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