Symmetric positive-definite matrices: From geometry to applications and visualization

Mathematics and Visualization

Volumn 0, Issue , 2006, Pages 285-298

  Moakher, Maher ^a   Batchelor, Philipp G ^b  

^a ENIT LAMSIN   (Tunisia)

^b GUY S HOSPITAL   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

CALCULATIONS; GEOMETRY;

ENGINEERING APPLICATIONS; POSITIVE DEFINITE; SYMMETRIC POSITIVE DEFINITE MATRICES; SYMMETRIC SPACES; TENSOR ANALYSIS; TENSOR IMAGING;

TENSORS;

EID: 85032187592     PISSN: 16123786     EISSN: 2197666X     Source Type: Book Series    
DOI: 10.1007/3-540-31272-2_17     Document Type: Conference Paper

References (13)

1. Amari, S. (1985) Differential-Geometrical Methods in Statistics. Springer-Verlag, Berlin Heidelberg.
2. Basser, P. and Pierpaoli, C. (1996) Microstructural and physiological features of tissues elucidated by quantitative-diffusion-tensor MRI, J. Magn. Reson. B 111/3, pp. 209–219.
3. Batchelor, P. G., Moakher, M., Atkinson, D., Calamante, F., Connelly, A. (2004) A rigorous framework for diffusion tensor analysis using Riemannian geometry. Magn. Reson. Med., in press.
4. Helgason, S. (1978) Differential Geometry, Lie Groups, and Symmetric spaces. Academic Press, New York.
5. Kullback, S. L. (1959) Information Theory and Statistics. Wiley, New York.
6. Lang, S. (1999) Fundamentals of Differential Geometry. Springer-Verlag, New York.
7. Lenglet, C., Rousson, M., Deriche, R. (2004) Segmentation of 3D Probability Density Fields by Surface Evolution: Application to Diffusion MRI, in: MICCAI 2004, Part I, C. Barillot, D. R. Haynor, P. Hellier, eds. Lecture Notes in Computer Science, Vol. 3216, Springer-Verlag, Berlin, pp. 18–25.
8. Moakher, M. (2003) A differential geometric approach to the geometric mean of symmetric positive-definite matrices. SIAM J. Matrix Anal. Appl., in press.
9. Moakher, M. (2004) On the averaging of symmetric positive-definite tensors, submitted to: J. Elasticity.
10. Papadakis, N. G., Xing, D., Houston, G. C., Smith, J.M., Smith, M. I., James, M. F., Parsons, A. A., Huang, C. L.-H., Hall, L. D., Carpenter, T. A. (1999) A study of rotationally invariant and symmetric indices of diffusion anisotropy, Magn. Reson. Imag., 17/6, pp. 881–892.
11. Pierpaoli, C. and Basser, P. J. (1996) Toward a quantitative assessment of diffusion anisotropy, Magn. Reson. Med., 36/6, pp. 893–906.
12. Smith, S. T. (1993) Geometric optimization methods for adaptive filtering. Ph.D. thesis, Harvard University, Cambridge, Massachussetts.
13. Terras, A. (1988) Harmonic Analysis on Symmetric Spaces and Applications 2. Springer-Verlag, New York.