R-refinement in image-processing via the PDE-approach
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(Digital) Signal Processing plays a huge role in computer vision. We will use two related Partial Differential Equations (PDEs), known for their smoothing feature, to investigate the removal of noise in (digital) signals, namely: the Heat and Perona- Malik equation. This report explains how we can do (digital) signal processing on a bounded domain $_ Rn (n = 1; 2)$, via a PDE approach. Depending on the type of noise present in the signal, the PDE approach gives desirable results. For faster iteration with the Perona-Malik equation we first need an (un)conditionally stable finite difference method or use a non uniform grid with $R$-refinement (adaptive grids) for a possibly better edge detection.