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Feature-oriented image enhancement using shock filters. (English) Zbl 0714.65096
Author’s summary: The paper deals with a development of shock filters for image enhancement. The filters use new nonlinear time dependent partial differential equations and their discretizations. The evolution of the initial image $$u_ 0(x,y)$$ as $$t\to \infty$$ into a steady state solution $$u_{\infty}(x,y)$$ through u(x,y,t), $$t>0$$, is the filtering process. The partial differential equations have solutions which satisfy a maximum principle. Moreover the total variation of the solution for any fixed $$t>0$$ is the same as that of the initial data. The processed image is piecewise smooth, nonoscillatory, and the jumps occur across zeros of an elliptic operator (edge detector). The algorithm is relatively fast and easy to program.
Reviewer: I.Dvořák

MSC:
 65Z05 Applications to the sciences 65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs 65R20 Numerical methods for integral equations 68U10 Computing methodologies for image processing 65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs 45E10 Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf type) 35K55 Nonlinear parabolic equations
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