Self-similar intermediate asymptotics for nonlinear degenerate parabolic free-boundary problems that occur in image processing

Proceedings of the National Academy of Sciences of the United States of America
G I Barenblatt

Abstract

In the boundary layers around the edges of images, basic nonlinear parabolic equations for image intensity used in image processing assume a special degenerate asymptotic form. An asymptotic self-similar solution to this degenerate equation is obtained in an explicit form. The solution reveals a substantially nonlinear effect-the formation of sharp steps at the edges of the images, leading to edge enhancement. Positions of the steps and the time shift parameter cannot be determined by direct construction of a self-similar solution; they depend on the initial condition of the pre-self-similar solution. The free-boundary problem is formulated describing the image intensity evolution in the boundary layer.

References

Feb 16, 2008·IEEE Transactions on Image Processing : a Publication of the IEEE Signal Processing Society·A R Yezzi

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Citations

Mar 20, 2001·Journal of Biosciences·A B MedvinskyH Malchow
Mar 30, 2005·IEEE Transactions on Visualization and Computer Graphics·Thomas DeschampsIgor Ravve

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