Scale Optimization in Topographic and Hydrographic Feature Mapping Using Fractal Analysis

Abstract

A new method for selecting optimal scales when mapping topographic or hydrographic features is introduced. The method employs rank-size partition of heavy-tailed distributions to detect nodes of rescaling invariance in the underlying hierarchy of the dataset. These nodes, known as head/tail breaks, can be used to indicate optimal scales. Then, the Fractal Net Evolution Assessment (FNEA) segmentation algorithm is applied with the topographic or hydrographic surfaces to produce optimally scaled objects. A topological transformation allows linking the two processes (partition and segmentation), while fractal dimension of the rescaling process is employed as an optimality metric. The new method is experimented with the two biggest river basins in Greece, namely Pinios and Acheloos river basins, using a digital elevation model as the only input dataset. The method proved successful in identifying a set of optimal scales for mapping elevation, slope, and flow accumulation. Deviation from the ideal conditions for implementing head/tail breaks are discussed. Implementation of the method requires an object-based analysis program and few common geospatial functions embedded in most GIS programs. The new method will assist in revealing underlying environmental processes in a variety of earth science fields and, thus, assist in land management decision-making and mapping generalization.