Characterization and representation of the lower semicontinuous envelope of the elastica functional
Bellettini, G. ; Mugnai, L.
Annales de l'I.H.P. Analyse non linéaire, Tome 21 (2004), p. 839-880 / Harvested from Numdam
@article{AIHPC_2004__21_6_839_0,
     author = {Bellettini, Giovanni and Mugnai, L.},
     title = {Characterization and representation of the lower semicontinuous envelope of the elastica functional},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     volume = {21},
     year = {2004},
     pages = {839-880},
     doi = {10.1016/j.anihpc.2004.01.001},
     mrnumber = {2097034},
     zbl = {1110.49014},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPC_2004__21_6_839_0}
}
Bellettini, G.; Mugnai, L. Characterization and representation of the lower semicontinuous envelope of the elastica functional. Annales de l'I.H.P. Analyse non linéaire, Tome 21 (2004) pp. 839-880. doi : 10.1016/j.anihpc.2004.01.001. http://gdmltest.u-ga.fr/item/AIHPC_2004__21_6_839_0/

[1] Ambrosio L., Fusco N., Pallara D., Functions of Bounded Variation and Free Discontinuity Problems, Oxford Science Publication, 2000. | MR 1857292 | Zbl 0957.49001

[2] Ambrosio L., Mantegazza C., Curvature and distance function from a manifold, J. Geom. Anal 5 (1998) 723-748. | MR 1731060 | Zbl 0941.53009

[3] L. Ambrosio, S. Masnou, A direct variational approach to a problem arising in image reconstruction, Interfaces and Free Boundaries, submitted for publication. | MR 1959769 | Zbl 1029.49037

[4] Bellettini G., Dal Maso G., Paolini M., Semicontinuity and relaxation properties of a curvature depending functional in 2D, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 20 (1993) 247-299. | Numdam | MR 1233638 | Zbl 0797.49013

[5] G. Bellettini, L. Mugnai, Characterization and representation of the lower semicontinuous envelope of the elastica functional, Preprint Univ. Pisa, May 2003.

[6] Bellettini G., Paolini M., Variational properties of an image segmentation functional depending on contours curvature, Adv. Math. Sci. Appl 5 (1995) 681-715. | MR 1361011 | Zbl 0853.49014

[7] Cartan H., Theorie Elementaire des Fonctions Analytiques d'Une ou Pluiseurs Variables Complexes, Hermann, 1961. | MR 147623 | Zbl 0094.04401

[8] Coscia A., On curvature sensitive image segmentation, Nonlin. Anal 39 (2000) 711-730. | MR 1733124 | Zbl 0942.68135

[9] Dacorogna B., Direct Methods in the Calculus of Variations, Springer-Verlag, 1989. | MR 990890 | Zbl 0703.49001

[10] Delladio S., Special generalized gauss graphs and their application to minimization of functionals involving curvatures, J. Reine Angew. Math 486 (1997) 17-43. | MR 1450749 | Zbl 0871.49034

[11] Euler L., Additamentum I de curvis elasticis, methodus inveniendi lineas curvas maximi minimive proprietate gaudentes, Opera Omnia I (24) (1744) 231-297.

[12] Federer H., Geometric Measure Theory, Springer-Verlag, 1969. | MR 257325 | Zbl 0874.49001

[13] Giaquinta M., Hildebrandt S., Calculus of Variations I, in: Grundleheren der Mathematischen Wissenschaften, vol. 310, Springer-Verlag, 1996. | MR 1368401 | Zbl 0853.49002

[14] De Giorgi E., Some remarks on Γ-convergence and least squares method, in: Proc. Composite Media and Homogeneization Theory, Trieste, 1991, pp. 135-142. | Zbl 0747.49008

[15] Gonzales O., Maddocks J.H., Schuricht F., Von Der Mosel H., Global curvature and self-contact of nonlinearly elastic curves and rods, Calc. Var. Partial Differential Equations 14 (2002) 29-68. | MR 1883599 | Zbl 1006.49001

[16] Hutchinson J.E., C1,α-multiple functions regularity and tangent cone behaviour for varifolds with second fundamental form in Lp, Proc. Symp. Pure Math 44 (1986) 281-306. | Zbl 0635.49020

[17] Love A.E.H., A Treatise on the Mathematical Theory of Elasticity, Dover, 1944. | MR 10851 | Zbl 0063.03651

[18] Masnou S., Disocclusion: a variational approach using level lines, IEEE Trans. Image Process 11 (2002) 68-76. | MR 1888912

[19] Masnou S., Morel J.M., Level lines based disocclusion, in: Proc. ICIP'98 IEEE Internat. Conf. on Image Processing, 1998, pp. 259-263.

[20] Morel J.M., Solimini S., Variational Methods in Image Segmentation, Progress in Nonlinear Differential Equations and Their Applications, vol. 14, Birkhäuser, 1995. | MR 1321598 | Zbl 0827.68111

[21] Mumford D., Elastica and computer vision, in: Algebraic Geometry and its Applications, 1994, pp. 491-506. | MR 1272050 | Zbl 0798.53003

[22] Mumford D., Nitzberg M., Shiota T., Filtering, Segmentation and Depth, in: Lecture Notes in Computer Science, vol. 662, Springer-Verlag, 1993. | MR 1226232 | Zbl 0801.68171

[23] Nitzberg M., Mumford D., The 2.1-D sketch, in: Proc. of the Third Internat. Conf. on Computer Vision, Osaka, 1990.

[24] Simon L., Existence of surfaces minimizing the Willmore functional, Comm. Anal. Geom 2 (1993) 281-326. | MR 1243525 | Zbl 0848.58012

[25] Willmore T.J., An introduction to Riemannian Geometry, Clarendon Press, 1993. | MR 1261641 | Zbl 0797.53002