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A nonlocal mean curvature flow for multi-dimensional image processing

Published online by Cambridge University Press:  23 March 2005

DAISUKE HIRATA
DAISUKE HIRATA
Affiliation:
Department of Mathematics, Faculty of Science and Technology, Tokyo University of Science, Noda, Chiba, 278-8510, Japan email: [email protected]
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Abstract

In this paper, we propose a mean curvature flow equation with nonlocal nonlinearities for an image processing model on noisy surfaces, which corresponds to the negative $L^2$-gradient flow of surface energy functional in (1.4). We investigate the initial value problem mathematically. Furthermore, numerical simulations are shown, which exhibit that the model performs smoothing operation on a complicated level surface of a given image data while preserving its geometric shape feature under suitable parameters chosen.

Type
Papers
Information
European Journal of Applied Mathematics , Volume 16 , Issue 1 , February 2005 , pp. 21 - 36
Copyright
2005 Cambridge University Press

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