Enclosed Laplacian Operator of Nonlinear Anisotropic Diffusion to preserve singularities and delete isolated points in image smoothing.
Liao, Zhiwu, Hu, Shaoxiang, Sun, Dan, Chen, Wufan (2011)
Mathematical Problems in Engineering
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Liao, Zhiwu, Hu, Shaoxiang, Sun, Dan, Chen, Wufan (2011)
Mathematical Problems in Engineering
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Weickert, J. (2001)
Acta Mathematica Universitatis Comenianae. New Series
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Prasath, V.B.Surya, Singh, Arindama (2010)
Journal of Applied Mathematics
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V.B. Surya Prasath (2011)
International Journal of Applied Mathematics and Computer Science
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We propose an edge adaptive digital image denoising and restoration scheme based on space dependent regularization. Traditional gradient based schemes use an edge map computed from gradients alone to drive the regularization. This may lead to the oversmoothing of the input image, and noise along edges can be amplified. To avoid these drawbacks, we make use of a multiscale descriptor given by a contextual edge detector obtained from local variances. Using a smooth transition from the...
Diewald, U., Preusser, T., Rumpf, M., Strzodka, R. (2001)
Acta Mathematica Universitatis Comenianae. New Series
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Radomír Chabiniok, Radek Máca, Michal Beneš, Jaroslav Tintěra (2013)
Kybernetika
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The article focuses on the application of the segmentation algorithm based on the numerical solution of the Allen-Cahn non-linear diffusion partial differential equation. This equation is related to the motion of curves by mean curvature. It exhibits several suitable mathematical properties including stable solution profile. This allows the user to follow accurately the position of the segmentation curve by bringing it quickly to the vicinity of the segmented object and by approaching...
de Oliveira Casaca, Wallace Correa, Boaventura, Maurílio (2010)
Mathematical Problems in Engineering
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Pavel Bochev, Kara Peterson (2013)
Open Mathematics
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We formulate and study numerically a new, parameter-free stabilized finite element method for advection-diffusion problems. Using properties of compatible finite element spaces we establish connection between nodal diffusive fluxes and one-dimensional diffusion equations on the edges of the mesh. To define the stabilized method we extend this relationship to the advection-diffusion case by solving simplified one-dimensional versions of the governing equations on the edges. Then we use...
Pavel Strachota (2009)
Kybernetika
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Magnetic Resonance Diffusion Tensor Imaging (MR–DTI) is a noninvasive in vivo method capable of examining the structure of human brain, providing information about the position and orientation of the neural tracts. After a short introduction to the principles of MR–DTI, this paper describes the steps of the proposed neural tract visualization technique based on the DTI data. The cornerstone of the algorithm is a texture diffusion procedure modeled mathematically by the problem for the...