Summary
This paper proposes a procedure for representing image functions by a computation in two layers. It is recalled that the general function representation needs more layers than two, using the Stone-Weierstrass theorem for approximation in three layers, and the Kolmogorov theorem for representation in four layers. For achieving representation in two layers only, the requirement on a continuous representation has to removed. The Sprecher construction presented here is a general procedure for yielding such a representation in two layers. It can be used to compress images, to represent pixels and their neighborhoods directly, or to represent image operators.
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Köppen, M., Yoshida, K. (2005). Universal Representation of Image Functions by the Sprecher Construction. In: Abraham, A., Dote, Y., Furuhashi, T., Köppen, M., Ohuchi, A., Ohsawa, Y. (eds) Soft Computing as Transdisciplinary Science and Technology. Advances in Soft Computing, vol 29. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-32391-0_28
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DOI: https://doi.org/10.1007/3-540-32391-0_28
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-25055-5
Online ISBN: 978-3-540-32391-4
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