On a functional depending on curvature and edges

 Access to full text

 Full (PDF)

1. [1] W.K. Allard, On the first variation of a varifold, Ann. of Math., 95 (1972), pp. 417-491. Zbl0252.49028MR307015
2. [2] W.K. Allard: On the first variation of a varifold: boundary behaviour, Ann. of Math., 101 (1975), pp. 418-446. Zbl0319.49026MR397520
3. [3] F.J. Almgren JR., Approximation of rectifiable currents by Lipschitz Q valued functions, in Seminar on minimal submanifolds, E. Bombieri ed., Annals of mathematics studies, 103, Princeton University Press (1983), 243-259. MR795240
4. [4] F.J. Almgren: Deformation and multiple-valued functions, in Geometric measure theory and the calculus of variations (Arcata, Calif., 1984), W. K. Allard and F. J. Almgren eds., Proc. Sympos. Pure Math. 44 Amer. Math. Soc., Providence, R.I. (1986), 29-130. Zbl0595.49028MR840268
5. [5] F.J. Almgren - B. Super: Multiple valued functions in the geometric calculus of variations, in Variational methods for equilibrium problems of fluids (Trento, 1983), Astérisque No. 118, Société Mathématique de France (1984), 13-32. Zbl0575.49025MR761735
6. [6] L. Ambrosio, A compactness theorem for a new class of functions of bounded variation, Boll. Un. Mat. Ital.B, 3 (1989), pp. 857-881. Zbl0767.49001MR1032614
7. [7] L. Ambrosio - N. FUSCO - D. PALLARA, Partial regularity of free discontinuity sets, II, Ann. Sc. Norm. Sup. Pisa Cl. Sci., 24, no. 1 (1997), pp. 39-62. Zbl0896.49024MR1475772
8. [8] L. Ambrosio - N. Fusco - D. Pallara, Functions of bounded variation and free discontinuity problems, Oxford University Press (to appear). Zbl0957.49001MR1857292
9. [9] L. Ambrosio - M. GOBBINO - D. PALLARA, Approximation problems for curvature varifolds, The Journal of GeometricAnalysis, 8, no. 1 (1998). Zbl0932.58013MR1704565
10. [10] L. Ambrosio - V. M. TORTORELLI, Approximation of functionals depending on jumps by elliptic functionals via Γ-convergence, Comm. Pure Appl. Math., 43, no. 8 (1990), pp. 999-1036. Zbl0722.49020
11. [11] G. Bellettini - G. Dal Maso - M. Paolini, Semicontinuity and relaxation properties of a curvature depending functional in 2d, Ann. Scuola Norm. Sup. Pisa Cl. Sc., 20, no. 2 (1993), pp. 247-297. Zbl0797.49013MR1233638
12. [12] A. Coscia, On curvature sensitive image segmentation, Non Linear Analysis T.M.A. (to appear). Zbl0942.68135MR1733124
13. [13] G. David, C1 arcs for the minimizers of the Mumford-Shah functional, SIAM J. Appl. Math., 56, no. 3 (1996), pp. 783-888. Zbl0870.49020MR1389754
14. [14] G. David - S. Semmes, On the singular set of minimizers of the Mumford-Shah functional, J. Math. Pures Appl., 75, no. 4 (1996), pp. 229-342. Zbl0853.49010MR1411155
15. [15] E. De Giorgi, Free discontinuity problems in calculus of variations, in Frontiers of pure and applied mathematics, a collection of papers dedicated to J. L. Lions on the occasion of his 60th birthday, R. Dautray ed., North-Holland, Amsterdam (1991), 55-62. Zbl0758.49002MR1110593
16. [16] E. De Giorgi, Introduzione ai problemi con discontinuità libere, in Symmetry in nature: a volume in honour of L. A. Radicati di Brozolo, I, Scuola Normale Superiore, Pisa (1989), 265-285. Zbl0742.49001
17. [17] L.C. Evans - R.F. Gariepy, Measure theory and fine properties of functions, Studies in Advanced Mathematics, CRC Press, Boca Raton, FL, 1992. Zbl0804.28001MR1158660
18. [18] H. Federer, Geometric measure theory, Springer, Berlin (1969). Zbl0874.49001MR257325
19. [19] J.M. Gauch - H.H. PIEN - J. SHAH, Hybrid boundary-based and region-based deformable models for biomedical image segmentation, SPIE Vol. 2299 (1994), pp. 72-83. 
20. [20] C.R. Grisanti, Lipschitz selections for multiple valued functions, preprint Dipartimento Metodi e Modelli Matematici per le Scienze Applicate, Roma (1999). 
21. [21] C.R. Grisanti - R. Schianchi, A criterion for the image segmentation in the framework of the varifolds theory, preprint n. 2 - 1999, Dipartimento Metodi e Modelli Matematici per le Scienze Applicate, Roma (1999). 
22. [22] J.E. Hutchinson, C1,α multiple function regularity and tangent cone behaviour for varifolds with second fundamental form in LP, in Geometric measure theory and the calculus of variations (Arcata, Calif., 1984), W. K. Allard and F. J. Almgren eds., Proc. Symp. Pure Math. 44 Ann. Math. Soc., Providence (1986), 281-306. Zbl0635.49020
23. [23] J.E. Hutchinson, Second fundamental form for varifold and the existence of surfaces minimizing curvature, Indiana Univ. Math. J., 35, no. 1 (1986), pp. 45-71. Zbl0561.53008MR825628
24. [24] C. Mantegazza, Su alcune definizioni deboli di curvatura per insiemi non orientati, Tesi di laurea Univ. di Pisa, a.a. 1992/93. 
25. [25] C. Mantegazza, Curvature Varifolds with boundary, J. Differential Geom., 43, no. 4 (1996), pp. 807-843. Zbl0865.49030MR1412686
26. [26] D. Mumford - J. SHAH, Optimal approximation by piecewise smooth functions and associated variational problems, Comm. Pure Appl. Math., 42, no. 5 (1989), 577-685. Zbl0691.49036MR997568
27. [27] R. March, Visual reconstruction with discontinuities using variational methods, Image and Vision Computing, 10 (1992), pp. 30-38. 
28. [28] L. Simon, Lectures on geometric measure theory, Proceedings of the Centre for Mathematical Analysis, Australian National University, 3. Australian National University, Centre for Mathematical Analysis, Canberra, 1983. Zbl0546.49019MR756417