The geometry of images is multiscale, because edges of natural images are often blurry, and textures contain a broad range of geometric structures.

This geometry is constructed directly over a multiscale domain and corresponds to a grouping process of wavelet coefficients. The resulting adaptive representations are discrete, orthogonal and allow a multiscale description of the geometric content of an image.

This leads to the construction of orthogonal bandelet bases, for which the grouping process is locally defined using a best orientation.  These orthogonal bases improve over state of the art schemes for images and surfaces compression and for the inversion of the tomography operator.

In order to understand and model the complex geometry of turbulent textures, we design an association field that is able to capture long range interactions.  This allows a statistical modelling of the geometry of natural textures.  We apply this construction to geometric texture synthesis.