Application Of Recurrent Iterated Function Systems To Images

Michael F. Barnsley; Arnaud E. Jacquin

doi:10.1117/12.968945

25 October 1988 Application Of Recurrent Iterated Function Systems To Images

Michael F. Barnsley, Arnaud E. Jacquin

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

Abstract

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.

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Michael F. Barnsley and 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); https://doi.org/10.1117/12.968945

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