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SUMMARY:On Implicit Image Differentiation and Filtering - Belyaev\, A (Her
 iot-Watt University)
DTSTART:20140213T114500Z
DTEND:20140213T123000Z
UID:TALK50851@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:The main goal of this talk is to demonstrate advantages of usi
 ng compact (implicit) finite differencing\, filtering\, and interpolating 
 schemes for image processing applications. \n\nFinite difference schemes c
 an be categorized as "explicit" and "implicit." Explicit schemes express t
 he nodal derivatives as a weighted sum of the function nodal values. For e
 xample\, f'i=(fi+1-fi-1)/2h is an explicit finite difference approximation
  of the first-order derivative. By comparison\, compact (implicit) finite 
 difference schemes equate a weighted sum of nodal derivatives to a weighte
 d sum of the function nodal values. For instance\, f'i-1+4f'i+f'i+1=3(fi+1
 -fi-1)/2h is an implicit (compact) scheme. Some implicit schemes correspon
 d to Pad{'e} approximations and produce significantly more accurate approx
 imations for the small scales to compare with explicit schemes having the 
 same stencil widths. Some other implicit schemes are designed to deliver a
 ccurate approximations of function derivatives over a wide range of spatia
 l scales. Compact (implicit) finite difference schemes\, as well as implic
 it filtering and interpolating schemes\, constitute advanced but standard 
 tools for accurate numerical simulations of problems involving linear and 
 nonlinear wave propagation phenomena. \n\nIn this talk\, I show how Fourie
 r-Pad{'e}-Galerkin approximations can be adapted for designing high-qualit
 y implicit finite difference schemes\, establish a link between implicit s
 chemes and standard explicit finite differences used for image gradient es
 timation\, and demonstrate usefulness of implicit differencing and filteri
 ng schemes for various image processing tasks including image deblurring\,
  feature detection\, and sharpening. \n\nSome of the results to be present
 ed in this talk can be found in my recent paper: A. Belyaev\, "Implicit im
 age differentiation and filtering with applications to image sharpening." 
 {m SIAM Journal on Imaging Sciences}\, 6(1):660-679\, 2013. \n\nRelated L
 inks: http://epubs.siam.org/doi/abs/10.1137/12087092X - link to the paper 
 mentioned in the abstract\n
LOCATION:Seminar Room 1\, Newton Institute
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