J. Weickert, S. Ishikawa, A. Imiya,
On the history of Gaussian scale-space axiomatics,
J. Sporring, M. Nielsen, L. Florack, P. Johansen (Eds.),
Gaussian scale-space theory, Kluwer, Dordrecht, 45-59, 1997.
Gaussian scale-space is considered to be a modern bottom-up tool in
computer vision, and in the last decade many efforts have been spent
to derive it from first principles (axioms).
The vision community, however, seems unaware of the fact that the
axiomatic derivation of Gaussian scale-space is much older:
In 1962 Taizo Iijima proves in a paper written in Japanese that
the one-dimensional Gaussian scale-space can be derived from
five axioms: linearity, translation invariance, scale invariance,
semigroup property and preservation of positivity.
A two-dimensional axiomatic of Gaussian scale-space has been
described by Nobuyuki Otsu in 1981. We review the main ideas in
these papers and juxtapose them to ten other Gaussian scale-space
axiomatics.
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