On finite difference schemes for curvature motions

M. Mondelli, A. Ciomaga, in:, Proceedings of the International Student Conference on Pure and Applied Mathematics, Editura Universitãtii „Alexandru Ioan Cuza” Iasi, 2011, pp. 137–156.

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Conference Paper | Published | English
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Abstract
In the present paper we give a thorough analysis of two finite difference schemes for the Mean Curvature Motion and its affine variant, the Affine Morphological Scale Space, schemes introduced in the Image Processing framework. This analysis brings in a series of parameters that allow us to compute an accurate discrete evolution of curvature motions. The choice of these parameters is based on intrinsic geometric properties of the evolution equations for linear, radial and elliptical functions. In the last part we present several examples, underlining the main advantages of the algorithms (the removal of pixelization effects and JPEG artifacts) as well as their major drawbacks (absence of contrast invariance and grid dependence). A detailed explanatory report, the ANSI C implementations and an on-line demo can be found at http://www.ipol.im/.
Publishing Year
Date Published
2011-01-01
Proceedings Title
Proceedings of the International Student Conference on Pure and Applied Mathematics
Page
137-156
Conference
ISCOPAM: International Student Conference on Pure and Applied Mathematics
Conference Location
Iasi, Romania
Conference Date
2010-07-12 – 2010-07-16
IST-REx-ID

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Mondelli M, Ciomaga A. On finite difference schemes for curvature motions. In: Proceedings of the International Student Conference on Pure and Applied Mathematics. Editura Universitãtii „Alexandru Ioan Cuza” Iasi; 2011:137-156. doi:10.13140/2.1.1862.4646
Mondelli, M., & Ciomaga, A. (2011). On finite difference schemes for curvature motions. In Proceedings of the International Student Conference on Pure and Applied Mathematics (pp. 137–156). Iasi, Romania: Editura Universitãtii „Alexandru Ioan Cuza” Iasi. https://doi.org/10.13140/2.1.1862.4646
Mondelli, Marco, and Adina Ciomaga. “On Finite Difference Schemes for Curvature Motions.” In Proceedings of the International Student Conference on Pure and Applied Mathematics, 137–56. Editura Universitãtii „Alexandru Ioan Cuza” Iasi, 2011. https://doi.org/10.13140/2.1.1862.4646.
M. Mondelli and A. Ciomaga, “On finite difference schemes for curvature motions,” in Proceedings of the International Student Conference on Pure and Applied Mathematics, Iasi, Romania, 2011, pp. 137–156.
Mondelli M, Ciomaga A. 2011. On finite difference schemes for curvature motions. Proceedings of the International Student Conference on Pure and Applied Mathematics. ISCOPAM: International Student Conference on Pure and Applied Mathematics 137–156.
Mondelli, Marco, and Adina Ciomaga. “On Finite Difference Schemes for Curvature Motions.” Proceedings of the International Student Conference on Pure and Applied Mathematics, Editura Universitãtii „Alexandru Ioan Cuza” Iasi, 2011, pp. 137–56, doi:10.13140/2.1.1862.4646.

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