cooperative Cleaning of Expanding Domains

International Journal of Robotics Research

Quantified Score

Hi-index	0.00

Visualization

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).