New diffusion models in image processing

Anisotropic diffusion in image processing

The cover image shows a thresholded nonwoven fabric image which was processed by applying a coherence-enhancing anisotropic diffusion filter (see Section 5.2 for more details). The goal was to visualize the quality relevant adjacent fibre structures , so-called stripes. The displayed equations describe the basic structure of nonlinear diffusion filtering in the continuous, semidiscrete, and ful...

Diffusion and Fractional Diffusion Based Image Processing

We consider the background to describing strong scattering in terms of diffusive processes based on the diffusion equation. Intermediate strength scattering is then considered in terms of a fractional diffusion equation which is studied using results from fractional calculus. This approach is justified in terms of the generalization of a random walk model with no statistical bias in the phase t...

A New Nonlocal Nonlinear Diffusion of Image Processing

A novel nonlocal nonlinear diffusion is analyzed which has proven useful as a denoising tool in image processing. The equation can be viewed as a new paradigm for the regularization of the well-known Perona-Malik equation. The regularization is implemented via nonlinearity intensity reduction through fractional derivatives. Well-posedness in the weak setting is established. Global existence and...

Mathematical models in image processing

Image processing is a particularization of signal processing of which Electrical Engineering is, maybe, the major contributor. Image processing is completely pervaded by more or less complex mathematical tools aimed at solving problems related to image reconstruction and restoration, boundary extraction, shape modeling, segmentation, registration, etc. For performing these tasks, mathematical t...

Anisotropic Geometric Diffusion in Image and Image-Sequence Processing