Jin Li, Principal Researcher & Manager
Compression Communication and Storage
Microsoft Research
Email: jinl@microsoft.com

Wavelet Fractal Compression

Fig. 1. The contractive mapping operation in fractal compression can be carried out via an equivalent fashion in the wavelet domain, by predicting coefficients of the higher resolution from those of the lower resolution (with possible linear scaling and rotation operators).

Fractal compression receives great attension in 1990s. Rather than directly encoding the image content, fractal compression uses the contractive mapping to represent an image.

This work shows that the fractal contractive mapping could be considered as a prediction operation in the wavelet domain. That is, the contractive mapping in the fractal compression operation can be equivalent considered as predicting coefficients of the higher resolution from those of the lower resolution. It establishes the link between fractal compression and wavelet.

  1. Jin Li and C.-C. J. Kuo, "Image Compression with a Hybrid Wavelet-Fractal Coder", IEEE Trans. on Image Processing, Vol. 8, No. 6, Jun. 1999.