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The Computer Journal 1998 41(5):319-336; doi:10.1093/comjnl/41.5.319
© 1998 by British Computer Society
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Fractal Compression and the Jigsaw Property I

S. G. Hoggar and L. Menzies

Department of Mathematics, Glasgow University, Glasgow G12 8QQ, UK Email: s.hoggar{at}maths.gla.ac.uk

We speed up the screening of a computer image compressed as an iterated function system (IFS) of affine transformations w1,...,wN. The idea is to avoid applying a given map to a given point if nothing new would be obtained.

Let w(x, y) be the result of applying transformation w to pixel coordinates (x, y) then rounding to the nearest integer pair, say (u, v). Then the w-jigsaw pieces w–1(u, v) tile the plane. We develop a foundation of results about such jigsaws based on the coefficients defining the transformations w, and apply them to a collection of 50 IFSs. Much time is indeed saved and the method is to be pursued further.

Received March 11, 1998. revised August 4, 1998.


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