 
Summary: Image coding with geometric wavelets
Dror Alani*, Amir Averbuch* and Shai Dekel**
*School of Computer Science
Tel Aviv University
Tel Aviv 69978, Israel
**GE Healthcare
6 Hamasger St.
OrYehuda 60408, Israel
Abstract
This paper describes a new and efficient method for low bitrate image coding which is based on
recent development in the theory of multivariate nonlinear piecewise polynomial approximation. It
combines a Binary Space Partition (BSP) scheme with Geometric Wavelet (GW) tree approximation
so as to efficiently capture curve singularities and provide a sparse representation of the image. The
GW method successfully competes with stateoftheart wavelet methods such as the EZW, SPIHT
and EBCOT algorithms. We report a gain of about 0.4 dB over the SPIHT and EBCOT algorithms
at the bitrate 0.0625 bitsperpixels (bpp). It also outperforms other recent methods that are based
on `sparse geometric representation'. For example, we report a gain of 0.27 dB over the Bandelets
algorithm at 0.1 bpp. Although the algorithm is computationally intensive, its time complexity
can be significantely reduced by collecting a `global' GW nterm approximation to the image from
a collection of GW trees, each constructed separately over tiles of the image.
