MSE=39.63 MSE=29.12 MSE=25.58
at 89.2 : 1 at 90.3 : 1 at 89.7 : 1
MSE=65.02 MSE=49.44 MSE=38.66
at 206.0 : 1 at 207.9 : 1 at 206.4 : 1
Figure 12: Images obtained with DICOM (using JPEG 2000), R-EED, and C- EED with compression rates close to 90:1 (top row) and 207:1 (bottom row). The test data set “trab64” (size 256 × 256 × 64) consists of the first 64 slices of a femured bone CT. The images above depict the last 2-D slice of “trab64”.
entropy encoding, and interpolation swapping.
Thirdly, we have demonstrated that EED-based compression is also applicable for shape coding, and that the concepts of our EED-based codec translate well to the 3-D setting. Especially, we showed that the use of 3-D EED offers significant advantages over slice-wise 2-D diffusion, and that our 3-D codec C-EED outper- forms R-EED as well as the DICOM/JPEG 2000 standard on medical data. It is evident that the basic ideas behind EED-based image compression generalise in a straightforward way to tensor data sets, if one uses the corresponding EED operators from [70]. It is more challenging to adapt our methods to the efficient compression of image sequences and surface data, see e.g. [6]. A more advanced handling of colour images and shapes is also on our agenda. Moreover, we are go- ing to focus on approaches that pay specific attention to highly textured images. On an algorithmic side, we are currently evaluating a number of efficient numer- ical methods, and we are also studying parallel implementations on multi-core architectures such as GPUs.
Acknowledgements
We thank Irena Gali´c (University of Osijek, Croatia) for fruitful discussions and for providing two images and code of her compression algorithm, David Tschumperlé (French National Center for Scientific Research, France) for provid- ing the image in Fig. 1, and Wiro Niessen (University Medical Center Rotterdam, The Netherlands) for providing the test image in Fig. 12.
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