25 October 1988 Application Of Recurrent Iterated Function Systems To Images
Author Affiliations +
Proceedings Volume 1001, Visual Communications and Image Processing '88: Third in a Series; (1988) https://doi.org/10.1117/12.968945
Event: Visual Communications and Image Processing III, 1988, Cambridge, MA, United States
A new fractal technique for the analysis and compression of digital images is presented. It is shown that a family of contours extracted from an image can be modelled geometrically as a single entity, based on the theory of recurrent iterated function systems (RIFS). RIFS structures are a rich source for deterministic images, including curves which cannot be generated by standard techniques. Control and stability properties are investigated. We state a control theorem - the recurrent collage theorem - and show how to use it to constrain a recurrent IFS structure so that its attractor is close to a given family of contours. This closeness is not only perceptual; it is measured by means of a min-max distance, for which shape and geometry is important but slight shifts are not. It is therefore the right distance to use for geometric modeling. We show how a very intricate geometric structure, at all scales, is inherently encoded in a few parameters that describe entirely the recurrent structures. Very high data compression ratios can be obtained. The decoding phase is achieved through a simple and fast reconstruction algorithm. Finally, we suggest how higher dimensional structures could be designed to model a wide range of digital textures, thus leading our research towards a complete image compression system that will take its input from some low-level image segmenter.
© (1988) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.
Michael F. Barnsley, Arnaud E. Jacquin, "Application Of Recurrent Iterated Function Systems To Images", Proc. SPIE 1001, Visual Communications and Image Processing '88: Third in a Series, (25 October 1988); doi: 10.1117/12.968945; https://doi.org/10.1117/12.968945


Back to Top