An Eulerian PDE Approach for Computing Tissue Thickness

IEEE Transactions on Medical Imaging

Volumn 22, Issue 10, 2003, Pages 1332-1339

  Yezzi Jr , Anthony J ^a   Prince, Jerry L ^b  

^a GEORGIA INSTITUTE OF TECHNOLOGY   (United States)

^b Johns Hopkins University   (United States)

Author keywords

Correspondence trajectory; Numerical methods; Partial differential equations (PDEs); Thickness

Indexed keywords

COMPUTER SIMULATION; IMAGE ANALYSIS; MAGNETIC RESONANCE IMAGING; NUMERICAL METHODS; PARTIAL DIFFERENTIAL EQUATIONS; TISSUE;

PARAMETERIZATIONS;

MEDICAL IMAGING;

ALGORITHM; ANATOMY; ANTHROPOMETRY; ARTICLE; ARTICULAR CARTILAGE; AUTOMATED PATTERN RECOGNITION; BIOLOGICAL MODEL; BRAIN CORTEX; COMPARATIVE STUDY; COMPUTER SIMULATION; CONNECTIVE TISSUE; EVALUATION; HEART; HISTOLOGY; HUMAN; IMAGE QUALITY; METHODOLOGY; NUCLEAR MAGNETIC RESONANCE IMAGING; THREE DIMENSIONAL IMAGING; TIBIA; VALIDATION STUDY;

ALGORITHMS; ANATOMY, CROSS-SECTIONAL; ANTHROPOMETRY; CARTILAGE, ARTICULAR; CEREBRAL CORTEX; COMPUTER SIMULATION; CONNECTIVE TISSUE; HEART; HUMANS; IMAGING, THREE-DIMENSIONAL; MAGNETIC RESONANCE IMAGING; MODELS, BIOLOGICAL; PATTERN RECOGNITION, AUTOMATED; PHANTOMS, IMAGING; TIBIA;

EID: 0141920425     PISSN: 02780062     EISSN: None     Source Type: Journal    
DOI: 10.1109/TMI.2003.817775     Document Type: Article

References (22)

1. M. E. DeBakey and A. M. Gotto, Jr., The New Living Heart. Holbrook, MA: Adams Media Corporation, 1997.
2. B. Fischl and A. M. Dale, "Measuring the thickness of the human cerebral cortex from magnetic resonance images," Proc. Nat. Acad. Sci., vol. 97, no. 20, pp. 11 050-11 055, 2000.
3. J. Nolte and I B. Angevine, Jr., The Human Brain: In Photographs and Diagrams. St. Louis, MO: Mosby, 1995.
4. S. Pizer, D. Eberly, D. Fritsch, and B. Morse, "Zoom-invariant vision of figural shape: The mathematics of cores," Comput. Vision Image Understanding, vol. 69, no. 1, pp. 55-71, 1998.
5. S. E. Jones, B. R. Buchbinder, and I. Aharon, "Three-dimensional mapping of the cortical thickness using Laplace's equation," Hum. Brain Mapping, vol. 11, pp. 12-32, 2000.
6. L. Cohen and R. Kimmel, "Global minimum for active contour models: A minimal path approach," Int. J. Comput. Vis., vol. 24, no. 1, pp. 57-78, Aug. 1997.
7. J. Sethian, Level Set Methods: Evolving Interfaces in Geometry, Fluid Mechanics, Computer Vision, and Material Science, Cambridge, U.K.: Cambridge Univ. Press, 1996.
8. J. Tsitsiklis, "Efficient algorithms for globally optimal trajectories," IEEE Trans. Automat. Contr., vol. 40, pp. 1528-1538, Sept. 1995.
9. W. Grossman, "Assessment of regional myocardial function," J. Amer. Coll. Cardiol., vol. 7, no. 2, pp. 327-328, 1986.
10. D. MacDonald, N. Kabani, D. Avis, and A. C. Evans, "Automated 3-D extraction of inner and outer surfaces of cerebral cortex from MRI," NeuroImage, vol. 12, pp. 340-356, 2000.
11. M. I. Miller, A. B. Massie, J. T. Ratnanather, K. N. Botteron, and J. G. Csernansky, "Bayesian construction of geometrically based cortical thickness metrics," NeuroImage, vol. 12, pp. 676-687, 2000.
12. J. C. McEachen, II and J. S. Duncan, "Shape-based tracking of left ventricular wall motion," IEEE Trans. Med. Imag., vol. 16, pp. 270-283, Mar. 1997.
13. H. D. Tagare, "Deformable 2-D template matching using orthogonal curves," IEEE Trans. Med. Imag., vol. 16, pp. 108-117, Feb. 1997.
14. C. Xu and J. L. Prince, "Snakes, shapes, and gradient vector flow," IEEE Trans. Image Processing, vol. 7, pp. 359-369, Mar. 1998.
15. W. Press, B. Flannery, S. Teukolsky, and W. Vetterling, Numerical Recipes: The Art of Scientific Computing. Cambridge, U.K.: Cambridge Univ. Press, 1988.
16. Y. Saad, Iterative Methods for Sparse Linear Systems. New York: PWS, 1996.
17. W. Briggs, A Multigrid Tutorial. Philadelphia, PA: Soc. Ind. Appl. Math., 1987.
18. S. Osher, "Riemann solvers, entropy condition, and difference approximations," SIAM J. Numer. Anal., vol. 21, no. 2, pp. 217-235, Apr. 1984.
19. S. Osher and J. A. Sethian, "Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulations," J. Comput. Phys., vol. 79, pp. 12-49, 1988.
20. R. LeVeque, Numerical Methods for Conservation Laws. Boston, MA: Birkhäuser, 1992.
21. C. Xu, D. L. Pham, M. E. Rettmann, D. N. Yu, and J. L. Prince, "Reconstruction of the human cerebral cortex from magnetic resonance images," IEEE Trans. Med. Imag., vol. 18, pp. 467-480, June 1999.
22. X. Zeng, L. H. Staib, R. T. Schultz, and J. S. Duncan, "Segmentation and measurement of the cortex from 3-D MR images using coupled-surfaces propagation," IEEE Trans. Med. Imag., vol. 18, pp. 927-937, Oct. 1999.