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.
KeywordsDEMs directed graphs cost functions problems of optimal paths
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- [Ahu93]Ahuja, R.K., T.L. Magnanti, and J.B. Orlin, Network flows, Prentice Hall, 1993.Google Scholar
- [Be158]Bellman, R., “On a toutin problem”, Quaterly of Applied Math., 16(1), pp.87–90, 1958.Google Scholar
- [Bor84]Borgefors, G., “Distance transformations in arbitrary dimensions”, CVGIP 27, pp.321–345, 1984.Google Scholar
- [Bor86]Borgefors, G.,“Distance transformations in digital images”, CVGIP 34, pp.344–371, 1986.Google Scholar
- [Dub95]Dubois, N., F. Semet, “Estimation and determination of shortest path length in a road network with obstacles”, European Journal of Operational Research 83, pp.105–116, 1995.Google Scholar
- [Gon84]Gondran, M., and M. Minoux, Graphs and Algorithms, Wiley, Chichester, 1984.Google Scholar
- [Kre94]van Kreveld, M., “On Quality Paths on Polyhedral Terrains”, IGIS'94, LNCS 884, Springer-Verlag, pp. 113–122, 1994.Google Scholar
- [Mit91]Mitchell, J.S.B., C.H. Papadimitriou, “The weighted region problem: finding shortest paths through a weighted planar subdivision”, Journal of ACM 38(11), pp. 18–73, 1991.Google Scholar
- [Pri94]Prins, C., Algorithmes de graphes, Eyrolles, 1994.Google Scholar
- [Ros66]Rosenfeld, A., and J.L. Pfaltz, “Sequential operations in digital picture processing”, Journal of ACM 13(4), pp.471–494, 1966.Google Scholar
- [Zha93]Zhan, C., S. Menon, and P. Gao, “A Directional Path Distance Model for Raster Distance Mapping”, COSIT'93, LNCS 716, Springer-Verlag, pp.434–443, 1993.Google Scholar