Wavelet-based solution to anisotropic diffusion equation for edge detection
✍ Scribed by Fred L. Fontaine; Sankar Basu
- Publisher
- John Wiley and Sons
- Year
- 1998
- Tongue
- English
- Weight
- 358 KB
- Volume
- 9
- Category
- Article
- ISSN
- 0899-9457
No coin nor oath required. For personal study only.
✦ Synopsis
We consider the problem of detection of edges in an the initial condition u(x, y, 0) and the variance of the smoothing image by solving an anisotropic diffusion equation, which has the Gaussian plays the role of the time variable t. The difficulties intrinsic property that low-contrast regions are smoothed and highassociated with discerning true edges from large local oscillations contrast ones are enhanced. Since wavelets are known to provide in intensity of the image arising from, for example, texture or better representation of singularities (i.e., edges), a more efficient statistically white noise were approached in the seminal paper scheme than those suggested earlier for solving the diffusion equation by Perona and Malik [1] in which essentially the conduction is formulated in terms of wavelet expansions of the image. These coefficient c is made space varying as in Equation (1). The expansions also provide a natural way of estimating the local contrast, strategy is to choose strong forward diffusion in regions of low and hence of implementing a space-varying parameterization of the contrast measured by low values of values of intensity gradient, diffusion equation for improved performance. Our method can be viewed as a wavelet counterpart of standard spectral methods for and to choose weak or even backward diffusion in regions of solving partial differential equations.