A Novel Index Based on Binary Entropy to Confirm the Spatial Expansion Degree of Urban Sprawl

The phenomenon of urban sprawl has received much attention. Accurately confirming the spatial expansion degree of urban sprawl (SEDUS) is a prerequisite to controlling urban sprawl. However, there is no reliable metric to accurately measure SEDUS. In this paper, based on binary entropy, we propose a new index named the spatial expansion degree index (SEDI), to overcome this difficulty. The study shows that the new index can accurately determine SEDUS and, compared with other commonly used measures, the new index has an obvious advantage in measuring SEDUS. The new index belongs to the second-order metrics of point pattern analysis, and greatly extends the concept of entropy. The new index can also be applied to other spatial differentiation research from a broader perspective. Although the new index is influenced by the scaling problem, because of small differences between different scales, given that the partition scheme in the research process is the same, the new index is a quite robust method for measuring SEDUS.