Adaptive Transformation of Cartographic Bases by Means of Multiresolution Spline Interpolation

GIS databases often need to include maps from diverse sources. These can differ one another by many characteristics: different projections or reference systems, (slightly) different scales, etc. Theoretical and/or empirical transformations are available in literature to obtain maps in a unique system with a fixed tolerance. These transformations are nevertheless insufficient to completely remove differences and deformations: the outcome is that the geographic features on the maps do not fit in a perfect way. To reduce the deformation several transformations (affine, polynomial, rubber-sheeting) exist. The paper presents a new approach to the problem based on an interpolation by means of multiresolution spline functions and least squares adjustment. One map is taken as reference and the others are warped to comply with it. The interpolation is made by comparison of coordinates of a set of homologous points identified on the maps. The use of spline functions, compared to affine or polynomial interpolation, allows to have a greater number of coefficients to make more adaptive and localized the transformation. The multiresolution approach removes the rank deficiency problem that ordinary spline approach suffers for. Moreover the resolution of the spline functions depends areawise on the spatial density of homologous points: the denser are the points in the area, the better adapted to them can be the interpolating surface. A statistical test has been built to automatically choose the maximum exploitable resolution. The paper presents the method and one application in the example.