Multiresolution approach to solving diffusion equation for edge detection

Considers the problem of edge detection by solving an anisotropic diffusion equation, which has the intrinsic property that low-contrast regions are smoothed and high-contrast regions are sharpened. Since wavelets are known to provide better representation of singularities (i.e., edges), a more efficient scheme than those suggested earlier for solving the diffusion equation is formulated in terms of wavelet expansions of the image. These expansions also provide a natural way of estimating the local contrast and hence of implementing a space-varying parametrization of the diffusion equation for improved performance. The method described can be viewed as the wavelet counterpart of the standard spectral method for solving partial differential equations