Wavelet-based solution to anisotropic diffusion equation for edge detection

Abstract

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. Int J Imaging Syst Technol, 9, 356–368, 1998

On the Equivalence of Soft Wavelet Shrinkage, Total Variation Diffusion, Total Variation Regularization, and SIDEs

“…Earlier applications of wavelets in the context of PDE-based denoising have been focusing on their use as basis functions in Galerkin schemes for nonlinear diffusion filtering [32,34]. More recently a number of interesting connections between wavelet shrinkage of functions, regularization methods and PDEs has been established.…”

High performance cluster computing with 3-D nonlinear diffusion filters

“…This has triggered a number of researchers to look for alternative algorithmic realisations of nonlinear diffusion filtering and related variational approaches. These alternatives include three-level methods [8], semi-implicit approaches [4,11] and their multiplicative [36] or additive operator splitting variants [37], multigrid methods [1], finite element techniques [2,16,23], finite and complementary volume methods [11], numerical schemes with wavelets as trial functions [7,8], pseudospectral methods [8], lattice Boltzmann techniques [15], and stochastic simulations [24]. Approximations in graphics hardware have been considered in [26], and realisations on analog hardware are discussed in [9,21].…”

Wavelet based method for edge detection of defect on coated board during production proccess

“…Pored toga, u slikama sa izraženim prisustvom šuma dolazi do pojave lažnih ivica [51], a javlja se i problem nestabilnog rešenja inverzne difuzije, što se u slici može uočiti kao stepenasti efekat [24], [26], [49] i [52]. Tada se dovodi u pitanje i jedinstvenost rešenja jednačine (3.31), jer veoma slične polazne slike mogu dati drastično različite rezultate nakon primene predloženog algoritma [51].…”

“…Tada se dovodi u pitanje i jedinstvenost rešenja jednačine (3.31), jer veoma slične polazne slike mogu dati drastično različite rezultate nakon primene predloženog algoritma [51]. Znatan broj autora se bavio problemom nestabilnosti rešenja anizotropne nelinearne difuzije [49], a postoje i pokušaji da se problem reši korišćenjem wavelet transformacije u cilju rešavanja nelinearne anizotropne difuzione jednačine [51], [53] i [54].…”

“…Znatan broj autora se bavio problemom nestabilnosti rešenja anizotropne nelinearne difuzije [49], a postoje i pokušaji da se problem reši korišćenjem wavelet transformacije u cilju rešavanja nelinearne anizotropne difuzione jednačine [51], [53] i [54]. Autori rada [51] su dali predlog za otklanjanje negativne osobine Perona i Malik algoritma.…”