Progressive transmission is concerned with the transmission of large data sets or over slow networks. The idea is here that the user may be able to see approximate images already at an early stage during the transmission. This means, that at any interruption of the data stream should result in an image which resemples the original as good as possible. Thus, the most important data should be transmitted first.
This problem becomes more severe for time-dependent data in an interactive environment. The main application here is video conferencing. Here, the amount and quality of the transmitted data should automatically adapt to the current transmission speed (quality of service) which has to be supported by the compression algorithms and software.
Above you see various reconstructions of the Lena image and corresponding adaptive hierarchical triangular grids based on recursive bisection. The compression rates are 1.37%, 4.53%, 11.83%, and 25.84% (from left to right). As the number of triangles increases, the quality gets better and better. Each vertex in the triangulation does not correspond to a point in the image but to a wavelet basis function which may cover a larger part of the images. Here, the coordinates and color/greyscale information (wavelet coefficient) of the points are transmitted.
Another type of hierarchical image compression leading to better compression rates is based on space-filling curves, in our examples the Sierpinski curve. Data can be coded very efficiently following the curve corresponding to an adaptive hierarchical triangulation. Above you see the curves corresponding to the images for a maximum error tolerance of 20 grey scale levels.