Measuring Inhomogeneity in Spatial Distributions

Abstract

Abstract-The spatial distribution of nodes in wireless networks has important impact on network performance properties, such as capacity and connectivity. Although random sample models based on a uniform distribution are widely used in the research community, they are inappropriate for scenarios with clustered, inhomogeneous node distribution. This paper proposes a well-defined measure for the level of inhomogeneity of a node distribution. It is based on the local deviation of the actual value of the density of nodes from its expected value. Desired properties of the measure are defined and mathematically proven to be fulfilled. The inhomogeneity measure is also compared to human perception of inhomogeneity gained via an online survey. The results reveal that the measure well fits human perception, although there are notable deviations if linear operations are applied.

A Simple Approximation of the Aggregate Interference From a Cluster of Many Interferers With Correlated Shadowing

“…This could reflect, for example, interferers being on or off. • The positions { r i } of the interferers need not be independent, but could include more complex statistical behaviors (see [10], [44] for examples). • The interference powers {I i } in this work are assumed to be long-term averages.…”

Automatic classification of defect page content in scanned document collections

“…where w = 4.79129 was derived in [23]. Images having spatially uniformly distributed keypoints obtain values of h → 0 and whereas for spatially concentrated keypoints we get h → 1.…”

“…We use a measure of inhomogeneity to characterize the spatial distribution of keypoints [23]. The image is subdivided into a sequence s 2 , s = 1, 2, 4, .…”

A Modified Inhomogeneity Measure in Spatial Distribution

“…The method to measure the inhomogeneity of spatial distribution was given in literature [10]. First, the simulation area A was divided into s 2 subareas with the same size.…”

“…The inhomogeneity of spatial distribution has great impact on various networks properties such as capacity, connectivity, and medium access behavior. The literature [10] has given a method to measure the inhomogeneity of spatial distribution. It adopted absolute value.…”