{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,23]],"date-time":"2025-10-23T20:48:23Z","timestamp":1761252503045,"version":"3.40.3"},"publisher-location":"Berlin, Heidelberg","reference-count":36,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"type":"print","value":"9783540437451"},{"type":"electronic","value":"9783540479697"}],"license":[{"start":{"date-parts":[[2002,1,1]],"date-time":"2002-01-01T00:00:00Z","timestamp":1009843200000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2002]]},"DOI":"10.1007\/3-540-47969-4_17","type":"book-chapter","created":{"date-parts":[[2007,6,1]],"date-time":"2007-06-01T06:31:40Z","timestamp":1180679500000},"page":"251-265","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":37,"title":["Constrained Flows of Matrix-Valued Functions: Application to Diffusion Tensor Regularization"],"prefix":"10.1007","author":[{"given":"C.","family":"Chefd\u2019hotel","sequence":"first","affiliation":[]},{"given":"D.","family":"Tschumperl\u00e9","sequence":"additional","affiliation":[]},{"given":"R.","family":"Deriche","sequence":"additional","affiliation":[]},{"given":"O.","family":"Faugeras","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2002,4,29]]},"reference":[{"key":"17_CR1","unstructured":"L. Alvarez, R. Deriche, J. Weickert, and J. S\u00e1nchez. Dense disparity map estimation respecting image discontinuities: A PDE and scale-space based approach. International Journal of Visual Communication and Image Representation, 2000."},{"key":"17_CR2","doi-asserted-by":"crossref","unstructured":"Y. Amit. A nonlinear variational problem for image matching. SIAM Journal on Scientific Computing, 15(1), January 1994.","DOI":"10.1137\/0915014"},{"key":"17_CR3","unstructured":"M. Bertalmio, L.T. Cheng, S. Osher, and G. Sapiro. Variational problems and partial differential equations on implicit surfaces: The framework and examples in image processing and pattern formation. UCLA Research Report, June 2000."},{"key":"17_CR4","doi-asserted-by":"crossref","unstructured":"M. Bertalmio, G. Sapiro, V. Caselles, and C. Ballester. Image inpainting. In Kurt Akeley, editor, Proceedings of the SIGGRAPH, pages 417\u2013424. ACM Press, ACM SIGGRAPH, Addison Wesley Longman, 2000.","DOI":"10.1145\/344779.344972"},{"key":"17_CR5","unstructured":"T. Chan and J. Shen. Variational restoration of non-flat image features: Models and algorithms. Research Report, Computational and applied mathematics, department of mathematics Los Angeles, June 1999."},{"key":"17_CR6","volume-title":"Technical Report 00-11","author":"T. Chan","year":"2000","unstructured":"T. Chan and J. Shen. Mathematical models for local deterministic inpaintings. Technical Report 00-11, Department of Mathematics, UCLA, Los Angeles, March 2000."},{"key":"17_CR7","doi-asserted-by":"publisher","first-page":"168","DOI":"10.1109\/ICIP.1994.413553","volume":"II","author":"P. Charbonnier","year":"1994","unstructured":"P. Charbonnier, G. Aubert, M. Blanc-F\u00e9raud, and M. Barlaud. Two deterministic half-quadratic regularization algorithms for computed imaging. In Proceedings of the International Conference on Image Processing, volume II, pages 168\u2013172, 1994.","journal-title":"Proceedings of the International Conference on Image Processing"},{"key":"17_CR8","unstructured":"C. Chefd\u2019hotel, D. Tschumperl\u00e9, O. Faugeras and R. Deriche. Geometric Integration of Constraint Preserving Flows and Applications to Image Processing. INRIA Research Report, to appear, 2002."},{"key":"17_CR9","unstructured":"O. Coulon, D.C. Alexander, and S.R. Arridge. A geometrical approach to 3d diffusion tensor magnetic resonance image regularisation. Technical Report, Department of Computer Science, University College London., 2001."},{"key":"17_CR10","doi-asserted-by":"crossref","unstructured":"O. Coulon, D.C. Alexander, and S.R. Arridge. A regularization scheme for diffusion tensor magnetic resonance images. In XVIIth International Conferenceon Information Processing in Medical Imaging, 2001.","DOI":"10.1007\/3-540-45729-1_8"},{"key":"17_CR11","doi-asserted-by":"crossref","unstructured":"R. Deriche, P. Kornprobst, and G. Aubert. Optical flow estimation while preserving its discontinuities: A variational approach. In Proceedings of the 2nd Asian Conference on Computer Vision, volume 2, pages 71\u201380, Singapore, December 1995.","DOI":"10.1007\/3-540-60793-5_63"},{"issue":"3","key":"17_CR12","doi-asserted-by":"crossref","first-page":"336","DOI":"10.1109\/83.661183","volume":"7","author":"O. Faugeras","year":"1998","unstructured":"O. Faugeras and R. Keriven. Variational principles, surface evolution, PDE\u2019s, level set methods and the stereo problem. IEEE Transactions on Image Processing, 7(3):336\u2013344, March 1998.","journal-title":"IEEE Transactions on Image Processing"},{"key":"17_CR13","volume-title":"Matrix computations","author":"G. Golub","year":"1989","unstructured":"G. Golub and C. Van Loan. Matrix computations. The John Hopkins University Press, Baltimore, Maryland, second edition, 1989.","edition":"second edition"},{"key":"17_CR14","doi-asserted-by":"crossref","unstructured":"G. Granlund and H. Knutsson. Signal Processing for Computer Vision. Kluwer Academic Publishers, 1995.","DOI":"10.1007\/978-1-4757-2377-9"},{"key":"17_CR15","doi-asserted-by":"crossref","unstructured":"U. Helmke and J. Moore. Optimization and Dynamical Systems. Springer, 1994.","DOI":"10.1007\/978-1-4471-3467-1"},{"key":"17_CR16","doi-asserted-by":"crossref","unstructured":"V. Kac, editor. Infinite Dimensional Lie Groups with Applications. Mathematical Sciences Research Institute Publications 4. Springer, 1985.","DOI":"10.1007\/978-1-4612-1104-4"},{"key":"17_CR17","unstructured":"R. Kimmel and N. Sochen. Orientation diffusion or how to comb a porcupine. Technical Report 2000-02, CIS, 2000. Accepted to special issue on PDEs in Image Processing, Computer Vision, and Computer Graphics, Journal of Visual Communication and Image Representation, 2000."},{"key":"17_CR18","unstructured":"W. Klingenberg. Riemannian Geometry. de Gruyter Studies in Mathematics 1. Walter de Gruyter, 1982."},{"key":"17_CR19","doi-asserted-by":"crossref","unstructured":"P. Kornprobst, R. Deriche, and G. Aubert. Nonlinear operators in image restoration. In Proceedings of the International Conference on Computer Vision and Pattern Recognition, pages 325\u2013331, Puerto Rico, June 1997. IEEE Computer Society, IEEE.","DOI":"10.1109\/CVPR.1997.609344"},{"key":"17_CR20","doi-asserted-by":"crossref","unstructured":"S. Lang. Differential Manifolds. Springer, 1985.","DOI":"10.1007\/978-1-4684-0265-0"},{"key":"17_CR21","unstructured":"D. Le Bihan. Methods and applications of diffusion MRI. In I.R. Young, editor, Magnetic Resonance Imaging and Spectroscopy in Medicine and Biology. John Wiley and Sons, 2000."},{"key":"17_CR22","doi-asserted-by":"publisher","first-page":"577","DOI":"10.1002\/cpa.3160420503","volume":"42","author":"D. Mumford","year":"1989","unstructured":"D. Mumford and J. Shah. Optimal approximations by piecewise smooth functions and associated variational problems. Communications on Pure and Applied Mathematics, 42:577\u2013684, 1989.","journal-title":"Communications on Pure and Applied Mathematics"},{"issue":"3","key":"17_CR23","doi-asserted-by":"crossref","first-page":"457","DOI":"10.1109\/83.661195","volume":"7","author":"P. Perona","year":"1998","unstructured":"P. Perona. Orientation diffusions. IEEE Transactions on Image Processing, 7(3):457\u2013467, March 1998.","journal-title":"IEEE Transactions on Image Processing"},{"issue":"7","key":"17_CR24","doi-asserted-by":"crossref","first-page":"629","DOI":"10.1109\/34.56205","volume":"12","author":"P. Perona","year":"1990","unstructured":"P. Perona and J. Malik. Scale-space and edge detection using anisotropic diffusion. IEEE Transactions on Pattern Analysis and Machine Intelligence, 12(7):629\u2013639, July 1990.","journal-title":"IEEE Transactions on Pattern Analysis and Machine Intelligence"},{"key":"17_CR25","doi-asserted-by":"publisher","first-page":"259","DOI":"10.1016\/0167-2789(92)90242-F","volume":"60","author":"L. Rudin","year":"1992","unstructured":"L. Rudin, S. Osher, and E. Fatemi. Nonlinear total variation based noise removal algorithms. Physica D, 60:259\u2013268, 1992.","journal-title":"Physica D"},{"key":"17_CR26","doi-asserted-by":"crossref","unstructured":"G. Sapiro. Geometric Partial Differential Equations and Image Analysis. Cambridge University Press, 2001.","DOI":"10.1017\/CBO9780511626319"},{"key":"17_CR27","doi-asserted-by":"crossref","unstructured":"S. Smith. Optimization Techniques on Riemannian Manifolds. Hamiltonian and Gradient Flows, Algorithms and Control. American Mathematical Society, 1994, Fields Institute for Research in Mathematical Sciences, A. Bloch editor, 1994.","DOI":"10.1090\/fic\/003\/09"},{"issue":"3","key":"17_CR28","doi-asserted-by":"crossref","first-page":"310","DOI":"10.1109\/83.661181","volume":"7","author":"N. Sochen","year":"1998","unstructured":"N. Sochen, R. Kimmel, and R. Malladi. A geometrical framework for low level vision. IEEE Transaction on Image Processing, Special Issue on PDE based Image Processing, 7(3):310\u2013318, 1998.","journal-title":"IEEE Transaction on Image Processing, Special Issue on PDE based Image Processing"},{"issue":"2","key":"17_CR29","doi-asserted-by":"crossref","first-page":"149","DOI":"10.1023\/A:1008152115986","volume":"36","author":"B. Tang","year":"2000","unstructured":"B. Tang, G. Sapiro, and V. Caselles. Diffusion of general data on non-flat manifolds via harmonic maps theory: The direction diffusion case. The International Journal of Computer Vision, 36(2):149\u2013161, February 2000.","journal-title":"The International Journal of Computer Vision"},{"issue":"3","key":"17_CR30","doi-asserted-by":"publisher","first-page":"213","DOI":"10.1023\/A:1008001603737","volume":"28","author":"A. Trouv\u00e9","year":"1998","unstructured":"A. Trouv\u00e9. Diffeomorphisms groups and pattern matching in image analysis. International Journal of Computer Vision, 28(3):213\u201321, 1998.","journal-title":"International Journal of Computer Vision"},{"key":"17_CR31","unstructured":"D. Tschumperl\u00e9 and R. Deriche. Constrained and unconstrained PDE\u2019s for vector image restoration. In Ivar Austvoll, editor, Proceedings of the 10th Scandinavian Conference on Image Analysis, pages 153\u2013160, Bergen, Norway, June 2001."},{"key":"17_CR32","unstructured":"D. Tschumperl\u00e9 and R. Deriche. Diffusion tensor regularization with constraints preservation. In Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition, Kauai Marriott, Hawaii, December 2001."},{"key":"17_CR33","unstructured":"D. Tschumperl\u00e9 and R. Deriche. Regularization of orthonormal vector sets using coupled PDE\u2019s. In Proceedings of the 1st IEEE Workshop on Variational and Level Set Methods (VLSM\u201901), July 2001."},{"key":"17_CR34","unstructured":"B. Vemuri, Y. Chen, M. Rao, T. McGraw, T. Mareci, and Z. Wang. Fiber tract mapping from diffusion tensor MRI. In Proceedings of the 1st IEEE Workshop on Variational and Level Set Methods in Computer Vision (VLSM\u201901), July 2001."},{"key":"17_CR35","volume-title":"Anisotropic Diffusion in Image Processing","author":"J. Weickert","year":"1998","unstructured":"J. Weickert. Anisotropic Diffusion in Image Processing. Teubner-Verlag, Stuttgart, 1998."},{"key":"17_CR36","doi-asserted-by":"crossref","unstructured":"C.-F. Westin, S. Maier, B. Khidhir, P. Everett, F. Jolesz, and R. Kikinis. Image processing for diffusion tensor magnetic resonance imaging. In Proceedings of the Second International Conference on Medical Image Computing and Computer-Assisted Intervention (MICCAI\u201999), Springer-Verlag, 1999.","DOI":"10.1007\/10704282_48"}],"container-title":["Lecture Notes in Computer Science","Computer Vision \u2014 ECCV 2002"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/3-540-47969-4_17","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,1,16]],"date-time":"2025-01-16T21:07:44Z","timestamp":1737061664000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/3-540-47969-4_17"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2002]]},"ISBN":["9783540437451","9783540479697"],"references-count":36,"URL":"https:\/\/doi.org\/10.1007\/3-540-47969-4_17","relation":{},"ISSN":["0302-9743"],"issn-type":[{"type":"print","value":"0302-9743"}],"subject":[],"published":{"date-parts":[[2002]]},"assertion":[{"value":"29 April 2002","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}}]}}