Beyond pure quality

We add new features to the diffusion-based codec R-EED that go beyond pure quality.Our new progressive modes for R-EED can outperform JPEG and JPEG2000.Tree-based subdivision allows efficient region of interest coding.Diffusion-based video decoding is possible in real-time without sacrificing quality.Our newly proposed features are pairwise compatible and can be used simultaneously. Compared to transform-based image compression methods such as JPEG2000, approaches based on partial-differential equations (PDEs) are in a proof-of-concept stage. Nevertheless, R-EED, a codec employing edge-enhancing anisotropic diffusion (EED) and rectangular subdivision, can surpass JPEG2000 quality-wise. However, today's requirements for compression algorithms go beyond pure compression performance. Codecs must also fulfil the feature requirements of specific applications such as online media or medical imaging. We propose three such features for the R-EED codec. By reordering grey values and exploiting the subdivision scheme, we incorporate a progressive mode into R-EED that can outperform JPEG and JPEG2000. Additionally, we show that rectangular subdivision is well-suited for region of interest coding and adapt the quality of image parts according to their importance. Finally, we propose a real-time video player that demonstrates how R-EED-based decoding can be performed efficiently. All of these extensions are compatible with each other and can be used simultaneously.