Normal offsets

This research has been discontinued.

In order to compress images with smoothly coloured regions separated by smooth contours, wavelet transforms are proven to perform suboptimal. Wavelets are good at catching point singularities (e.g. texture), but fail when line singularities come up. A more compact representation can be obtained if we adapt the lifting idea to better approximate to the contours lying in the domain.

The proposed scheme is a refinement scheme, where finer points are expressed as normal distances with respect to the coarser approximating mesh. This allows an adaptive triangulation of the domain, instead of dyadic refinements of tensor product wavelets. This will lead to much more efficient methods for compression.

Normal offsets are better in capting the singularities (edges) in 2D images.

Notice that the triangulation rapidly becomes very dense in the neighborhood of the image contours (see below).

use wavelets here