Multiscale joint segmentation and registration of image morphology

IEEE Transactions on Pattern Analysis and Machine Intelligence

Volumn 29, Issue 12, 2007, Pages 2181-2194

  Droske, Marc ^b   Rumpf, Martin ^a  

^a UNIVERSITY OF BONN   (Germany)

^b NONE

Author keywords

Finite element discretization; Image morphology; Multiscale phase field approximation; Mumford Shah approach; Nonlinear elasticity; Nonrigid multimodal registration

Indexed keywords

ALGORITHMS; APPROXIMATION THEORY; EDGE DETECTION; FINITE ELEMENT METHOD; IMAGE REGISTRATION; IMAGE SEGMENTATION;

DENOISING; EDGE PRESERVING; FINITE ELEMENT DISCRETIZATION; IMAGE MORPHOLOGY; MULTISCALE PHASE FIELD APPROXIMATION; MUMFORD-SHAH APPROACH;

IMAGE ANALYSIS;

ALGORITHM; ARTICLE; ARTIFICIAL INTELLIGENCE; AUTOMATED PATTERN RECOGNITION; BIOLOGICAL MODEL; COMPUTER ASSISTED DIAGNOSIS; COMPUTER SIMULATION; IMAGE ENHANCEMENT; IMAGE SUBTRACTION; METHODOLOGY; REPRODUCIBILITY; SENSITIVITY AND SPECIFICITY;

ALGORITHMS; ARTIFICIAL INTELLIGENCE; COMPUTER SIMULATION; IMAGE ENHANCEMENT; IMAGE INTERPRETATION, COMPUTER-ASSISTED; MODELS, BIOLOGICAL; PATTERN RECOGNITION, AUTOMATED; REPRODUCIBILITY OF RESULTS; SENSITIVITY AND SPECIFICITY; SUBTRACTION TECHNIQUE;

EID: 36248953676     PISSN: 01628828     EISSN: None     Source Type: Journal    
DOI: 10.1109/TPAMI.2007.1120     Document Type: Article

References (58)

1. M. Miller, A. Trouvé, and L. Younes, "On the Metrics and Euler-Lagrange Equations of Computational Anatomy," Ann. Rev. Biomedical Eng., vol. 4, pp. 375-405, 2002.
2. U. Grenander and M.I. Miller, "Computational Anatomy: An Emerging Discipline," Quarterly Applied Math., vol. LVI, no. 4, pp. 617-694, 1998.
3. J. Modersitzki and B. Fischer, "Fast Diffusion Registration," AMS Contemporary Math., Inverse Problems, Image Analysis, and Medical Imaging, special issue, 2000.
4. J.P. Thirion, "Image Matching as a Diffusion Process: An Analogy with Maxwell's Demon," Medical Image Analysis, vol. 2, pp. 243-260, 1998.
5. P.A. Viola and W. Wells III, "Alignment by Maximization of Mutual Information," Technical Report AITR-1548, 1995.
6. W. Wells, P. Viola, H. Atsumi, S. Nakajima, and R. Kikinis, Multi-Modal Volume Registration by Maximization of Mutual Information 1996.
7. A.E.A. Collignon, "Automated Multi-Modality Image Registration Based on Information Theory," Proc. 14th Conf. Information Processing in Medical Imaging, pp. 263-274, 1995.
8. M. Mellor and M. Brady, "Phase Mutual Information as a Similarity Measure for Registration," Medical Image Analysis, vol. 9, no. 4, pp. 330-343, 2005.
9. M. Droske and M. Rumpf, "A Variational Approach to Non-Rigid Morphological Registration," SIAM Applied Math., vol. 64, no. 2, pp. 668-687, 2004.
10. Y.N. Young and D. Levy, "Registration-Based Morphing of Active Contours for Segmentation of CT-Scans," Math. Biosciences and Eng., vol. 2, no. 1, pp. 79-96, 2005.
11. J.-P. Thirion and A. Gourdon, "Computing the Differential Characteristics of Isointensity Surfaces," Computer Vision and Image Understanding, vol. 61, no. 2, pp. 190-202, 1995.
12. T. Kapur, L. Yezzi, and L. Zöllei, "A Variational Framework for Joint Segmentation and Registration," Proc. IEEE Math. Methods in Biomedical Image Analysis, 2001.
13. T.F. Chan and L.A. Vese, "Active Contours without Edges," IEEE Trans. Image Processing, vol. 10, no. 2, pp. 266-277, 2001.
14. G. Unal and G. Slabaugh, "Coupled PDEs for Nonrigid Registration and Segmentation," Proc. 23rd IEEE Int'l Conf. Computer Vision and Pattern Recognition, 2005.
15. Y. Chen, S. Thiruvenkadam, F. Huang, K.S. Gopinath, and R.W. Brigg, Simultaneous Segmentation and Registration for Functional MR Images," Proc. 16th Int'l Conf. Pattern Recognition, vol. 01, p. 10747, 2002.
16. P.P. Wyatt and J.A. Noble, "MAP MRF Joint Segmentation and Registration," Proc. Int'l Conf. Medical Image Computing and Computer-Assisted Intervention, vol. 1, pp. 580-587, 2002.
17. O. Féron and A. Mohammad-Djafari, "Image Fusion and Unsupervised Joint Segmentation Using HMM and MCMC Algorithms," J. Electronic Imaging, 2004.
18. Proc. Fifth Int'l Conf. Medical Image Computing and Computer-Assisted Intervention, Part I, Sept. 25-28, 2002.
19. G. Matheron, Random Sets and Integral Geometry. John Wiley & Sons, 1975.
20. V. Caselles, B. Coll, and J.M. Morel, "Topographics Maps and Local Contrast Invariance in Natural Images," Int'l J. Computer Vision, vol. 33, pp. 5-27, 1999.
21. D. Mumford and J. Shah, "Optimal Approximation by Piecewise Smooth Functions and Associated Variational Problems," Comm. Pure Applied Math., vol. 42, pp. 577-685, 1989.
22. L. Ambrosio, N. Fusco, and D. Pallara, Functions of Bounded Variation and Free Discontinuity Problems. Oxford Univ. Press, 2000.
23. L.C. Evans and R.F. Gariepy, Measure Theory and Fine Properties of Functions. CRC Press, 1992.
24. L. Rudin, S. Osher, and E. Fatemi, "Nonlinear Total Variation Based Noise-Removal," Physica D, vol. 60, pp. 259-268, 1992.
25. L. Ambrosio and V.M. Tortorelli, "On the Approximation of Free Discontinuity Problems," Bollettino dell'Unione Matematica Italiana, Sezione B, vol. 6, no. 7, pp. 105-123, 1992.
26. L.G. Brown, Α Survey of Image Registration Techniques," ACM Computing Surveys, vol. 24, no. 4, pp. 325-376, 1992.
27. P.A. van den Elsen, E.-J.J. Pol, and M.A. Viergever, "Medical Image Matching: A Review with Classification," IEEE Eng. in Medicine and Biology, vol. 12, pp. 26-39, 1993.
28. A. Trouvé, "Diffeomorphisms Groups and Pattern Matching in Image Analysis," Int'l J. Computer Vision, vol. 28, no. 3, pp. 213-221, 1998.
29. M.F. Beg, M. Miller, A. Trouvé, and L. Younes, "Computing Large Deformation Metric Mappings via Geodesic Flows of Diffeomorphisms," Int'l J. Computer Vision, vol. 61, no. 2, pp. 139-157, Feb. 2005.
30. R. Bajcsy and C. Breit, "Matching of Deformed Images," Proc. Sixth IEEE Int'l Conf. Pattern Recognition, pp. 351-353, 1982.
31. G.E. Christensen, S.C. Joshi, and M.I. Miller, "Volumetric Transformations of Brain Anatomy," IEEE Trans. Medical Imaging, vol. 16, no. 6, pp. 864-877, 1997.
32. G.E. Christensen, R.D. Rabbitt, and M.I. Miller, "Deformable Templates Using Large Deformation Kinematics," IEEE Trans. Medical Imaging, vol. 5, no. 10, pp. 1435-1447, 1996.
33. C.A. Davatzikos, R.N. Bryan, and J.L. Prince, "Image Registration Based on Boundary Mapping," IEEE Trans. Medical Imaging, vol. 15, no. 1, pp. 112-115, 1996.
34. J. Modersitzki and B. Fischer, "Curvature-Based Image Registration," J. Math. Imaging and Vision, vol. 18, no. 1, 2003.
35. I. Cohen, "Nonlinear Variational Method for Optical Flow Computation," Proc. Eighth Scandinavian Conf. Image Analysis, pp. 523-530, June 1993.
36. N. Litke, M. Droske, M. Rumpf, and P. Schröder, "An Image Processing Approach to Surface Matching," Proc. Third Eurographics Symp. Geometry Processing, 2005.
37. L. Alvarez, F. Guichard, P.L. Lions, and J.M. Morel, "Axioms and Fundamental Equations of Image Processing," Archives of Rational and Mechanical Analysis, vol. 123, no. 3, pp. 199-257, 1993.
38. G. Sapiro, Geometric Partial Differential Equations and Image Analysis. Cambridge Univ. Press, 2001.
39. B. Dacorogna, Direct Methods in the Calculus of Variations, Applied Math. Sciences, vol. 78, Springer, 1989.
40. L. Evans, Partial Differential Equations, Am. Math. Sec., reprint with corrections ed., 2002.
41. P.G. Ciarlet, Three-Dimensional Elasticity. Elsevier, 1988.
42. J.E. Marsden and T.J.R. Hughes, Mathematical Foundations of Elasticity. Prentice Hall, 1983.
43. W. Hinterberger, O. Scherzer, C. Schnörr, and J. Weickert, "Analysis of Optical Flow Models in the Framework of Calculus of Variations," Numerical Functional Analysis and Optimization, Technical Report 8/2001 (revised version), Computer Science Series, Univ. of Mannheim, Germany, 2001.
44. R.W. Ogden, Non-Linear Elastic Deformations. John Wiley & Sons, 1984.
45. M. Droske and W. Ring, "A Mumford-Shah Level-Set Approach for Geometric Image Registration," SIAM Applied Math., 2005.
46. L. Alvarez, J. Weickert, and J. Sánchez, "A Scale-Space Approach to Nonlocal Optical Flow Calculations," Proc. Second Int'l Conf. Scale-Space Theories in Computer Vision, pp. 235-246, Sept. 1999.
47. L. Ambrosio and V.M. Tortorelli, "Approximation of Functionals Depending on Jumps by Elliptic Functionals via Γ-Convergence," Comm. Pure Applied Math., vol. 43, pp. 999-1036, 1990.
48. G. Belletini and A. Coscia, "Discrete Approximation of a Free Discontinuity Problem," Numerical Functional Analysis and Optimization, vol. 15, pp. 201-224, 1994.
49. T.J. Richardson and S.K. Mitter, "A Variational Formulation-Based Edge Focusing Algorithm," Sadhana (Academy Proc. Eng. Sciences , vol. 22, no. 4, pp. 553-574, 1997.
50. B. Bourdin, "Image Segmentation with a Finite Element Method," ESIAM: Math. Modeling and Numerical Analysis, vol. 33, no. 2, pp. 229-244, 1999.
51. U. Clarenz, M. Droske, and M. Rumpf, "Towards Fast Non-Rigid Registration," Inverse Problems, Image Analysis and Medical Imaging: AMS Special Session Interaction of Inverse Problems and Image Analysis vol. 313 pp. 67-84, 2002.
52. S. Henn and K. Witsch, "Iterative Multigrid Regularization Techniques for Image Matching," SIAM J. Scientific Computing, vol. 23, no. 4, pp. 1077-1093, 2001.
53. P. Kosmol, Optimierung und Approximation, 1991, in German.
54. M. Droske, "On Variational Problems and Gradient Flows in Image Processing," PhD dissertation, Universität Duisburg-Essen, 2005.
55. W. Hackbusch, Iterative Solution of Large Sparse Systems of Equations Applied Math. Sciences, F. John, J.E. Marsden, and L. Sirovich, eds., vol. 95., Springer, 1994.
56. The Visualization Toolkit, http://www.vtk.org, 2007.
57. J. Ball, "Discontinuous Equilibrium Solutions and Cavitation in Nonlinear Elasticity," Philosophical Trans. Royal Soc. London, vol. 306, pp. 557-611, 1982.
58. J. Ball, "Global Invertibility of Sobolev Functions and the Interpenetration of Matter," Proc. Royal Sec. Edinburgh, vol. 88A, pp. 315-328, 1988.