Free Access
Volume 17, Number 1, January-March 2011
Page(s) 190 - 221
Published online 31 March 2010
  1. E. Acerbi and N. Fusco, Semicontinuity problems in the calculus of variations. Arch. Rat. Mech. Anal. 86 (1984) 125–145. [Google Scholar]
  2. L. Alvarez, J. Weickert and J. Sánchez, Reliable estimation of dense optical flow fields with large displacements. Int. J. Computer Vision 39 (2000) 41–56. [CrossRef] [Google Scholar]
  3. G. Aubert and P. Kornprobst, Mathematical Problems in Image Processing: Partial Differential Equations and the Calculus of Variations. Second edn., Springer, New York etc. (2006). [Google Scholar]
  4. J.M. Ball and F. Murat, W1,p-quasiconvexity and variational problems for multiple integrals. J. Funct. Anal. 58 (1984) 225–253. [Google Scholar]
  5. N. Bourbaki, Éléments de Mathématique, Livre VI : Intégration, Chapitres I–IV. Hermann, Paris, France (1952). [Google Scholar]
  6. M. Brokate, Pontryagin's principle for control problems in age-dependent population dynamics. J. Math. Biology 23 (1985) 75–101. [Google Scholar]
  7. A. Brøndsted, An Introduction to Convex Polytopes. Springer, New York-Heidelberg-Berlin (1983). [Google Scholar]
  8. C. Brune, H. Maurer and M. Wagner, Detection of intensity and motion edges within optical flow via multidimensional control. SIAM J. Imaging Sci. 2 (2009) 1190–1210. [Google Scholar]
  9. G. Buttazzo, Semicontinuity, Relaxation and Integral Representation in the Calculus of Variations, Pitman Research Notes in Mathematics 207. Longman, Harlow (1989). [Google Scholar]
  10. S. Conti, Quasiconvex functions incorporating volumetric constraints are rank-one convex. J. Math. Pures Appl. 90 (2008) 15–30. [CrossRef] [MathSciNet] [Google Scholar]
  11. B. Dacorogna, Introduction to the Calculus of Variations. Imperial College Press, London, UK (2004) [Google Scholar]
  12. B. Dacorogna, Direct Methods in the Calculus of Variations. Second edn., Springer, New York etc. (2008). [Google Scholar]
  13. B. Dacorogna and P. Marcellini, General existence theorems for Hamilton-Jacobi equations in the scalar and vectorial case. Acta Math. 178 (1997) 1–37. [CrossRef] [MathSciNet] [Google Scholar]
  14. M. Droske and M. Rumpf, A variational approach to nonrigid morphological image registration. SIAM J. Appl. Math. 64 (2004) 668–687. [CrossRef] [Google Scholar]
  15. N. Dunford and J.T. Schwartz, Linear Operators. Part I: General Theory. Wiley-Interscience, New York etc. (1988). [Google Scholar]
  16. I. Ekeland and R. Témam, Convex Analysis and Variational Problems. Second edn., SIAM, Philadelphia, USA (1999). [Google Scholar]
  17. L.C. Evans and R.F. Gariepy, Measure Theory and Fine Properties of Functions. CRC Press, Boca Raton etc. (1992). [Google Scholar]
  18. G. Feichtinger, G. Tragler and V.M. Veliov, Optimality conditions for age-structured control systems. J. Math. Anal. Appl. 288 (2003) 47–68. [CrossRef] [MathSciNet] [Google Scholar]
  19. L. Franek, M. Franek, H. Maurer and M. Wagner, Image restoration and simultaneous edge detection by optimal control methods. BTU Cottbus, Preprint-Reihe Mathematik, Preprint Nr. M-05/2008. Optim. Contr. Appl. Meth. (submitted). [Google Scholar]
  20. L.A. Gallardo and M.A. Meju, Characterization of heterogeneous near-surface materials by joint 2D inversion of dc resistivity and seismic data. Geophys. Res. Lett. 30 (2003) 1658. [CrossRef] [Google Scholar]
  21. E. Haber and J. Modersitzki, Intensity gradient based registration and fusion of multi-modal images. Methods Inf. Med. 46 (2007) 292–299. [PubMed] [Google Scholar]
  22. S. Henn and K. Witsch, A multigrid approach for minimizing a nonlinear functional for digital image matching. Computing 64 (2000) 339–348. [CrossRef] [MathSciNet] [Google Scholar]
  23. S. Henn and K. Witsch, Iterative multigrid regularization techniques for image matching. SIAM J. Sci. Comput. 23 (2001) 1077–1093. [CrossRef] [MathSciNet] [Google Scholar]
  24. G. Hermosillo, C. Chefd'hotel and O. Faugeras, Variational methods for multimodal image matching. Int. J. Computer Vision 50 (2002) 329–343. [CrossRef] [Google Scholar]
  25. W. Hinterberger, O. Scherzer, C. Schnörr and J. Weickert, Analysis of optical flow models in the framework of the calculus of variations. Num. Funct. Anal. Optim. 23 (2002) 69–89. [CrossRef] [Google Scholar]
  26. D. Kinderlehrer and P. Pedregal, Characterizations of Young measures generated by gradients. Arch. Rat. Mech. Anal. 115 (1991) 329–365. [Google Scholar]
  27. P. Marcellini and C. Sbordone, Semicontinuity problems in the calculus of variations. Nonlinear Anal. 4 (1980) 241–257. [CrossRef] [MathSciNet] [Google Scholar]
  28. J. Modersitzki, Numerical Methods for Image Registration. Oxford University Press, Oxford, UK (2004). [Google Scholar]
  29. C.B. Morrey, Multiple Integrals in the Calculus of Variations, Grundlehren 130. Springer, Berlin-Heidelberg-New York (1966). [Google Scholar]
  30. S. Pickenhain and M. Wagner, Critical points in relaxed deposit problems, in Calculus of Variations and Optimal Control, Technion 98, Vol. II, A. Ioffe, S. Reich and I. Shafrir Eds., Research Notes in Mathematics 411, Chapman & Hall/CRC Press, Boca Raton etc. (2000) 217–236. [Google Scholar]
  31. T. Roubíček, Relaxation in Optimization Theory and Variational Calculus. De Gruyter, Berlin-New York (1997). [Google Scholar]
  32. R. Schneider, Convex Bodies: The Brunn-Minkowski Theory. Cambridge University Press, Cambridge, UK (1993). [Google Scholar]
  33. T.W. Ting, Elastic-plastic torsion of convex cylindrical bars. J. Math. Mech. 19 (1969) 531–551. [MathSciNet] [Google Scholar]
  34. T.W. Ting, Elastic-plastic torsion problem III. Arch. Rat. Mech. Anal. 34 (1969) 228–244. [CrossRef] [Google Scholar]
  35. M. Wagner, Erweiterungen des mehrdimensionalen Pontrjaginschen Maximumprinzips auf meßbare und beschränkte sowie distributionelle Steuerungen. Ph.D. Thesis, University of Leipzig, Germany (1996). [Google Scholar]
  36. M. Wagner, Mehrdimensionale Steuerungsprobleme mit quasikonvexen Integranden. Habilitation Thesis, BTU Cottbus, Germany (2006). [Google Scholar]
  37. M. Wagner, Nonconvex relaxation properties of multidimensional control problems, in Recent Advances in Optimization, A. Seeger Ed., Lecture Notes in Economics and Mathematical Systems 563, Springer, Berlin etc. (2006) 233–250. [Google Scholar]
  38. M. Wagner, Quasiconvex relaxation of multidimensional control problems. Adv. Math. Sci. Appl. 18 (2008) 305–327. [MathSciNet] [Google Scholar]
  39. M. Wagner, Jensen's inequality for the lower semicontinuous quasiconvex envelope and relaxation of multidimensional control problems. J. Math. Anal. Appl. 355 (2009) 606–619. [CrossRef] [MathSciNet] [Google Scholar]
  40. M. Wagner, On the lower semicontinuous quasiconvex envelope for unbounded integrands (I). ESAIM: COCV 15 (2009) 68–101. [CrossRef] [EDP Sciences] [Google Scholar]
  41. M. Wagner, On the lower semicontinuous quasiconvex envelope for unbounded integrands (II): Representation by generalized controls. J. Convex Anal. 16 (2009) 441–472. [MathSciNet] [Google Scholar]
  42. M. Wagner, Pontryagin's maximum principle for multidimensional control problems in image processing. J. Optim. Theory Appl. 140 (2009) 543–576. [CrossRef] [MathSciNet] [Google Scholar]
  43. M. Wagner, Elastic/hyperelastic image registration unter Nebenbedingungen als mehrdimensionales Steuerungsproblem. Preprint-Reihe Mathematik, Preprint Nr. M-09/2009, BTU Cottbus, Germany (2009). [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.