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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:On Implicit Image Differentiation and Filtering -
Belyaev\, A (Heriot-Watt University)
DTSTART;TZID=Europe/London:20140213T114500
DTEND;TZID=Europe/London:20140213T123000
UID:TALK50851AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/50851
DESCRIPTION:The main goal of this talk is to demonstrate advan
tages of using compact (implicit) finite differenc
ing\, filtering\, and interpolating schemes for im
age processing applications. \n\nFinite difference
schemes can be categorized as "explicit" and "imp
licit." Explicit schemes express the nodal derivat
ives as a weighted sum of the function nodal value
s. For example\, f'i=(fi+1-fi-1)/2h is an explicit
finite difference approximation of the first-orde
r derivative. By comparison\, compact (implicit) f
inite difference schemes equate a weighted sum of
nodal derivatives to a weighted sum of the functio
n nodal values. For instance\, f'i-1+4f'i+f'i+1=3(
fi+1-fi-1)/2h is an implicit (compact) scheme. Som
e implicit schemes correspond to Pad{'e} approxima
tions and produce significantly more accurate appr
oximations for the small scales to compare with ex
plicit schemes having the same stencil widths. Som
e other implicit schemes are designed to deliver a
ccurate approximations of function derivatives ove
r a wide range of spatial scales. Compact (implici
t) finite difference schemes\, as well as implicit
filtering and interpolating schemes\, constitute
advanced but standard tools for accurate numerical
simulations of problems involving linear and nonl
inear wave propagation phenomena. \n\nIn this talk
\, I show how Fourier-Pad{'e}-Galerkin approximati
ons can be adapted for designing high-quality impl
icit finite difference schemes\, establish a link
between implicit schemes and standard explicit fin
ite differences used for image gradient estimation
\, and demonstrate usefulness of implicit differen
cing and filtering schemes for various image proce
ssing tasks including image deblurring\, feature d
etection\, and sharpening. \n\nSome of the results
to be presented in this talk can be found in my r
ecent paper: A. Belyaev\, "Implicit image differen
tiation and filtering with applications to image s
harpening." {m SIAM Journal on Imaging Sciences}\
, 6(1):660-679\, 2013. \n\nRelated Links: http://e
pubs.siam.org/doi/abs/10.1137/12087092X - link to
the paper mentioned in the abstract\n
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:Mustapha Amrani
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