Remote Access Bulletin of the American Mathematical Society

Bulletin of the American Mathematical Society

ISSN 1088-9485(online) ISSN 0273-0979(print)

Book Review

The AMS does not provide abstracts of book reviews. You may download the entire review from the links below.


Full text of review: PDF   This review is available free of charge.
Book Information:

Authors: Jean-Michel Morel and Sergio Solimini
Title: Variational methods in image segmentation
Additional book information: Progress in Nonlinear Differential Equations and Their Applications, vol. 14, Birkhäuser, Boston, 1995, xvi + 245 pp., ISBN 0-8176-3720-6, $59.00$

References [Enhancements On Off] (What's this?)

  • Luigi Ambrosio, Variational problems in ${\rm SBV}$ and image segmentation, Acta Appl. Math. 17 (1989), no. 1, 1–40. MR 1029833, DOI https://doi.org/10.1007/BF00052492
  • Andrew Blake and Andrew Zisserman, Visual reconstruction, MIT Press Series in Artificial Intelligence, MIT Press, Cambridge, MA, 1987. MR 919733
  • D. Cooper, H. Elliott, F. Cohen, L. Reiss, and P. Symosek, Stochastic boundary estimation and object recognition, Image Modeling (A. Rosenfeld, ed.), Academic Press, 1981. B. Dubuc and S. Zucker, Indexing visual representations through the complexity map, Proc. 5th Int. Conf. Comp. Vision, IEEE Comp. Soc. Press, 1995.
  • K. J. Falconer, The geometry of fractal sets, Cambridge Tracts in Mathematics, vol. 85, Cambridge University Press, Cambridge, 1986. MR 867284
  • O. Faugeras, Three-dimensional computer vision, MIT Press, Cambridge, MA, 1993. S. Geman and D. Geman, Stochastic relaxation, Gibbs distributions and the Bayesian restoration of images, IEEE Trans. Patt. Anal. Mach. Int. 6 (1984). U. Grenader, General pattern theory, Oxford Univ. Press, 1995. H. von Helmholtz, Physiological optics, orig. German edition, 1909; Dover translation, 1962.
  • Jan J. Koenderink, Solid shape, MIT Press Series in Artificial Intelligence, MIT Press, Cambridge, MA, 1990. MR 1045203
  • Ernst Mach, The analysis of sensations and the relation of the physical to the psychical, orig. German edition, 1895; Dover translation, 1959. D. Marr, Vision, Freeman and Co., 1982. D. Mumford, Pattern theory, Proc. 1st European Congr. Math., Birkhäuser, Boston, 1994. MR 1:341 824 D. Mumford and J. Shah, Boundary detection by minimizing functionals, Proc. IEEE Conf. Comp. Vis. Pattern Recognition, 1985.
  • David Mumford and Jayant Shah, Optimal approximations by piecewise smooth functions and associated variational problems, Comm. Pure Appl. Math. 42 (1989), no. 5, 577–685. MR 997568, DOI https://doi.org/10.1002/cpa.3160420503
  • Joseph L. Mundy and Andrew Zisserman (eds.), Geometric invariance in computer vision, Artificial Intelligence, MIT Press, Cambridge, MA, 1992. MR 1200461


Review Information:

Reviewer: David Mumford
Affiliation: Harvard University
Email: mumford@math.harvard.edu
Journal: Bull. Amer. Math. Soc. 33 (1996), 211-216
DOI: https://doi.org/10.1090/S0273-0979-96-00643-X
Review copyright: © Copyright 1996 American Mathematical Society