On implicit image derivatives and their applications

Alexander Belyaev

doi:10.5244/C.25.72

On implicit image derivatives and their applications

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Abstract

The paper demonstrates advantages of using implicit finite differences for fast, accurate, and reliable differentiating and filtering of multidimensional signals defined on regular grids. In particular, applications to image enhancement and edge detection problems are considered. The theoretical contribution of the paper is threefold. The first adapts the Fourier-Padé-Galerkin approximations approach for constructing compact implicit finite difference schemes with desirable spectral resolution properties. The second establishes a link between implicit and explicit finite differences used for gradient direction estimation. Finally, the third one consists of introducing new implicit finite difference schemes with good spectral resolution properties.

Original language	English
Title of host publication	Proceedings of the British Machine Vision Conference
Editors	Jesse Hoey, Stephen McKenna, Emanuele Trucco
Publisher	BMVA Press
Pages	72.1-72.12
Number of pages	12
DOIs	https://doi.org/10.5244/C.25.72
Publication status	Published - Sept 2011
Event	The 22nd British Machine Vision Conference - Dundee, United Kingdom Duration: 29 Aug 2011 → 2 Sept 2011

Conference

Conference	The 22nd British Machine Vision Conference
Abbreviated title	BMVC 2011
Country/Territory	United Kingdom
City	Dundee
Period	29/08/11 → 2/09/11

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10.5244/C.25.72

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title = "On implicit image derivatives and their applications",

abstract = "The paper demonstrates advantages of using implicit finite differences for fast, accurate, and reliable differentiating and filtering of multidimensional signals defined on regular grids. In particular, applications to image enhancement and edge detection problems are considered. The theoretical contribution of the paper is threefold. The first adapts the Fourier-Pad{\'e}-Galerkin approximations approach for constructing compact implicit finite difference schemes with desirable spectral resolution properties. The second establishes a link between implicit and explicit finite differences used for gradient direction estimation. Finally, the third one consists of introducing new implicit finite difference schemes with good spectral resolution properties.",

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note = "The 22nd British Machine Vision Conference, BMVC 2011 ; Conference date: 29-08-2011 Through 02-09-2011",

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N2 - The paper demonstrates advantages of using implicit finite differences for fast, accurate, and reliable differentiating and filtering of multidimensional signals defined on regular grids. In particular, applications to image enhancement and edge detection problems are considered. The theoretical contribution of the paper is threefold. The first adapts the Fourier-Padé-Galerkin approximations approach for constructing compact implicit finite difference schemes with desirable spectral resolution properties. The second establishes a link between implicit and explicit finite differences used for gradient direction estimation. Finally, the third one consists of introducing new implicit finite difference schemes with good spectral resolution properties.

AB - The paper demonstrates advantages of using implicit finite differences for fast, accurate, and reliable differentiating and filtering of multidimensional signals defined on regular grids. In particular, applications to image enhancement and edge detection problems are considered. The theoretical contribution of the paper is threefold. The first adapts the Fourier-Padé-Galerkin approximations approach for constructing compact implicit finite difference schemes with desirable spectral resolution properties. The second establishes a link between implicit and explicit finite differences used for gradient direction estimation. Finally, the third one consists of introducing new implicit finite difference schemes with good spectral resolution properties.

U2 - 10.5244/C.25.72

DO - 10.5244/C.25.72

M3 - Conference contribution

SP - 72.1-72.12

BT - Proceedings of the British Machine Vision Conference

A2 - Hoey, Jesse

A2 - McKenna, Stephen

A2 - Trucco, Emanuele

PB - BMVA Press

T2 - The 22nd British Machine Vision Conference

Y2 - 29 August 2011 through 2 September 2011

ER -

On implicit image derivatives and their applications

Abstract

Conference

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