zbMATH — the first resource for mathematics

Examples
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.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
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)
A numerical method for preserving curve edges in nonlinear anisotropic smoothing. (English) Zbl 1213.76040
Summary: We focus on nonlinearity for images and propose a new method which can preserve curve edges in image smoothing using nonlinear anisotropic diffusion (NAD). Unlike existing methods which diffuse only among the spatial variants, the new method suggests that the diffusion should be performed both among the time variants and spatial variants, named time and space nonlinear anisotropic diffusion (TSNAD). That is, not only the differences of the spatial variants should be estimated by the nearby spatial points but also the differences of the time variants should be approximated by the weighted time differences of nearby points, according to the differences of gray levels between them and the consideration point. Since the time differences of nearby points using NAD can find more points with similar gray levels which form a curve belt for the center pixel on a curve edge, TSNAD can provide satisfied smoothing results while preserving curve edges. The experiments for digital images also show us the ability of TSNAD to preserve curve edges.
MSC:
76B15Water waves, gravity waves; dispersion and scattering, nonlinear interaction
74F10Fluid-solid interactions
74J15Surface waves (solid mechanics)