The statistical method of closed-Euler histogram

Euler histogram is a kind of simple but valid method and it is applied to the estimation of spatial queries costs. Much work has been done based on such method. This paper investigates the statistical method of Euler histogram and points out its some statistical errors for some distributions of the spatial objects - called the boundary problem. We present an improved statistical method, named as the statistical method of closed-Euler histogram, and prove its correctness.