Surface analysis is a challenging research topic, which has gathered a lot of interest over the last few decades. When surface data is given as a set of points, which are the typical output of 3D laser scanners, the lack of structure makes it even more challenging. In this thesis, we tackle surface analysis by introducing a new function basis: the Wavejets. This basis allows to decompose locally the surface into a radial polynomial component and an angular frequency component. Stability properties with regards to a bad normal direction are demonstrated. By linking Wavejets coefficients to a high order differential tensor, we also define high order
principal directions on the surface. Furthermore, locally splitting surfaces with respect to frequencies leads us to define new integral invariants, permitting to locally describe the surface. Such descriptors are quite robust since they result from an integration process. Finally, we develop an application of these new integral invariants for geometric detail amplification, either based on point position or on normal direction modification, creating in this case the illusion of a surface change.