Image Restoration via Topological Derivative

I. LARRABIDE; R. A. FEIJÓO

Image Restoration.

InTech

Lugar: Rijeka; Año: 2012; p. 1 - 22

The problem of image restoration has deserved considerable attention in resent years. For the visual analysis of images, clarity and visibility of details are important factors, but for advanced processing, a high signal-to-noise ratio (SNR) is essential, as further processing steps (such as segmentation and classification) are sensitive to noise. Though the years, different techniques have been studied to improve the SNR or a degraded image. Techniques based on post-processing have the advantage of not affecting the acquisition process (Gonzalez & Woods (2001); Jain (1989); Weickert (1995)). More recently, the work of Tschumperle (2006) has explored the more extensive use of curve-preserving PDE’s for restoration of images. The calculation of mean intensities over neighboring pixels, equivalent to isotropic diffusion, considerably increases the SNR, but degrades the quality of image features (edges, lines and dots). This effect can be reduced with non-linear filters. The median filter has the characteristic of maintaining these features, but details are lost, degrading the image resolution. Perhaps the most popular technique introduced in the last couple of years is anisotropic diffusion, initially proposed by Perona and Malik (Black et al. (1998); Perona & Malik (1990)).