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Feature-Oriented Image Enhancement Using Shock Filters

Stanley Osher and Leonid I. Rudin
SIAM Journal on Numerical Analysis
Vol. 27, No. 4 (Aug., 1990), pp. 919-940
Stable URL: http://www.jstor.org/stable/2157689
Page Count: 22
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Feature-Oriented Image Enhancement Using Shock Filters
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Abstract

Shock filters for image enhancement are developed. The filters use new nonlinear time dependent partial differential equations and their discretizations. The evolution of the initial image u0(x, y) as t → ∞ into a steady state solution u∞(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.

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