Combining wavelet and fractal coding for 3-D video coding

Smooth regions and edges are very self similar and can be coded efficiently by fractal coders. One problem of fractal image coding is to achieve a high quality or a lossless representation of an image. This can be overcome by a hybrid coding approach as proposed by the authors in [3]. An extension to 3-D fractal video coding is described in [4]. Due to the block based algorithm, however, blocking artifacts occur at very low bitrates. For low bitrates the visual quality of coded image sequences is more important than objective PSNR error measures. Especially at very low bit rates standard transform coding based methods like H.261 and MPEG suffer from annoying blocking artifacts. Wavelet-based coding schemes using overlapping basis functions avoid these blocking artifacts. At sharp edges however, ringing artifacts become visible. Well designed fractal coders are able to preserve sharp edges even at very low bitrates. But due to the block based algorithm of conventional fractal coders blocking artifacts cannot be avoided. The discrete wavelet transform of an image provides a set of wavelet coefficients which represent the image at multiple scales [5]. The wavelet representation can be seen as a multilevel pyramid tree-structure with the coarsest scale coefficients at the top and the finest scale coefficients at the bottom of the pyramid. Typically, coefficients at different levels of the pyramid are assumed independent and they are quantized according to the signal statistics of the corresponding pyramid level. As an extension zerotree wavelet coding schemes exploit the correlation between different pyramid levels by setting entire insignificant subtrees to zero, so their coefficients do not have to be transmitted [6]. At low bitrates a coarse quantization sets many high frequency coefficients to zero, so that sharp edges cannot be represented well and are distorted by ringing artifacts. In order to combine the advantages of wavelet and fractal coding, we propose a coding scheme that uses a hybrid approximation of "video cubes" in the 3-D-wavelet domain. The combination of a 3-D-fractal approximation and a direct encoding of the 3-D-wavelet coefficients allows to exploit inter and intra redundancy of the video cubes. The usage of smooth wavelet basis functions leads to sharper edges without blocking artifacts even at very low bitrates.