Defining Cost Functions and Profitability Measures for Digraphs Associated with Raster DEMs

With a raster Digital Elevation Model, it is usual to associate a directed graph. Firstly, the problem of defining cost functions for such digraphs is discussed in a general and formal framework, and a particularly simple and natural way to tackle this problem is proposed. Secondly, the notion of profitability, which is commonly linked with the notion of cost, is put forward. Thus, profitability measures are introduced. In particular, the profitability of a point according to a region is defined. Finally, it is shown that profitability measures and cost functions provide complementary information.