Wavelet-based solution to anisotropie diffusion equation for edge detection

We consider the problem of detection of edges in an image by solving an anisotropic diffusion equation, which has the intrinsic property that low-contrast regions are smoothed and high-contrast ones are enhanced. 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 parameterization of the diffusion equation for improved performance. Our method can be viewed as a wavelet counterpart of standard spectral methods for solving partial differential equations. ©1998 John Wiley & Sons, Inc.