Minimizing flows for the Monge-Kantorovich problem

SIAM Journal on Mathematical Analysis

Volumn 35, Issue 1, 2004, Pages 61-97

  Angenent, Sigurd ^a   Haker, Steven ^b   Tannenbaum, Allen ^c  

^a UNIVERSITY OF WISCONSIN MADISON   (United States)

^b BRIGHAM AND WOMEN S HOSPITAL   (United States)

^c GEORGIA INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

Gradient flows; Image registration; Medical imaging; Optimal transport; Weak solutions

Indexed keywords

EID: 1342309266     PISSN: 00361410     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0036141002410927     Document Type: Article

References (17)

1. L. AMBROSIO. Lecture Notes on Optimal Transport Theory, CIME Series of Springer Lecture Notes, Euro Summer School Mathematical Aspects of Evolving Interfaces, Madeira, Portugal, Springer-Verlag, New York, 2000.
2. S. ANGENENT, S. HAKER, A. TANNENBAUM, AND R. KIKINIS, On area preserving maps of minimal distortion, in System Theory: Modeling, Analysis, and Control, T. Djaferis and I. Schick, eds., Kluwer Academic, The Netherlands, 1999, pp. 275-287.
3. J.-D. BENAMOU AND Y. BRENIER, A computational fluid mechanics solution to the MongeKantorovich mass transfer problem, Numer. Math., 84 (2000), pp. 375-393.
4. Y. BRENIER, Polar factorization and monotone rearrangement of vector-valued functions, Comm. Pure Appl. Math., 64 (1991), pp. 375-417.
5. M. CULLEN AND R. PURSER, An extended Lagrangian theory of semigeostrophic frontogenesis, J. Atmospheric Sci., 41 (1984), pp. 1477-1497.
6. B. DACOROGNA AND J. MOSER, On a partial differential equation involving the Jacobian determinant, Ann. Inst. H. Poincaré Anal. Non Linéaire, 7 (1990), pp. 1-26.
7. L. C. EVANS, Partial Differential Equations, Grad. Stud. Math. 19, AMS, Providence, RI, 1998.
8. L. C. EVANS, Partial differential equations and Monge-Kantorovich mass transfer, in Current Developments in Mathematics, International Press, Boston, MA, 1999, pp. 65-126.
9. W. GANGBO AND R. MCCANN, The geometry of optimal transportation, Acta Math., 177 (1996), pp. 113-161.
10. D. GILBARG AND N. TRUDINGER, Elliptic Partial Differential Equations of Second Order, Springer-Verlag, Berlin, 2001.
11. S. HAKER, A. TANNENBAUM, AND S. ANGENENT, Optimal transport and image registration, Internat. J. Comput. Vision, submitted.
12. S. HAKER, A. TANNENBAUM, AND R. KIKINIS, Mass-preserving mappings and surface registration, in Proceedings of the Medical Image Computing and Computer-Assisted Intervention (MICCAI'01), 4th International Conference, Utrecht, The Netherlands, 2001.
13. L. V. KANTOROVICH, On a problem of Monge, Uspekhi Mat. Nauk., 3 (1948), pp. 225-226.
14. M. KNOTT AND C. SMITH, On the optimal mapping of distributions, J. Optim. Theory, 43 (1984), pp. 39-49.
15. S. RACHEV AND L. RÜSCHENDORF, Mass Transportation Problems, Vol. I, Probab. Appl., Springer-Verlag, New York, 1998.
16. S. RACHEV AND L. RÜSCHENDORF, Mass Transportation Problems, Vol. II, Probab. Appl., Springer-Verlag, New York, 1998.
17. A. TOGA, Brain Warping, Academic Press, San Diego, 1999.