Contextual Image Compression based on Adaptive Delaunay Triangulations

Delaunay triangulations. Classical spectral decompositions -like Fourier or
wavelets- are not optimal for images which contain smooth
geometrical objects delimited by regular curves. Here we focus on
a fully non-linear geometric image approximations: adaptive
refinement of continuous, piecewise affine functions over
Delaunay triangulations which provide very flexible
and sparse representations of the target functions. In this talk
the design and implementation of a new efficient compression
scheme of the corresponding information, which makes use of local
redundancies in the triangulation, are discussed. In particular,
suitable contextual encoding of the positions of the vertices and
of the greyscale values is proposed, which takes into account the
specific local geometrical structure of the triangulation and
combines it with appropriate combinatorial encoding. Finally some
examples are shown where our method significantly outperforms
JPEG2000.