{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,3,19]],"date-time":"2025-03-19T16:38:38Z","timestamp":1742402318124},"publisher-location":"Berlin, Heidelberg","reference-count":32,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"type":"print","value":"9783540250326"},{"type":"electronic","value":"9783540312727"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2006]]},"DOI":"10.1007\/3-540-31272-2_25","type":"book-chapter","created":{"date-parts":[[2007,6,25]],"date-time":"2007-06-25T02:36:54Z","timestamp":1182739014000},"page":"399-414","source":"Crossref","is-referenced-by-count":5,"title":["PDEs for Tensor Image Processing"],"prefix":"10.1007","author":[{"given":"Joachim","family":"Weickert","sequence":"first","affiliation":[]},{"given":"Christian","family":"Feddern","sequence":"additional","affiliation":[]},{"given":"Martin","family":"Welk","sequence":"additional","affiliation":[]},{"given":"Bernhard","family":"Burgeth","sequence":"additional","affiliation":[]},{"given":"Thomas","family":"Brox","sequence":"additional","affiliation":[]}],"member":"297","reference":[{"key":"25_CR1","doi-asserted-by":"publisher","first-page":"845","DOI":"10.1137\/0729052","volume":"29","author":"L. Alvarez","year":"1992","unstructured":"L. Alvarez, P.-L. Lions, and J.-M. Morel. Image selective smoothing and edge detection by nonlinear diffusion. II. SIAM Journal on Numerical Analysis, 29:845\u2013866, 1992.","journal-title":"SIAM Journal on Numerical Analysis"},{"key":"25_CR2","series-title":"Applied Mathematical Sciences","doi-asserted-by":"crossref","DOI":"10.1007\/b97428","volume-title":"Mathematical Problems in Image Processing: Partial Differential Equations and the Calculus of Variations","author":"G. Aubert","year":"2002","unstructured":"G. Aubert and P. Kornprobst. Mathematical Problems in Image Processing: Partial Differential Equations and the Calculus of Variations, volume 147 of Applied Mathematical Sciences. Springer, New York, 2002."},{"key":"25_CR3","series-title":"Technical Report","volume-title":"Nonlinear structure tensors","author":"T. Brox","year":"2004","unstructured":"T. Brox, J. Weickert, B. Burgeth, and P. Mr\u00e1zek. Nonlinear structure tensors. Technical Report 113, Dept. of Mathematics, Saarland University, Saarbr\u00fccken, Germany, October 2004."},{"key":"25_CR4","series-title":"Lecture Notes in Mathematics","doi-asserted-by":"crossref","DOI":"10.1007\/b10404","volume-title":"Geometric Curve Evolution and Image Processing","author":"F. Cao","year":"2003","unstructured":"F. Cao. Geometric Curve Evolution and Image Processing, volume 1805 of Lecture Notes in Mathematics. Springer, Berlin, 2003."},{"key":"25_CR5","doi-asserted-by":"publisher","first-page":"61","DOI":"10.1023\/A:1007979827043","volume":"22","author":"V. Caselles","year":"1997","unstructured":"V. Caselles, R. Kimmel, and G. Sapiro. Geodesic active contours. International Journal of Computer Vision, 22:61\u201379, 1997.","journal-title":"International Journal of Computer Vision"},{"key":"25_CR6","doi-asserted-by":"publisher","first-page":"1895","DOI":"10.1137\/0732085","volume":"32","author":"F. Catt\u00e9","year":"1992","unstructured":"F. Catt\u00e9, P.-L. Lions, J.-M. Morel, and T. Coll. Image selective smoothing and edge detection by nonlinear diffusion. SIAM Journal on Numerical Analysis, 32:1895\u20131909, 1992.","journal-title":"SIAM Journal on Numerical Analysis"},{"key":"25_CR7","doi-asserted-by":"publisher","first-page":"16","DOI":"10.1109\/ICIP.1994.413266","volume":"1","author":"A. Chambolle","year":"1994","unstructured":"A. Chambolle. Partial differential equations and image processing. In Proc. 1994 IEEE International Conference on Image Processing, volume 1, pp. 16\u201320, Austin, TX, November 1994. IEEE Computer Society Press.","journal-title":"Proc. 1994 IEEE International Conference on Image Processing"},{"key":"25_CR8","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"251","DOI":"10.1007\/3-540-47969-4_17","volume-title":"Computer Vision \u2014 ECCV 2002","author":"C. ChefdHotel","year":"2002","unstructured":"C. Chefd\u2019Hotel, D. Tschumperl\u00e9, R. Deriche, and O. Faugeras. Constrained flows of matrix-valued functions: Application to diffusion tensor regularization. In A. Heyden, G. Sparr, M. Nielsen, and P. Johansen, editors, Computer Vision \u2014 ECCV 2002, volume 2350 of Lecture Notes in Computer Science, pp. 251\u2013265. Springer, Berlin, 2002."},{"issue":"9","key":"25_CR9","doi-asserted-by":"publisher","first-page":"241","DOI":"10.1109\/97.863143","volume":"7","author":"D. H. Chung","year":"2000","unstructured":"D. H. Chung and G. Sapiro. On the level lines and geometry of vector-valued images. IEEE Signal Processing Letters, 7(9):241\u2013243, 2000.","journal-title":"IEEE Signal Processing Letters"},{"issue":"1","key":"25_CR10","doi-asserted-by":"publisher","first-page":"47","DOI":"10.1016\/j.media.2003.06.002","volume":"8","author":"O. Coulon","year":"2004","unstructured":"O. Coulon, D. C. Alexander, and S. A. Arridge. Diffusion tensor magnetic resonance image regularisation. Medical Image Analysis, 8(1):47\u201367, 2004.","journal-title":"Medical Image Analysis"},{"key":"25_CR11","doi-asserted-by":"publisher","first-page":"116","DOI":"10.1016\/0734-189X(86)90223-9","volume":"33","author":"S. Zenzo Di","year":"1986","unstructured":"S. Di Zenzo. A note on the gradient of a multi-image. Computer Vision, Graphics and Image Processing, 33:116\u2013125, 1986.","journal-title":"Computer Vision, Graphics and Image Processing"},{"key":"25_CR12","unstructured":"C. Feddern, J. Weickert, and B. Burgeth. Level-set methods for tensor-valued images. In O. Faugeras and N. Paragios, editors, Proc. Second IEEE Workshop on Geometric and Level Set Methods in Computer Vision, pp. 65\u201372, Nice, France, October 2003. INRIA."},{"key":"25_CR13","doi-asserted-by":"crossref","unstructured":"C. Feddern, J. Weickert, B. Burgeth, and M. Welk. Curvature-driven PDE methods for matrix-valued images. International Journal of Computer Vision, 2005. In press.","DOI":"10.1007\/s11263-006-6854-8"},{"key":"25_CR14","doi-asserted-by":"publisher","first-page":"221","DOI":"10.1109\/42.141646","volume":"11","author":"G. Gerig","year":"1992","unstructured":"G. Gerig, O. K\u00fcbler, R. Kikinis, and F. A. Jolesz. Nonlinear anisotropic filtering of MRI data. IEEE Transactions on Medical Imaging, 11:221\u2013232, 1992.","journal-title":"IEEE Transactions on Medical Imaging"},{"key":"25_CR15","first-page":"368","volume":"26","author":"T. Iijima","year":"1962","unstructured":"T. Iijima. Basic theory on normalization of pattern (in case of typical onedimensional pattern). Bulletin of the Electrotechnical Laboratory, 26:368\u2013388, 1962. In Japanese.","journal-title":"Bulletin of the Electrotechnical Laboratory"},{"key":"25_CR16","doi-asserted-by":"publisher","first-page":"321","DOI":"10.1007\/BF00133570","volume":"1","author":"M. Kass","year":"1988","unstructured":"M. Kass, A. Witkin, and D. Terzopoulos. Snakes: Active contour models. International Journal of Computer Vision, 1:321\u2013331, 1988.","journal-title":"International Journal of Computer Vision"},{"key":"25_CR17","doi-asserted-by":"publisher","first-page":"275","DOI":"10.1007\/BF00379537","volume":"134","author":"S. Kichenassamy","year":"1996","unstructured":"S. Kichenassamy, A. Kumar, P. Olver, A. Tannenbaum, and A. Yezzi. Conformal curvature flows: from phase transitions to active vision. Archive for Rational Mechanics and Analysis, 134:275\u2013301, 1996.","journal-title":"Archive for Rational Mechanics and Analysis"},{"key":"25_CR18","volume-title":"Numerical Geometry of Images: Theory, Algorithms, and Applications","author":"R. Kimmel","year":"2003","unstructured":"R. Kimmel. Numerical Geometry of Images: Theory, Algorithms, and Applications. Springer, New York, 2003."},{"key":"25_CR19","doi-asserted-by":"publisher","first-page":"318","DOI":"10.1016\/0262-8856(90)80008-H","volume":"8","author":"N. Nordstr\u00f6m","year":"1990","unstructured":"N. Nordstr\u00f6m. Biased anisotropic diffusion \u2014 a unified regularization and diffusion approach to edge detection. Image and Vision Computing, 8:318\u2013327, 1990.","journal-title":"Image and Vision Computing"},{"volume-title":"Geometric Level Set Methods in Imaging, Vision and Graphics","year":"2003","key":"25_CR20","unstructured":"S. Osher and N. Paragios, editors. Geometric Level Set Methods in Imaging, Vision and Graphics. Springer, New York, 2003."},{"key":"25_CR21","doi-asserted-by":"publisher","first-page":"919","DOI":"10.1137\/0727053","volume":"27","author":"S. Osher","year":"1990","unstructured":"S. Osher and L. I. Rudin. Feature-oriented image enhancement using shock filters. SIAM Journal on Numerical Analysis, 27:919\u2013940, 1990.","journal-title":"SIAM Journal on Numerical Analysis"},{"key":"25_CR22","doi-asserted-by":"publisher","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, 12:629\u2013639, 1990.","journal-title":"IEEE Transactions on Pattern Analysis and Machine Intelligence"},{"issue":"5","key":"25_CR23","doi-asserted-by":"publisher","first-page":"1772","DOI":"10.1137\/S0036139901384662","volume":"62","author":"T. Preu\u00dfer","year":"2002","unstructured":"T. Preu\u00dfer and M. Rumpf. A level set method for anisotropic geometric diffusion in 3D image processing. SIAM Journal on Applied Mathematics, 62(5):1772\u20131793, 2002.","journal-title":"SIAM Journal on Applied Mathematics"},{"key":"25_CR24","doi-asserted-by":"publisher","first-page":"817","DOI":"10.1109\/ICIP.1996.559624","volume-title":"Proc. 1996 IEEE International Conference on Image Processing","author":"G. Sapiro","year":"1996","unstructured":"G. Sapiro. Vector (self) snakes: a geometric framework for color, texture and multiscale image segmentation. In Proc. 1996 IEEE International Conference on Image Processing, volume 1, pp. 817\u2013820, Lausanne, Switzerland, September 1996."},{"key":"25_CR25","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511626319","volume-title":"Geometric Partial Differential Equations and Image Analysis","author":"G. Sapiro","year":"2001","unstructured":"G. Sapiro. Geometric Partial Differential Equations and Image Analysis. Cambridge University Press, Cambridge, UK, 2001."},{"issue":"1","key":"25_CR26","doi-asserted-by":"publisher","first-page":"43","DOI":"10.1023\/A:1008344608808","volume":"12","author":"O. Scherzer","year":"2000","unstructured":"O. Scherzer and J. Weickert. Relations between regularization and diffusion filtering. Journal of Mathematical Imaging and Vision, 12(1):43\u201363, February 2000.","journal-title":"Journal of Mathematical Imaging and Vision"},{"issue":"3","key":"25_CR27","doi-asserted-by":"publisher","first-page":"237","DOI":"10.1023\/A:1020870207168","volume":"50","author":"D. Tschumperl\u00e9","year":"2002","unstructured":"D. Tschumperl\u00e9 and R. Deriche. Orthonormal vector sets regularization with PDE\u2019s and applications. International Journal of Computer Vision, 50(3):237\u2013252, December 2002.","journal-title":"International Journal of Computer Vision"},{"key":"25_CR28","doi-asserted-by":"crossref","unstructured":"B. Vemuri, Y. Chen, M. Rao, T. McGraw, Z. Wang, and T. Mareci. Fiber tract mapping from diffusion tensor MRI. In Proc. First IEEE Workshop on Variational and Level Set Methods in Computer Vision, pp. 73\u201380, Vancouver, Canada, July 2001. IEEE Computer Society Press.","DOI":"10.1109\/VLSM.2001.938885"},{"key":"25_CR29","doi-asserted-by":"publisher","first-page":"228","DOI":"10.1109\/CVPR.2004.1315036","volume":"1","author":"Z. Wang","year":"2004","unstructured":"Z. Wang and B. C. Vemuri. An affine invariant tensor dissimilarity measure and its applications to tensor-valued image segmentation. In Proc. 2004 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, volume 1, pp. 228\u2013233, Washington, DC, June 2004. IEEE Computer Society Press.","journal-title":"Proc. 2004 IEEE Computer Society Conference on Computer Vision and Pattern Recognition"},{"key":"25_CR30","volume-title":"Anisotropic Diffusion in Image Processing","author":"J. Weickert","year":"1998","unstructured":"J. Weickert. Anisotropic Diffusion in Image Processing. Teubner, Stuttgart, 1998."},{"key":"25_CR31","series-title":"Contemporary Mathematics","doi-asserted-by":"crossref","first-page":"251","DOI":"10.1090\/conm\/313\/05378","volume-title":"Inverse Problems, Image Analysis, and Medical Imaging","author":"J. Weickert","year":"2002","unstructured":"J. Weickert and T. Brox. Diffusion and regularization of vector-and matrixvalued images. In M. Z. Nashed and O. Scherzer, editors, Inverse Problems, Image Analysis, and Medical Imaging, volume 313 of Contemporary Mathematics, pp. 251\u2013268. AMS, Providence, 2002."},{"key":"25_CR32","first-page":"142","volume-title":"Proc. 2001 IEEE International Conference on Image Processing","author":"R. T. Whitaker","year":"2001","unstructured":"R. T. Whitaker and X. Xue. Variable-conductance, level-set curvature for image denoising. In Proc. 2001 IEEE International Conference on Image Processing, pp. 142\u2013145, Thessaloniki, Greece, October 2001."}],"container-title":["Mathematics and Visualization","Visualization and Processing of Tensor Fields"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/3-540-31272-2_25.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,11,17]],"date-time":"2020-11-17T20:50:16Z","timestamp":1605646216000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/3-540-31272-2_25"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2006]]},"ISBN":["9783540250326","9783540312727"],"references-count":32,"URL":"https:\/\/doi.org\/10.1007\/3-540-31272-2_25","relation":{},"ISSN":["1612-3786"],"issn-type":[{"type":"print","value":"1612-3786"}],"subject":[],"published":{"date-parts":[[2006]]}}}