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Finite element approximation of a forward and backward anisotropic diffusion model in image denoising and form generalization
Author(s) -
Ebmeyer Carsten,
Vogelgesang Jens
Publication year - 2008
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.20284
Subject(s) - mathematics , piecewise , finite element method , mathematical analysis , generalization , anisotropic diffusion , partial differential equation , backward euler method , limit (mathematics) , a priori and a posteriori , euler equations , diffusion , image (mathematics) , philosophy , physics , epistemology , artificial intelligence , computer science , thermodynamics
A new forward–backward anisotropic diffusion model is introduced. The two limit cases are the Perona‐Malik equation and the Total Variation flow model. A fully discrete finite element scheme is studied using C 0 ‐piecewise linear elements in space and the backward Euler difference scheme in time. A priori estimates are proven. Numerical results in image denoising and form generalization are presented.© 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2008