Limit theorems for a variational problem arising in computer vision

Thomas J. Richardson

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (1992)

  • Volume: 19, Issue: 1, page 1-49
  • ISSN: 0391-173X

How to cite


Richardson, Thomas J.. "Limit theorems for a variational problem arising in computer vision." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 19.1 (1992): 1-49. <>.

author = {Richardson, Thomas J.},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
keywords = {free discontinuity problem; computer vision},
language = {eng},
number = {1},
pages = {1-49},
publisher = {Scuola normale superiore},
title = {Limit theorems for a variational problem arising in computer vision},
url = {},
volume = {19},
year = {1992},

AU - Richardson, Thomas J.
TI - Limit theorems for a variational problem arising in computer vision
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 1992
PB - Scuola normale superiore
VL - 19
IS - 1
SP - 1
EP - 49
LA - eng
KW - free discontinuity problem; computer vision
UR -
ER -


  1. [1] R. Adams, Sobolev Spaces, Academic PressN.Y.1975. Zbl0314.46030MR450957
  2. [2] L. Ambrosio, A Compactness Theorem for a Special Class of Functions of Bounded Variation, Boll. Un. Mat. Ital., 3-B No. 4, 1989, 857-881. Zbl0767.49001MR1032614
  3. [3] L. Ambrosio, Variational Problems on SBV, Center for Intelligent Control Systems Report CICS-P-86, MIT, 1989. 
  4. [4] A. Blake - A. Zisserman, Visual Reconstruction, MIT Press, Cambridge, 1987. MR919733
  5. [5] G. Congedo - I. Tamanini, On the Existence of Solutions to a Problem in Image Segmentation, preprint. 
  6. [6] G. Dal Maso - J.M. Morel - S. Solimini, A Variational Method in Image Segmentation: Existence and Approximation Results, S.I.S.S.A. 48 M, April 1989. Zbl0772.49006
  7. [7] E. De Giorgi - L. Amrbosio, Un nuovo tipo di funzionale del calcolo delle variazioni, Atti Accad. Naz. Lincei, 1988. 
  8. [8] E. De Giorgi, Free Discontinuity Problems in Calculus of Variations, to appear in proceedings of the meeting in J.L. Lions' honor, Paris1988. Zbl0758.49002
  9. [9] E. De Giorgi - M. Carriero - A. Leaci, Existence Theorem for a Minimum Problem with Free Discontinuity Set, preprint, University of Lecce1988. 
  10. [10] K.J. Falconer, The Geometry of Fractal Sets, Cambridge University Press, 1985. Zbl0587.28004MR867284
  11. [11] H. Federer, Geometric Measure Theory, Springer-Verlag, 1969. Zbl0176.00801MR257325
  12. [12] E. Giusti, Minimal Surfaces and Functions of Bounded Variation, Birkhäuser, Basel, 1983. Zbl0545.49018MR775682
  13. [13] D. Marr, Vision, W.H. Freeman and Co.1982Proc. Roy. Soc. LondonB, 207, 187-217, 1980. 
  14. [14] J.-M. Morel - S. Solimini, Segmentation of Images by Variational Methods: a Constructive Approach, Rev. Mat. Univ. Complut. Madrid, 1, 1, 2, 3; 1988. Zbl0679.68205MR977048
  15. [15] D. Mumford - J. Shah, Boundary Detection by Minimizing Functionals, IEEE Conf. on Computer Vision and Pattern Recognition, San Francisco1985. 
  16. [16] D. Mumford - J. Shah, Optimal Approximations by Piecewise Smooth Functions and Associated Variational Problems, Comm. Pure Appl. Math., XLII, No. 4 July, 1989, 577-685. Zbl0691.49036MR997568
  17. [17] T.J. Richardson, Scale Independent Piecewise Smooth Segmentation of Images via Variational Methods, Ph.D. Thesis Dept. of E.E. & C.S., M.I.T.1990. 
  18. [18] C.A. Rogers, Hausdorff Measure, Cambridge University Press, 1970. Zbl0204.37601MR281862
  19. [19] A. Rosenfeld - M. Thurston, Edge and Curve Dectection for Visual Scene Analysis, IEEE Trans. Comput.C-20, May 1971, 562-569. 
  20. [20] W. Rudin, Functional Analysis, McGraw Hill, 1973. Zbl0253.46001MR365062
  21. [21] J. Serra, Image Analysis and Mathematical Morphology, Academic Press Inc., 1982. Zbl0565.92001MR753649
  22. [22] J. Shah, Segmentation by Minimizing Functionals: Smoothing Properties, preprint. 
  23. [23] Y. Wang, Ph.D. ThesisHarvard University Math. Dept. 1989. 

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