zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
The structure of images. (English) Zbl 0537.92011
In this paper it is shown that any image can be embedded in a one- parameter family of derived images (with resolution as the parameter) in essentially only one unique way if the constraint that no spurious detail should be generated when the resolution is diminished, is applied. The structure of this family is governed by the well known diffusion equation. As such the structure fits into existing theories that treat the front end of the visual system as a continuous stack of homogeneous layers, characterized by iterated local processing schemes.

92CxxPhysiological, cellular and medical topics
91E30Psychophysics and psychophysiology; perception
Full Text: DOI
[1] Burt, P.J., Hong, Tsai-Hong, Rosenfeld, A.: Segmentation and estimation of image region properties through cooperative hierarchical computation. IEEE Trans. SMC-11, 802--825 (1981)
[2] Cayley, A.: On contour and slope lines. The London, Edinburgh, and Dublin Philosophical Magazine and J. of Science 18 (120), 264--268 (Oct. 1859)
[3] Maxwell, J.C.: On hills and dales. The London, Edinburgh, and Dublin Philosophical Magazine and J. of Science 4th Series 40 (269), 421--425 (Dec. 1870)
[4] Ehrich, R.W., Foith, J.P.: Representation of random waveforms by relational trees. IEEE Trans. Comput. 25, 725--736 (1976) · Zbl 0334.68057 · doi:10.1109/TC.1976.1674681
[5] Guillemin, V., Pollack, A.: Differential topology. Englewood Cliffs, NJ: Prentice-Hall 1974 · Zbl 0361.57001
[6] Hay, G.A., Chesters, M.S.: A model of visual threshold detection. J. Theor. Biol. 67, 221--240 (1977) · doi:10.1016/0022-5193(77)90196-5
[7] Koenderink, J.J., Doorn, A.J. van: The structure of two-dimensional scalar fields with applications to vision. Biol. Cybern. 33, 151--158 (1979) · Zbl 0406.92006 · doi:10.1007/BF00337293
[8] Koenderink, J.J., Doorn, A.J. van: Visual detection of spatial contrast: influence of location in the visual field, target extent and illuminance level. Biol. Cybern. 30, 157--167 (1978) · doi:10.1007/BF00337144
[9] Koenderink, J.J., Doorn, A.J. van: Invariant features of contrast detection: an explanation in terms of self-similar detector arrays. J. Opt. Soc. Am. 72, 83--87 (1982) · doi:10.1364/JOSA.72.000083
[10] Marko, H.: Die Systemtheorie homogener Schichten. Kybernetik 5, 221 (1969) · Zbl 0181.16201 · doi:10.1007/BF00274977
[11] Marr, D., Poggio, T., Ullman, S.: Bandpass channels, zero-crossings, and early visual information processing. J. Opt. Soc. Am. 69, 914--916 (1977) · doi:10.1364/JOSA.69.000914
[12] Marr, D., Hildreth, E.: Theory of edge detection. Proc. Royal Soc. Lond. B 207, 187--217 (1980) · doi:10.1098/rspb.1980.0020
[13] Roehler, R.: Ein Modell zur örtlich-zeitlichen Signalübertragung im visuellen System des Menschen auf der Basis der linearen Systemtheorie kontinuierlichen Medien. Biol. Cybern. 27, 97--105 (1976) · Zbl 0325.92004 · doi:10.1007/BF00320134
[14] Spivak, M.: A comprehensive introduction to differential geometry, Vol. III. Berkeley, CA: Publish or Perish Inc. 1975 · Zbl 0306.53001
[15] Thom, R.: Stabilité structurelle et morphogenésè. Reading, MA: Benjamin 1972
[16] Witkin, A.P.: Scale-space filtering. Proc. of IJCAI, 1019-1021, Karlsruhe 1983