Abstract
Banach Constructor and Image Compression. The Banach constructor is defined as a concept unifying special cases of deterministic fractal modeling. The fractal compression of digital images is presented as a Banach constructor defined by a patchwork. The patchwork concept is a formal mathematical model which allowed for: a compact definition of the fractal operator, specification of a condition for its contractivity (for all v norms, 1 ≤ v ≤ ∞), and formulating conditions ensuring the required fidelity of the reconstructed image. Fast fractal compression algorithm (FFC) is based on patchworks which are affine (with contrast and scaling fixed), sparse, and local. Formulas for the best fit, affine, contrast fixed transforms which perform the best fit of two digital patches, are given for v norms with v = 1, v = 2, and v = ∞. Experiments confirm superiority of quadratic norm at quality-time tradeoff.
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© 1996 Springer-Verlag Wien
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Skarbek, W. (1996). Banach Constructor and Image Compression. In: Kropatsch, W., Klette, R., Solina, F., Albrecht, R. (eds) Theoretical Foundations of Computer Vision. Computing Supplement, vol 11. Springer, Vienna. https://doi.org/10.1007/978-3-7091-6586-7_10
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DOI: https://doi.org/10.1007/978-3-7091-6586-7_10
Publisher Name: Springer, Vienna
Print ISBN: 978-3-211-82730-7
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