Non-linear generalization of a digital terrain model using neural networks

W artykule omówiono wybrane współczesne koncepcje generalizacji numerycznego modelu rzeźby terenu. Przedstawiono także podstawowe własności sztucznych sieci neuronowych. Szczególną uwagę zwrócono na możliwość zastosowania sieci neuronowych jako narzędzia nieliniowego uogólniania modelu danych przestrzennych na przykładzie generalizacji NMT.The article discusses selected contemporary concepts of generalization of a digital model of terrain relief. Basic properties of artificial neural networks are also presented. Special attention is paid to the possibility of application of neural networks as a tool for non-linear approximation of a spatial data model on the example of ganeralization of a digital tarrain model (DTM). Contemporary understanding of the concept of spatial data generalization differentiates between two models of spatial data connected to two types of generalization: cartographic generalization, linked to digital cartographic model (DCM) and model generalization linked to digital landscape model (DLM). Generalization of a terrain relief model (understood as DTM generalization, representing DLM model, and not as generalization of contour map - DCM model) requires one of three methods: global filtration, local filtration (usually multi-stage) or heuristic approach. Proper generalization of a digital terrain model is especially vital for powering of geographic information systems (GIS). In order to conduct credible spatial analyses it is essential to preserve the actual location of key terrain forms. Generalization of DLM model should therefore be applied, rather than cartographic generalization. Automatization of large scale DTM modeling understood this way requires local filtration. It should be noted that the question of source data selection from base model is only one of the aspects of DTM generalization. Interpolation methods applied have more complex impact on the resulting model. Classic methods of statistical surface creation usually base on linear interpolation. The article discusses non-linear methods of DTM interpolation using artificial neural networks. In mathematical modeling of physical surface of the Earth - in interpolation of digital terrain model - especially good results can be achieved with the use of regression networks. Generalized Regression Neural Networks (GRNN), due to the modification of the amoothing coefficient of radial function, permit fluent control of the level of executed generalization. Networks of this type can be used to refine and smooth DTM, preceding the stage of automatic generation of contours.Neural networks of the Radial Basis Function (RBF) type can be used as a tool for complex generalization of terrain relief model (the more radial neurons the lower generalization level)