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Diffusion models and their accelerated solution in image and surface processing. (English) Zbl 0993.65109
Nonlinear anisotropic diffusion models based on partial differential equations play a significant role in the field of computer vision and image processing.
Several anisotropic diffusion methods, especially those concerning vector field visualization and surface processing are discussed. In the parametric surface processing model the diffusion tensor is defined in such a way that diffusion on the surface is significantly reduced in directions of high principle curvature, i.e., those perpendicular to an edge. Models based on the level set method for geometric image smoothing are also discussed. Discretization and implementation of the nonlinear diffusion methods is based on the finite element method with regular 2D or 3D bilinear or trilinear elements. The end of the article is devoted to using texture hardware of modern graphics cards, that plays an important role in accelerating the solution process.

MSC:
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
35K55 Nonlinear parabolic equations
65Y10 Numerical algorithms for specific classes of architectures
68U10 Computing methodologies for image processing
65D18 Numerical aspects of computer graphics, image analysis, and computational geometry
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