  The Easy Path Wavelet Transform is an adaptive transform for bivariate
functions (in particular natural images) which has been proposed in [1]. It
provides a sparse representation by finding a path in the domain of the
function leveraging the local correlations of the function values. It then
applies a one dimensional wavelet transform to the obtained vector, decimates
the points and iterates the procedure. The main drawback of such method is the
need to store, for each level of the transform, the path which vectorizes the
two dimensional data. Here we propose a variation on the method which consists
of firstly applying a segmentation procedure to the function domain,
partitioning it into regions where the variation in the function values is low;
in a second step, inside each such region, a path is found in some
deterministic way, i.e. not data-dependent. This circumvents the need to store
the paths at each level, while still obtaining good quality lossy compression.
This method is particularly well suited to encode a Region of Interest in the
image with different quality than the rest of the image.
  [1] Gerlind Plonka. The easy path wavelet transform: A new adaptive wavelet
transform for sparse representation of two-dimensional data. Multiscale
Modeling & Simulation, 7(3):1474$-$1496, 2008.
