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Image segmentation, level set, regularised Riemannian mean curvature flow equation, finite volume method, approximation of the nonlinear smoothing term

References:

[1] Eymard, R., Handlovičová, A., Mikula, K.: **Study of a finite volume scheme for regularised mean curvature flow level set equation**. IMA J. on Numerical Analysis, Vol. 31, 813-846, 2011. DOI 10.1093/imanum/drq025 | MR 2832781

[2] Osher, S., A., J. Sethian: **Fronts propagating with curvature-dependent speed: Algorithms basedon Hamilton-Jacobi formulations**. J. Comput. Phys., 79(1):12-49, 1988. MR 0965860

[3] Mikula, K., Sarti, A., Sgallarri, A.: **Co-volume method for Riemannian mean curvature flow in subjective surfaces multiscale segmentation**. Computing and Visualization in Science, Vol. 9, No. 1, 23-31, 2006. DOI 10.1007/s00791-006-0014-0 | MR 2214835

[4] Mikula, K., Sarti, A., Sgallari, F.: **Co-volume level set method in subjective surface based medicalimage segmentation**. in: Handbook of Medical Image Analysis: Segmentation and Registration Models (J.Suri et al., Eds.), Springer, New York, 583-626, 2005.

[5] Handlovičová, A., Tibenský, M.: **Convergence of the numerical scheme for regularised Riemannian mean curvature flow equation**. submitted to Tatra Mountains Mathematical Publications, 2017. MR 3939443

[6] Mikula, K., Ramarosy, N.: **Semi-implicit finite volume scheme for solving nonlinear diffusion equations in image processing**. Numerische Mathematik 89, No. 3, 561-590, 2001. DOI 10.1007/PL00005479 | MR 1864431

[7] Tibenský, M.: **Využitie metód založených na level set rovnici v spracovaní obrazu**. Faculty of Mathematics, Physics and Informatics, Comenius University, 2016.

[8] Droniou, J., Nataraj, N.: **Improved $L^2$ estimate for gradient schemes, and super-convergence of the TPFA finite volume scheme**. IMA Journal of Numerical Analysis 2017, 2016. MR 3829161