Estimation of number-area-frequency dimensions of surface water bodies

Abstract

This paper proposes a technique that includes a set of mathematical morphological transformations to estimate the frequency dimension. The dimension computed through a power law relationship is tallied with the dimension computed through a correlational plot. This technique is demonstrated on a two-dimensional section embodying a large number of surface water bodies, extracted from remotely sensed data, situated randomly, and the frequency dimension (D) for surface water bodies yields straight-line dependence of lnC(r) (correlational integral) on ln(r) (radius of structuring template). The correlational integral is computed for two aspects by considering the number of water bodies and their corresponding occupied areas. The number-frequency dimension and the area frequency dimension computed through correlational plots yield straight-line dependencies with slopes that are greater than unity but less than 2.0 (1.3 and 1.7, respectively).