A multiscale analysis model applied to natural surfaces

Multiscale Analysis of surfaces allows a hierarchical representation of their composing features. To represent a surface at a given scale, structures that are insignificant at that scale have to be eliminated. A typical example for this approach is cartography. However, the aims of cartographers reach beyond simply gradually eliminating the structures; in the majority of cases, the nature of geomorphological structures which compose the surface have to be preserved across all scales. Thus a global smoothing of the surface is not suitable to solve the present problem, since that would cause inevitably morphological modifications of certain important structures. In fact, the points to be preserved across scale variations are to be chosen interactively by the user. The authors present a surface model which allows them to perform a Multiscale Analysis which takes the importance of local structures into consideration, i.e. structures which are inherent to the relief morphology. From that discrete model we extract a context-dependent Multiscale Analysis Operator which can be isotropic or anisotropic and can be expressed in different forms