A directional path distance model for raster distance mapping
This paper proposes a directional model for weighted path distance mapping on raster data structures. The approach that is used to map the shortest path distance from a set of source cells to any background cell incorporates both non-directional and directional weights on the links between adjacent cells. Nondirectional weights allow users to model impedance in terms of the traditional cell based friction costs used in raster distance mapping. Directional weights allow users to model non-symmetric travel costs incurred in traveling through value-gradients in continuous fields such as elevation, temperature or density, or incurred when traveling through a prevailing flow field. The model has been implemented as a cell-based raster distance mapping tool with user selectable directional factor functions, using both Dijkstra's and the Bellman-Ford's shortest distance algorithms. Two experimental results are included.
KeywordsDistance Mapping Zenith Angle Output Factor Path Distance Friction Layer
Unable to display preview. Download preview PDF.
- 1.Bellman, R., “On a toutin problem,” Quarterly of Applied Mathematics, 16(1), pp.87–90, 1958.Google Scholar
- 2.Borgefors, G., “Distance transformations in digital images,” Computer vision, Graphics and Image Processing, Vol. 34, pp. 344–371, 1986.Google Scholar
- 3.Danielsson, P., “Euclidean distance mapping”, Computer Graphics and Image Processing, Vol. 14, pp. 227–248, 1980.Google Scholar
- 4.Dijkstra, E. W., “A note on two problems in connect with graphs,” Numerishe Mathematik, Vol. 1, pp. 269–271, 1959.Google Scholar
- 5.Eastman, J. R., “Pushbroom algorithm for calculating distances in raster grids,” AUTO-CARTO 9, pp. 288–297, 1989.Google Scholar
- 6.Gatrell, A, Distance and space: A geographical perspective, Clearendon Press, 1983.Google Scholar
- 7.Menon, S., P. Gao, C. Zhan, “Grid: a data model and functional map algebra for raster geo-processing,” Proceedings, GIS/LIS'91, Vol. 2, pp. 551–561, Atlanda Gorgia, 1991.Google Scholar
- 8.Smith, T. E., “Shortest-path distances: An axiomatic approach,” Geographical Analysis, Vol. 21. No. 1, 1989.Google Scholar
- 9.Tomlin, D., The Map Analysis Package (MAP Manual), part of doctoral dissertation, 1980.Google Scholar
- 10.Tomlin, D., Geographic Information Systems and Cartographic Modeling, Prentice-Hall Inc., Englewood Cliffs, NJ 07632.Google Scholar