In this paper, we prove that the C-C balls are not isoperimetric sets on the one-dimensional Heisenberg group H~ 1.Under the hypothesis that there were isoperimetric sets in the class A, we obtain the best constant in the isoperimetric inequality. 证明了在一维Heisenberg群H1上C-C球不是等周集;同时在A类集中有等周集的假设前提下,给出了Heisenberg群H1上等周不等式的最佳常数。
In addition, we present another statistical method for some images having similar statistical distributions on the object and background, and relate it with isoperimetric constant of a graph. 此外,针对目标和背景具有相似统计分布的特性,设计了一种统计阈值方法,并将其与图(graph)的等周常数联系起来,进一步说明了此方法的合理性。