6 November 1998 Making copies or originals of nature: a feature-based compressed fractal encoding of natural objects and its evaluation
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Abstract
It is shown by evaluation against the standard fractal encoding by partitioned IFS that global IFS are suited best because which are often self similar even not always exactly. Global iterated function system (IFS) represent an object by the union of affine contractive transformed copies of the object itself. The objects are decomposed into a minimal set of copies by calculating their touching points (TP) - which have no neighborhood that can be affinely and expansively be mapped to a neighborhood of any other TP - on the object boundary. This boundary is computed by a fractal hull. An affine invariant representation of feature points are mapped to those of the sub objects to calculate their affine transformations. This technique can be generalized to encode assemblies of arbitrary colored objects, using extensions of the IFS-Theory. According to Barnsley's collage theorem not exactly affine self similar objects can be also encoded. Even for worse approximations by an IFS, compression ratios in the range of the standard encoding methods can be reached. For good approximations the compression is even far better.
© (1998) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.
Erwin Hocevar, Walter G. Kropatsch, "Making copies or originals of nature: a feature-based compressed fractal encoding of natural objects and its evaluation", Proc. SPIE 3456, Mathematics of Data/Image Coding, Compression, and Encryption, (6 November 1998); doi: 10.1117/12.330358; https://doi.org/10.1117/12.330358
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