{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,22]],"date-time":"2026-08-22T04:52:24Z","timestamp":1787374344120,"version":"build-2736575974"},"publisher-location":"Berlin, Heidelberg","reference-count":89,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"value":"9783540631675","type":"print"},{"value":"9783540691969","type":"electronic"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[1997]]},"DOI":"10.1007\/3-540-63167-4_37","type":"book-chapter","created":{"date-parts":[[2012,2,26]],"date-time":"2012-02-26T23:14:43Z","timestamp":1330298083000},"page":"1-28","source":"Crossref","is-referenced-by-count":147,"title":["A review of nonlinear diffusion filtering"],"prefix":"10.1007","author":[{"given":"Joachim","family":"Weickert","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2005,6,8]]},"reference":[{"key":"1_CR1","first-page":"865","volume":"1","author":"S.T. Acton","year":"1996","unstructured":"S.T. Acton, Edge enhancement of infrared imagery by way of the anisotropic diffusion pyramid, Proc. IEEE Int. Conf. Image Processing (ICIP-96, Lausanne, Sept. 16\u201319, 1996), Vol. 1, 865\u2013868, 1996.","journal-title":"Proc. IEEE Int. Conf. Image Processing (ICIP-96, Lausanne, Sept. 16\u201319, 1996"},{"key":"1_CR2","first-page":"478","volume-title":"Anisotropic diffusion pyramids for image segmentation","author":"S.T. Acton","year":"1994","unstructured":"S.T. Acton, A.C. Bovik, M.M. Crawford, Anisotropic diffusion pyramids for image segmentation, Proc. IEEE Int. Conf. Image Processing (ICIP-94, Austin, Nov. 13\u201316, 1994), Vol. 3, IEEE Computer Society Press, Los Alamitos, 478\u2013482, 1994."},{"key":"1_CR3","doi-asserted-by":"crossref","first-page":"845","DOI":"10.1109\/IGARSS.1992.578273","volume":"2","author":"S.T. Acton","year":"1992","unstructured":"S.T. Acton, M.M. Crawford, A mean field solution to anisotropic edge detection of remotely sensed data, Proc. 12th Int. Geoscience and Remote Sensing Symposium (IGARSS '92, Houston, May 26\u201329, 1992), Vol. 2, 845\u2013847, 1992.","journal-title":"Proc. 12th Int. Geoscience and Remote Sensing Symposium (IGARSS '92, Houston, May 26\u201329, 1992)"},{"key":"1_CR4","unstructured":"L. Alvarez, J. Esclarin, Image quantization by nonlinear smoothing, L.I. Rudin, S.K. Bramble (Eds.), Investigative and trial image processing, SPIE Vol. 2567, 182\u2013192, 1995."},{"key":"1_CR5","doi-asserted-by":"crossref","first-page":"199","DOI":"10.1007\/BF00375127","volume":"123","author":"L. Alvarez","year":"1993","unstructured":"L. Alvarez, F. Guichard, P.-L. Lions, J.-M. Morel, Axioms and fundamental equations in image processing, Arch. Rational Mech. Anal., Vol. 123, 199\u2013257, 1993.","journal-title":"Arch. Rational Mech. Anal."},{"key":"1_CR6","volume-title":"Preprint No. 18\/1996","author":"E. B\u00e4nsch","year":"1996","unstructured":"E. B\u00e4nsch, K. Mikula, A coarsening finite element strategy in image selective smoothing, Preprint No. 18\/1996, Faculty of Mathematics, University of Freiburg, Hebelstr. 27, 79104 Freiburg, Germany, 1996; submitted to Computation and Visualization in Sciences."},{"key":"1_CR7","series-title":"Lecture Notes in Comp. Science, Vol. 719","doi-asserted-by":"crossref","first-page":"90","DOI":"10.1007\/3-540-57233-3_11","volume-title":"Computer analysis of images and patterns","author":"I. Bajla","year":"1993","unstructured":"I. Bajla, M. Maru\u0161iak, M. \u0160r\u00e1mek, Anisotropic filtering of MRI data based upon image gradient histogram, D. Chetverikov, W.G. Kropatsch (Eds.), Computer analysis of images and patterns, Lecture Notes in Comp. Science, Vol. 719, Springer, Berlin, 90\u201397, 1993."},{"key":"1_CR8","doi-asserted-by":"crossref","first-page":"1414","DOI":"10.1137\/0524082","volume":"24","author":"G.I. Barenblatt","year":"1993","unstructured":"G.I. Barenblatt, M. Bertsch, R. Dal Passo, M. Ughi, A degenerate pseudoparabolic regularization of a nonlinear forward-backward heat equation arising in the theory of heat and mass exchange in stably stratified turbulent shear flow, SIAM J. Math. Anal., Vol. 24, 1414\u20131439, 1993.","journal-title":"SIAM J. Math. Anal."},{"key":"1_CR9","volume-title":"master thesis","author":"B. Benhamouda","year":"1994","unstructured":"B. Benhamouda, Parameter adaptation for nonlinear diffusion in image processing, master thesis, Dept. of Mathematics, University of Kaiserslautern, P.O. Box 3049, 67653 Kaiserslautern, Germany, 1994."},{"key":"1_CR10","doi-asserted-by":"crossref","first-page":"474","DOI":"10.1109\/ICIP.1995.529749","volume":"1","author":"L. Blanc-F\u00e9raud","year":"1995","unstructured":"L. Blanc-F\u00e9raud, P. Charbonnier, G. Aubert, M. Barlaud, Nonlinear image processing: modelling and fast algorithm for regularization with edge detection, Proc. IEEE Int. Conf. Image Processing (ICIP-95, Washington, Oct. 22\u201325, 1995), Vol. 1, 474\u2013477, 1995.","journal-title":"Proc. IEEE Int. Conf. Image Processing (ICIP-95, Washington, Oct. 22\u201325, 1995)"},{"key":"1_CR11","volume-title":"Op\u00e9rateurs maximaux monotones et semi-groupes de contractions dans les espaces de Hilbert","author":"H. Brezis","year":"1973","unstructured":"H. Brezis, Op\u00e9rateurs maximaux monotones et semi-groupes de contractions dans les espaces de Hilbert, North Holland, Amsterdam, 1973."},{"key":"1_CR12","doi-asserted-by":"crossref","first-page":"182","DOI":"10.1137\/0729012","volume":"29","author":"F. Catt\u00e9","year":"1992","unstructured":"F. Catt\u00e9, P.-L. Lions, J.-M. Morel, T. Coll, Image selective smoothing and edge detection by nonlinear diffusion, SIAM J. Numer. Anal., Vol. 29, 182\u2013193, 1992.","journal-title":"SIAM J. Numer. Anal."},{"key":"1_CR13","first-page":"168","volume-title":"Two deterministic half-quadratic regularization algorithms for computed imaging","author":"P. Charbonnier","year":"1994","unstructured":"P. Charbonnier, L. Blanc-F\u00e9raud, G. Aubert, M. Barlaud, Two deterministic half-quadratic regularization algorithms for computed imaging, Proc. IEEE Int. Conf. Image Processing (ICIP-94, Austin, Nov. 13\u201316, 1994), Vol. 2, IEEE Computer Society Press, Los Alamitos, 168\u2013172, 1994."},{"key":"1_CR14","doi-asserted-by":"crossref","first-page":"403","DOI":"10.1109\/ICPR.1996.546058","volume":"A","author":"G. Cong","year":"1996","unstructured":"G. Cong, S.D. Ma, Nonlinear diffusion for early vision, Proc. 13th Int. Conf. Pattern Recognition (ICPR 13, Vienna, Aug. 25\u201330, 1996), Vol. A, 403\u2013406, 1996.","journal-title":"Proc. 13th Int. Conf. Pattern Recognition (ICPR 13, Vienna, Aug. 25\u201330, 1996)"},{"key":"1_CR15","first-page":"3","volume-title":"Diffusion approximation on neural networks and applications for image processing","author":"G.-H. Cottet","year":"1992","unstructured":"G.-H. Cottet, Diffusion approximation on neural networks and applications for image processing, F. Hodnett (Ed.), Proc. Sixth European Conf. on Mathematics in Industry, Teubner, Stuttgart, 3\u20139, 1992."},{"key":"1_CR16","doi-asserted-by":"crossref","first-page":"1131","DOI":"10.1142\/S0218339095001027","volume":"3","author":"G.-H. Cottet","year":"1995","unstructured":"G.-H. Cottet, Neural networks: Continuous approach and applications to image processing, J. Biological Systems, Vol. 3, 1131\u20131139, 1995.","journal-title":"J. Biological Systems"},{"key":"1_CR17","doi-asserted-by":"crossref","first-page":"481","DOI":"10.1109\/ICIP.1996.559538","volume":"1","author":"G.-H. Cottet","year":"1996","unstructured":"G.-H. Cottet, M. El Ayyadi, Nonlinear PDE operators with memory terms for image processing, Proc. IEEE Int. Conf. Image Processing (ICIP-96, Lausanne, Sept. 16\u201319, 1996), Vol. 1, 481\u2013483, 1996.","journal-title":"Proc. IEEE Int. Conf. Image Processing (ICIP-96, Lausanne, Sept. 16\u201319, 1996)"},{"key":"1_CR18","doi-asserted-by":"crossref","first-page":"659","DOI":"10.1090\/S0025-5718-1993-1195422-2","volume":"61","author":"G.-H. Cottet","year":"1993","unstructured":"G.-H. Cottet, L. Germain, Image processing through reaction combined with nonlinear diffusion, Math. Comp., Vol. 61, 659\u2013673, 1993.","journal-title":"Math. Comp."},{"key":"1_CR19","first-page":"290","volume":"2","author":"R. Deriche","year":"1995","unstructured":"R. Deriche, P. Kornprobst, G. Aubert, Optical-flow estimation while preserving its discontinuities: A variational approach, Proc. Second Asian Conf. Computer Vision (ACCV '95, Singapore, December 5\u20138, 1995), Vol. 2, 290\u2013295, 1995.","journal-title":"Proc. Second Asian Conf. Computer Vision (ACCV '95, Singapore, December 5\u20138, 1995)"},{"key":"1_CR20","unstructured":"R. Deriche, O. Faugeras, Les EDP en traitement des images et vision par ordinateur, Traitement du Signal, in press."},{"issue":"No.4","key":"1_CR21","doi-asserted-by":"crossref","first-page":"45","DOI":"10.1016\/S0041-5553(83)80127-X","volume":"23","author":"S. D. Magazieva","year":"1983","unstructured":"S.K. Dzhu Magazieva, Numerical study of a partial differential equation, U.S.S.R. Comput. Maths. Math. Phys., Vol. 23, No. 4, 45\u201349, 1983.","journal-title":"U.S.S.R. Comput. Maths. Math. Phys."},{"key":"1_CR22","series-title":"Lecture Notes in Comp. Science, Vol. 800","doi-asserted-by":"crossref","first-page":"427","DOI":"10.1007\/3-540-57956-7_46","volume-title":"Computer vision \u2014 ECCV '94","author":"P. Fiddelaers","year":"1994","unstructured":"P. Fiddelaers, E.J. Pauwels, L.J. Van Gool, Geometry-driven curve evolution, J.-O. Eklundh (Ed.), Computer vision \u2014 ECCV '94, Lecture Notes in Comp. Science, Vol. 800, Springer, Berlin, 427\u2013432, 1994."},{"key":"1_CR23","doi-asserted-by":"crossref","first-page":"276","DOI":"10.1109\/ICPR.1996.547430","volume":"D","author":"B. Fischl","year":"1996","unstructured":"B. Fischl, E.L. Schwartz, Adaptive nonlinear filtering for nonlinear diffusion approximation in image processing, Proc. 13th Int. Conf. Pattern Recognition (ICPR 13, Vienna, Aug. 25\u201330, 1996), Vol. D, 276\u2013280, 1996.","journal-title":"Proc. 13th Int. Conf. Pattern Recognition (ICPR 13, Vienna, Aug. 25\u201330, 1996)"},{"key":"1_CR24","doi-asserted-by":"crossref","DOI":"10.1007\/978-94-015-8845-4","volume-title":"The structure of scalar images","author":"L.M.J. Florack","year":"1997","unstructured":"L.M.J. Florack, The structure of scalar images, Kluwer, Dordrecht, 1997, to appear."},{"key":"1_CR25","doi-asserted-by":"crossref","first-page":"165","DOI":"10.1109\/ICASSP.1992.226250","volume":"3","author":"G.E. Ford","year":"1992","unstructured":"G.E. Ford, R.R. Estes, H. Chen, Scale-space analysis for image sampling and interpolation, Proc. IEEE Int. Conf. Acoustics, Speech and Signal Processing (ICASSP-92, San Francisco, March 23\u201326, 1992), Vol. 3, 165\u2013168, 1992.","journal-title":"Proc. IEEE Int. Conf. Acoustics, Speech and Signal Processing (ICASSP-92, San Francisco, March 23\u201326, 1992)"},{"key":"1_CR26","unstructured":"M.A. F\u00f6rstner, E. G\u00fclch, A fast operator for detection and precise location of distinct points, corners and centres of circular features, Proc. ISPRS Intercommission Conf. on Fast Processing of Photogrammetric Data, Interlaken, 1987."},{"key":"1_CR27","unstructured":"D.S. Fritsch, A medial description of greyscale image structure by gradient-limited diffusion, R.A. Robb (Ed.), Visualization in biomedical computing '92, SPIE Vol. 1808, 105\u2013117, 1992."},{"key":"1_CR28","volume-title":"Report No. 104","author":"J. Fr\u00f6hlich","year":"1994","unstructured":"J. Fr\u00f6hlich, J. Weickert, Image processing using a wavelet algorithm for nonlinear diffusion, Report No. 104, Laboratory of Technomathematics, University of Kaiserslautern, P.O. Box 3049, 67653 Kaiserslautern, Germany, 1994."},{"key":"1_CR29","doi-asserted-by":"crossref","first-page":"227","DOI":"10.1007\/BF00115697","volume":"6","author":"D. Geiger","year":"1991","unstructured":"D. Geiger, A. Yuille, A common framework for image segmentation, Int. J. Comput. Vision, Vol. 6, 227\u2013243, 1991.","journal-title":"Int. J. Comput. Vision"},{"key":"1_CR30","doi-asserted-by":"crossref","first-page":"367","DOI":"10.1109\/34.120331","volume":"14","author":"D. Geman","year":"1992","unstructured":"D. Geman, G. Reynolds, Constrained restoration and the recovery of discontinuities, IEEE Trans. Pattern Anal. Mach. Intell., Vol. 14, 367\u2013383, 1992.","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"1_CR31","doi-asserted-by":"crossref","first-page":"221","DOI":"10.1109\/42.141646","volume":"11","author":"G. Gerig","year":"1992","unstructured":"G. Gerig, O. K\u00fcbler, R. Kikinis, F.A. Jolesz, Nonlinear anisotropic filtering of MRI data, IEEE Trans. Medical Imaging, Vol. 11, 221\u2013232, 1992.","journal-title":"IEEE Trans. Medical Imaging"},{"key":"1_CR32","doi-asserted-by":"crossref","first-page":"398","DOI":"10.1109\/VLSISP.1994.574764","volume":"7","author":"T. Gijbels","year":"1994","unstructured":"T. Gijbels, P. Six, L. Van Gool, F. Catthoor, H. De Man, A. Oosterlinck, A VLSI-architecture for parallel non-linear diffusion with applications in vision, Proc. IEEE Workshop on VLSI Signal Processing, Vol. 7, 398\u2013707, 1994.","journal-title":"Proc. IEEE Workshop on VLSI Signal Processing"},{"key":"1_CR33","volume-title":"Geometry-driven diffusion in computer vision","year":"1994","unstructured":"B.M. ter Haar Romeny (Ed.), Geometry-driven diffusion in computer vision, Kluwer, Dordrecht, 1994."},{"key":"1_CR34","doi-asserted-by":"crossref","first-page":"299","DOI":"10.2307\/1999317","volume":"278","author":"K. H\u00f6llig","year":"1983","unstructured":"K. H\u00f6llig, Existence of infinitely many solutions for a forward-backward heat equation, Trans. Amer. Math. Soc., Vol. 278, 299\u2013316, 1983.","journal-title":"Trans. Amer. Math. Soc."},{"key":"1_CR35","first-page":"204","volume-title":"Representations based on zero-crossings in scale space","author":"R.A. Hummel","year":"1986","unstructured":"R.A. Hummel, Representations based on zero-crossings in scale space, Proc. IEEE Comp. Soc. Conf. Computer Vision and Pattern Recognition (CVPR '86, Miami Beach, June 22\u201326, 1986), IEEE Computer Society Press, Washington, 204\u2013209, 1986."},{"key":"1_CR36","first-page":"368","volume":"26","author":"T. Iijima","year":"1962","unstructured":"T. Iijima, Basic theory of pattern normalization (for the case of a typical one-dimensional pattern), Bulletin of the Electrotechnical Laboratory, Vol. 26, 368\u2013388, 1962 (in Japanese).","journal-title":"Bulletin of the Electrotechnical Laboratory"},{"key":"1_CR37","first-page":"195","volume-title":"Saliency maps and attention selection in scale and spatial coordinates: an information theoretic approach","author":"M. J\u00e4gersand","year":"1995","unstructured":"M. J\u00e4gersand, Saliency maps and attention selection in scale and spatial coordinates: an information theoretic approach, Proc. Fifth Int. Conf. on Computer Vision (ICCV '95, Cambridge, June 20\u201323, 1995), IEEE Computer Society Press, Los Alamitos, 195\u2013202, 1995."},{"key":"1_CR38","doi-asserted-by":"crossref","first-page":"47","DOI":"10.1016\/0168-9274(95)00008-I","volume":"17","author":"J. Ka\u010dur","year":"1995","unstructured":"J. Ka\u010dur, K. Mikula, Solution of nonlinear diffusion appearing in image smoothing and edge detection, Appl. Num. Math., Vol. 17, 47\u201359, 1995.","journal-title":"Appl. Num. Math."},{"key":"1_CR39","series-title":"Lecture Notes in Control and Information Sciences, Vol. 219","doi-asserted-by":"crossref","first-page":"119","DOI":"10.1007\/3-540-76076-8_124","volume-title":"ICAOS '96: Images, wavelets and PDEs","author":"S. Kichenassamy","year":"1996","unstructured":"S. Kichenassamy, Nonlinear diffusions and hyperbolic smoothing for edge enhancement, M.-O. Berger, R. Deriche, I. Herlin, J. Jaffr\u00e9, J.-M. Morel (Eds.), ICAOS '96: Images, wavelets and PDEs, Lecture Notes in Control and Information Sciences, Vol. 219, Springer, London, 119\u2013124, 1996."},{"key":"1_CR40","doi-asserted-by":"crossref","unstructured":"S. Kichenassamy, The Perona-Malik paradox, SIAM J. Appl. Math., to appear.","DOI":"10.1137\/S003613999529558X"},{"key":"1_CR41","doi-asserted-by":"crossref","first-page":"363","DOI":"10.1007\/BF00336961","volume":"50","author":"J.J. Koenderink","year":"1984","unstructured":"J.J. Koenderink, The structure of images, Biol. Cybern., Vol. 50, 363\u2013370, 1984.","journal-title":"Biol. Cybern."},{"key":"1_CR42","doi-asserted-by":"crossref","first-page":"576","DOI":"10.1109\/34.387504","volume":"17","author":"S.Z. Li","year":"1995","unstructured":"S.Z. Li, On dis continuity-adaptive smoothness priors in computer vision, IEEE Trans. Pattern Anal. Mach. Intell., Vol. 17, 576\u2013586, 1995.","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"1_CR43","doi-asserted-by":"crossref","first-page":"1029","DOI":"10.1016\/0031-3203(94)90142-2","volume":"27","author":"X. Li","year":"1994","unstructured":"X. Li, T. Chen, Nonlinear diffusion with multiple edginess thresholds, Pattern Recognition, Vol. 27, 1029\u20131037, 1994.","journal-title":"Pattern Recognition"},{"key":"1_CR44","first-page":"1872","volume":"14","author":"C. Lamberti","year":"1992","unstructured":"C. Lamberti, M. Sitta, F. Sgallari, Improvements to the anisotropic diffusion model for 2-D echo image processing, Proc. Annual Int. Conf. of the IEEE Engineering in Medicine and Biology Society, Vol. 14, 1872\u20131873, 1992.","journal-title":"Proc. Annual Int. Conf. of the IEEE Engineering in Medicine and Biology Society"},{"key":"1_CR45","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4757-6465-9","volume-title":"Scale-space theory in computer vision","author":"T. Lindeberg","year":"1994","unstructured":"T. Lindeberg, Scale-space theory in computer vision, Kluwer, Boston, 1994."},{"key":"1_CR46","volume-title":"Research Note 95-72","author":"P. Lobel","year":"1996","unstructured":"P. Lobel, L. Blanc-F\u00e9raud, C. Pichot, M. Barlaud, A new regularization scheme for inverse scattering, Research Note 95-72, I3S Laboratory, University of Nice-Sopia Antipolis, B\u00e2t. 4, 250 rue Albert Einstein, Sophia Antipolis, 06560 Valbonne, France, 1996; submitted to Inverse Problems."},{"key":"1_CR47","unstructured":"M.H. Loew, J. Rosenman, J. Chen, A clinical tool for enhancement of portal images, M.H. Loew (Ed.), Image processing, SPIE Vol. 2167, 543\u2013550, 1994."},{"key":"1_CR48","doi-asserted-by":"crossref","first-page":"2800","DOI":"10.1109\/23.340650","volume":"41","author":"D.-S. Luo","year":"1994","unstructured":"D.-S. Luo, M.A. King, S. Glick, Local geometry variable conductance diffusion for post-reconstruction filtering, IEEE Trans. Nuclear Sci., Vol. 41, 2800\u20132806, 1994.","journal-title":"IEEE Trans. Nuclear Sci."},{"key":"1_CR49","first-page":"408","volume":"55","author":"J.L. Marroquin","year":"1993","unstructured":"J.L. Marroquin, Deterministic interactive particle models for image processing and computer graphics, CVGIP: Graphical Models and Image Processing, Vol. 55, 408\u2013417, 1993.","journal-title":"CVGIP: Graphical Models and Image Processing"},{"key":"1_CR50","doi-asserted-by":"crossref","unstructured":"W.J. Niessen, K.L. Vincken, J.A. Weickert, M.A. Viergever, Nonlinear multiscale representations for image segmentation, Computer Vision and Image Understanding, 1997, in press.","DOI":"10.1006\/cviu.1997.0614"},{"key":"1_CR51","doi-asserted-by":"crossref","first-page":"826","DOI":"10.1109\/34.149593","volume":"14","author":"M. Nitzberg","year":"1992","unstructured":"M. Nitzberg, T. Shiota, Nonlinear image filtering with edge and corner enhancement, IEEE Trans. Pattern Anal. Mach. Intell., Vol. 14, 826\u2013833, 1992.","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"1_CR52","doi-asserted-by":"crossref","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 Vision Comput., Vol. 8, 318\u2013327, 1990.","journal-title":"Image Vision Comput."},{"key":"1_CR53","doi-asserted-by":"crossref","first-page":"47","DOI":"10.1007\/978-94-015-8749-5_4","volume-title":"Three-dimensional image reconstruction in radiation and nuclear medicine","author":"E. Payot","year":"1996","unstructured":"E. Payot, R. Guillemaud, Y. Trousset, F. Preteux, An adaptive and constrained model for 3D X-ray vascular reconstruction, P. Grangeat, J.-L. Amans (Eds.), Three-dimensional image reconstruction in radiation and nuclear medicine, Kluwer, Dordrecht, 47\u201357, 1996."},{"key":"1_CR54","first-page":"16","volume-title":"Scale space and edge detection using anisotropic diffusion","author":"P. Perona","year":"1987","unstructured":"P. Perona, J. Malik, Scale space and edge detection using anisotropic diffusion, Proc. IEEE Comp. Soc. Workshop on Computer Vision (Miami Beach, Nov. 30\u2013Dec. 2, 1987), IEEE Computer Society Press, Washington, 16\u201322, 1987."},{"key":"1_CR55","doi-asserted-by":"crossref","unstructured":"P. Perona, J. Malik, A network for multiscale image segmentation, Proc. IEEE Int. Symp. Circuits and Systems (ISCAS-88, Espoo, June 7\u20139, 1988), 2565\u20132568, 1988.","DOI":"10.1109\/ISCAS.1988.15465"},{"key":"1_CR56","doi-asserted-by":"crossref","first-page":"629","DOI":"10.1109\/34.56205","volume":"12","author":"P. Perona","year":"1990","unstructured":"P. Perona, J. Malik, Scale space and edge detection using anisotropic diffusion, IEEE Trans. Pattern Anal. Mach. Intell., Vol. 12, 629\u2013639, 1990.","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"1_CR57","first-page":"72","volume-title":"Geometry-driven diffusion in computer vision","author":"P. Perona","year":"1994","unstructured":"P. Perona, T. Shiota, J. Malik, Anisotropic diffusion, B.M. ter Haar Romeny (Ed.), Geometry-driven diffusion in computer vision, Kluwer, Dordrecht, 72\u201392, 1994."},{"key":"1_CR58","doi-asserted-by":"crossref","first-page":"298","DOI":"10.1175\/1520-0485(1977)007<0298:TGOSFB>2.0.CO;2","volume":"7","author":"E.S. Posmentier","year":"1977","unstructured":"E.S. Posmentier, The generation of salinity finestructure by vertical diffusion, J. Phys. Oceanogr., Vol. 7, 298\u2013300, 1977.","journal-title":"J. Phys. Oceanogr."},{"key":"1_CR59","unstructured":"I. Rambaux, P. Gar\u00e7on, Nonlinear anisotropic diffusion filtering of 3D images, project work, D\u00e9partement G\u00e9nie Math\u00e9matique, INSA de Rouen and Laboratory of Technomathematics, University of Kaiserslautern, 1994."},{"key":"1_CR60","first-page":"157","volume":"53","author":"A.R. Rao","year":"1991","unstructured":"A.R. Rao, B.G. Schunck, Computing oriented texture fields, CVGIP: Graphical Models and Image Processing, Vol. 53, 157\u2013185, 1991.","journal-title":"CVGIP: Graphical Models and Image Processing"},{"key":"1_CR61","series-title":"Lecture Notes in Comp. Science, Vol. 1064","doi-asserted-by":"crossref","first-page":"439","DOI":"10.1007\/BFb0015556","volume-title":"Computer vision \u2014 ECCV '96, Volume I","author":"L. Robert","year":"1996","unstructured":"L. Robert, R. Deriche, Dense depth map reconstruction: A minimization and regularization approach which preserves discontinuities, B. Baxton, R. Cipolla (Eds.), Computer vision \u2014 ECCV '96, Volume I, Lecture Notes in Comp. Science, Vol. 1064, Springer, Berlin, 439\u2013451, 1996."},{"key":"1_CR62","doi-asserted-by":"crossref","first-page":"189","DOI":"10.1007\/BF01249896","volume":"4","author":"C. Schnorr","year":"1994","unstructured":"C. Schnorr, Unique reconstruction of piecewise smooth images by minimizing strictly convex non-quadratic functionals, J. Math. Imag. Vision, Vol. 4, 189\u2013198, 1994.","journal-title":"J. Math. Imag. Vision"},{"key":"1_CR63","first-page":"661","volume-title":"Segmentation of visual motion by minimizing convex non-quadratic functionals","author":"C. Schnorr","year":"1994","unstructured":"C. Schnorr, Segmentation of visual motion by minimizing convex non-quadratic functionals, Proc. 12th Int. Conf. Pattern Recognition (ICPR 12, Jerusalem, Oct. 9\u201313, 1994), Vol. A, IEEE Computer Society Press, Los Alamitos, 661\u2013663, 1994."},{"key":"1_CR64","series-title":"Lecture Notes in Control and Information Sciences, Vol. 219","doi-asserted-by":"crossref","first-page":"201","DOI":"10.1007\/3-540-76076-8_133","volume-title":"ICAOS '96: Images, wavelets and PDEs","author":"C. Schnorr","year":"1996","unstructured":"C. Schnorr, Convex variational segmentation of multi-channel images, M.-O. Berger, R. Deriche, I. Herlin, J. Jaffr\u00e9, J.-M. Morel (Eds.), ICAOS '96: Images, wavelets and PDEs, Lecture Notes in Control and Information Sciences, Vol. 219, Springer, London, 201\u2013207, 1996."},{"key":"1_CR65","doi-asserted-by":"crossref","unstructured":"J. Sijbers, P. Scheunders, M. Verhoye, A. Van der Linden, D. Van Dyck, E. Raman, Watershed-based segmentation of 3D MR data for volume quantization, Magnetic Resonance Imaging, Vol. 15, No. 4, 1997; to appear.","DOI":"10.1016\/S0730-725X(97)00033-7"},{"key":"1_CR66","doi-asserted-by":"crossref","first-page":"620","DOI":"10.1109\/34.387509","volume":"17","author":"W. Snyder","year":"1995","unstructured":"W. Snyder, Y.-S. Han, G. Bilbro, R. Whitaker, S. Pizer, Image relaxation: Restoration and feature extraction, IEEE Trans. Pattern Anal. Mach. Intell., Vol. 17, 620\u2013624, 1995.","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"1_CR67","doi-asserted-by":"crossref","first-page":"900","DOI":"10.1109\/ICPR.1996.546154","volume":"A","author":"J. Sporring","year":"1996","unstructured":"J. Sporring, The entropy of scale-space, Proc. 13th Int. Conf. Pattern Recognition (ICPR 13, Vienna, Aug. 25\u201330, 1996), Vol. A, 900\u2013904, 1996.","journal-title":"Proc. 13th Int. Conf. Pattern Recognition (ICPR 13, Vienna, Aug. 25\u201330, 1996)"},{"key":"1_CR68","volume-title":"Gaussian scale-space theory","year":"1997","unstructured":"J. Sporring, M. Nielsen, L. Florack, P. Johansen (Eds.), Gaussian scale-space theory, Kluwer, Dordrecht, 1997."},{"key":"1_CR69","unstructured":"J. Sporring, J. Weickert, On generalized entropies and scale-space, this volume."},{"key":"1_CR70","volume-title":"Ph.D. thesis","author":"R. Sprengel","year":"1995","unstructured":"R. Sprengel, Entwurf und Analyse nichtlinearer Diffusionsverfahren f\u00fcr die Bildverarbeitung, Ph.D. thesis, Dept. of Computer Science, University of Hamburg, Germany, 1995."},{"key":"1_CR71","unstructured":"E. Steen, B. Olstad, Scale-space and boundary detection in ultrasonic imaging using nonlinear signal-adaptive anisotropic diffusion, M.H. Loew (Ed.), Image processing, SPIE Vol. 2167, 116\u2013127, 1994."},{"key":"1_CR72","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-86405-6","volume-title":"Differential and integral inequalities","author":"W. Walter","year":"1970","unstructured":"W. Walter, Differential and integral inequalities, Springer, Berlin, 1970."},{"key":"1_CR73","first-page":"355","volume-title":"Anisotropic diffusion filters for image processing based quality control","author":"J. Weickert","year":"1994","unstructured":"J. Weickert, Anisotropic diffusion filters for image processing based quality control, A. Fasano, M. Primicerio (Eds.), Proc. Seventh European Conf. on Mathematics in Industry, Teubner, Stuttgart, 355\u2013362, 1994."},{"key":"1_CR74","series-title":"Lecture Notes in Comp. Science, Vol. 970","doi-asserted-by":"crossref","first-page":"230","DOI":"10.1007\/3-540-60268-2_301","volume-title":"Computer analysis of images and patterns","author":"J. Weickert","year":"1995","unstructured":"J. Weickert, Multiscale texture enhancement, V. Hlav\u00e1\u010d, R. \u0160\u00e1ra (Eds.), Computer analysis of images and patterns, Lecture Notes in Comp. Science, Vol. 970, Springer, Berlin, 230\u2013237, 1995."},{"key":"1_CR75","volume-title":"Report No. 110","author":"J. Weickert","year":"1994","unstructured":"J. Weickert, Scale-space properties of nonlinear diffusion filtering with a diffusion tensor, Report No. 110, Laboratory of Technomathematics, University of Kaiserslautern, P.O. Box 3049, 67653 Kaiserslautern, Germany, 1994."},{"key":"1_CR76","doi-asserted-by":"crossref","first-page":"221","DOI":"10.1007\/978-3-7091-6586-7_13","volume-title":"Theoretical foundations of computer vision, Computing Suppl. 11","author":"J. Weickert","year":"1996","unstructured":"J. Weickert, Theoretical foundations of anisotropic diffusion in image processing, W. Kropatsch, R. Klette, F. Solina (Eds.), Theoretical foundations of computer vision, Computing Suppl. 11, Springer, Wien, 221\u2013236, 1996."},{"key":"1_CR77","series-title":"Lecture Notes in Control and Information Sciences, Vol. 219","doi-asserted-by":"crossref","first-page":"111","DOI":"10.1007\/3-540-76076-8_123","volume-title":"ICAOS '96: Images, wavelets and PDEs","author":"J. Weickert","year":"1996","unstructured":"J. Weickert, Nonlinear diffusion scale-spaces: From the continuous to the discrete setting, M.-O. Berger, R. Deriche, I. Herlin, J. Jaffr\u00e9, J.-M. Morel (Eds.), ICAOS '96: Images, wavelets and PDEs, Lecture Notes in Control and Information Sciences, Vol. 219, Springer, London, 111\u2013118, 1996."},{"key":"1_CR78","unstructured":"J. Weickert, Coherence-enhancing diffusion of colour images, Proc. Seventh National Symposium on Pattern Recognition and Image Analysis (VII NSPRIA, Barcelona, April 21\u201325, 1997), in press."},{"key":"1_CR79","unstructured":"J. Weickert, Recursive separable schemes for nonlinear diffusion filters, this volume."},{"key":"1_CR80","volume-title":"Anisotropic diffusion in image processing","author":"J. Weickert","year":"1997","unstructured":"J. Weickert, Anisotropic diffusion in image processing, Teubner Verlag, Stuttgart, 1997, to appear."},{"key":"1_CR81","volume-title":"A semidiscrete nonlinear scale-space theory and its relation to the Perona-Malik paradox","author":"J. Weickert","year":"1997","unstructured":"J. Weickert, B. Benhamouda, A semidiscrete nonlinear scale-space theory and its relation to the Perona-Malik paradox, F. Solina, W.G. Kropatsch, R. Klette, R. Bajcsy (Eds.), Theoretical foundations of computer vision (TFCV '96, Dagstuhl, March 18\u201322, 1996), Springer, Wien, 1997, in press."},{"key":"1_CR82","unstructured":"J. Weickert, B.M. ter Haar Romeny, A. Lopez, W.J. van Enk, Orientation analysis by coherence-enhancing diffusion, Proc. Symp. Real World Computing (RWC '97, Tokyo, Jan. 29\u201331, 1997), 96\u2013103, 1997."},{"key":"1_CR83","volume-title":"Gaussian scale-space theory","author":"J. Weickert","year":"1997","unstructured":"J. Weickert, S. Ishikawa, A. Imiya, On the history of Gaussian scale-space axiomatics, J. Sporring, M. Nielsen, L. Florack, P. Johansen (Eds.), Gaussian scale-space theory, Kluwer, Dordrecht, 1997, in press."},{"key":"1_CR84","unstructured":"J. Weickert, K.J. Zuiderveld, B.M. ter Haar Romeny, W.J. Niessen, Parallel implementations of AOS schemes: A fast way of nonlinear diffusion filtering, submitted."},{"key":"1_CR85","doi-asserted-by":"crossref","first-page":"111","DOI":"10.1006\/ciun.1993.1007","volume":"57","author":"R.T. Whitaker","year":"1993","unstructured":"R.T. Whitaker, Geometry limited diffusion in the characterization of geometric patches in images, CVGIP: Image Understanding, Vol. 57, 111\u2013120, 1993.","journal-title":"CVGIP: Image Understanding"},{"key":"1_CR86","doi-asserted-by":"crossref","first-page":"93","DOI":"10.1007\/978-94-017-1699-4_4","volume-title":"Geometry-driven diffusion in computer vision","author":"R. Whitaker","year":"1994","unstructured":"R. Whitaker, G. Gerig, Vector-valued diffusion, B.M. ter Haar Romeny (Ed.), Geometry-driven diffusion in computer vision, Kluwer, Dordrecht, 93\u2013134, 1994."},{"key":"1_CR87","doi-asserted-by":"crossref","first-page":"99","DOI":"10.1006\/ciun.1993.1006","volume":"57","author":"R.T. Whitaker","year":"1993","unstructured":"R.T. Whitaker, S.M. Pizer, A multi-scale approach to nonuniform diffusion, CVGIP: Image Understanding, Vol. 57, 99\u2013110, 1993.","journal-title":"CVGIP: Image Understanding"},{"key":"1_CR88","first-page":"1019","volume":"2","author":"A.P. Witkin","year":"1983","unstructured":"A.P. Witkin, Scale-space filtering, Proc. Eighth Int. Joint Conf. on Artificial Intelligence (IJCAI '83, Karlsruhe, Aug. 8\u201312, 1983), Vol. 2, 1019\u20131022, 1983.","journal-title":"Proc. Eighth Int. Joint Conf. on Artificial Intelligence (IJCAI '83, Karlsruhe, Aug. 8\u201312, 1983)"},{"key":"1_CR89","doi-asserted-by":"crossref","first-page":"461","DOI":"10.1109\/ICIP.1996.560885","volume":"2","author":"Y.-L. You","year":"1996","unstructured":"Y.-L. You, M. Kaveh, Anisotropic blind image restoration, Proc. IEEE Int. Conf. Image Processing (ICIP-96, Lausanne, Sept. 16\u201319, 1996), Vol. 2, 461\u2013464, 1996.","journal-title":"Proc. IEEE Int. Conf. Image Processing (ICIP-96, Lausanne, Sept. 16\u201319, 1996)"}],"container-title":["Lecture Notes in Computer Science","Scale-Space Theory in Computer Vision"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/3-540-63167-4_37.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,4,28]],"date-time":"2021-04-28T01:42:31Z","timestamp":1619574151000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/3-540-63167-4_37"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1997]]},"ISBN":["9783540631675","9783540691969"],"references-count":89,"URL":"https:\/\/doi.org\/10.1007\/3-540-63167-4_37","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"value":"0302-9743","type":"print"},{"value":"1611-3349","type":"electronic"}],"subject":[],"published":{"date-parts":[[1997]]}}}