{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,6,12]],"date-time":"2025-06-12T11:10:02Z","timestamp":1749726602757,"version":"3.41.0"},"reference-count":268,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2001,11,1]],"date-time":"2001-11-01T00:00:00Z","timestamp":1004572800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2001,11,1]],"date-time":"2001-11-01T00:00:00Z","timestamp":1004572800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Mathematical Imaging and Vision"],"published-print":{"date-parts":[[2001,11]]},"DOI":"10.1023\/a:1012282305022","type":"journal-article","created":{"date-parts":[[2002,12,23]],"date-time":"2002-12-23T12:42:15Z","timestamp":1040647335000},"page":"127-168","source":"Crossref","is-referenced-by-count":5,"title":["A Dynamic Scale\u2013Space Paradigm"],"prefix":"10.1007","volume":"15","author":[{"given":"Alfons H.","family":"Salden","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Bart M. Ter Haar","family":"Romeny","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Max A.","family":"Viergever","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","reference":[{"key":"356826_CR1","doi-asserted-by":"crossref","first-page":"309","DOI":"10.1090\/S0002-9947-1965-0175106-9","volume":"114","author":"R.L. Adler","year":"1965","unstructured":"R.L. Adler, A.G.Konheim, and M.H. McAndrew, \u201cTopological entropy, \u201d Amer. Math. Soc., Vol. 114, pp. 309\u2013319, 1965.","journal-title":"Amer. Math. Soc."},{"key":"356826_CR2","first-page":"135","volume":"315","author":"L. Alvarez","year":"1992","unstructured":"L. Alvarez, F. Guichard, P.L. Lions, and J.M. Morel, \u201cAxiomes et \u00e9quations fondamentales du traitement d'images, \u201d C. R. Acad. Sci. Paris, Vol. 315, pp. 135\u2013138, 1992.","journal-title":"C. R. Acad. Sci. Paris"},{"key":"356826_CR3","first-page":"265","volume":"315","author":"L. Alvarez","year":"1992","unstructured":"L. Alvarez, F. Guichard, P.L. Lions, and J.M. Morel, \u201cAxiomatisation et nouveaux operateurs de la morphologie mathematique, \u201d C. R. Acad. Sci. Paris, Vol. 315, pp. 265\u2013268, 1992.","journal-title":"C. R. Acad. Sci. Paris"},{"key":"356826_CR4","unstructured":"L. Alvarez, F. Guichard, P.L. Lions, and J.M. Morel, \u201c\u00c9quations fondamentales de l'analyse de films, \u201d C. R. Acad. Sci. Paris, 1992."},{"key":"356826_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, and J.M. Morel, \u201cAxioms and fundamental equations of image processing, \u201d Arch. for Rational Mechanics, Vol. 123, pp. 199\u2013257, 1993.","journal-title":"Arch. for Rational Mechanics"},{"key":"356826_CR6","doi-asserted-by":"crossref","first-page":"229","DOI":"10.1007\/978-94-017-1699-4_10","volume-title":"Geometry-Driven Diffusion in Computer Vision","author":"L. Alvarez","year":"1994","unstructured":"L. Alvarez and J.M. Morel, \u201cMorphological approach to multiscale analysis, \u201d in Geometry-Driven Diffusion in Computer Vision, Kluwer Academic Publishers: Dordrecht, 1994, pp. 229\u2013254."},{"key":"356826_CR7","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"235","DOI":"10.1007\/3-540-48236-9_21","volume-title":"Scale-Space Theories in Computer Vision","author":"A. Alvarez","year":"1999","unstructured":"A. Alvarez, J. Weickert, and J. S\u00e1nchez, \u201cA scale-space approach to nonlocal optical flow calculations, \u201d in Scale-Space Theories in Computer Vision, Lecture Notes in Computer Science, Springer: Berlin, 1999, Vol. 1682, pp. 235\u2013246."},{"key":"356826_CR8","doi-asserted-by":"crossref","first-page":"837","DOI":"10.4310\/jdg\/1214458529","volume":"43","author":"L. Ambrosio","year":"1996","unstructured":"L. Ambrosio and H.M. Soner, \u201cLevel set approach to mean curvature flow in arbitrary co-dimension, \u201d Journal of Differential Geometry, Vol. 43, pp. 837\u2013865, 1996.","journal-title":"Journal of Differential Geometry"},{"key":"356826_CR9","volume-title":"Field Theory, the Renormalisation and Critical Phenomena","author":"P.J. Amit","year":"1978","unstructured":"P.J. Amit, Field Theory, the Renormalisation and Critical Phenomena, McGraw-Hill: New York, 1978."},{"key":"356826_CR10","doi-asserted-by":"crossref","first-page":"2869","DOI":"10.1103\/PhysRevLett.78.2869","volume":"78","author":"S.C. Anco","year":"1997","unstructured":"S.C. Anco and G. Bluman, \u201cDirect construction of conservation laws from field equations, \u201d Physical Review Letters, Vol. 78, pp. 2869\u20132873, 1997.","journal-title":"Physical Review Letters"},{"key":"356826_CR11","unstructured":"S.C. Anco and G. Bluman, \u201cDirect construction method for conservation laws of partial differential equations, \u201d 1998."},{"key":"356826_CR12","doi-asserted-by":"crossref","first-page":"245","DOI":"10.1017\/S0956792598003477","volume":"9","author":"S.C. Anco","year":"1998","unstructured":"S.C. Anco and G. Bluman, \u201cIntegrating factors and first integrals for ordinary differential equations, \u201d European Journal of Applied Mathematics, Vol. 9, pp. 245\u2013259, 1998.","journal-title":"European Journal of Applied Mathematics"},{"key":"356826_CR13","doi-asserted-by":"crossref","first-page":"26","DOI":"10.1109\/TPAMI.1986.4767749","volume":"8","author":"J. Babaud","year":"1986","unstructured":"J. Babaud, A.P. Witkin, M. Baudin, and R.O. Duda, \u201cUniqueness of the Gaussian kernel for scale-space filtering, \u201d IEEE Trans. Pattern Analysis and Machine Intelligence, Vol. 8, pp. 26\u201333, 1986.","journal-title":"IEEE Trans. Pattern Analysis and Machine Intelligence"},{"key":"356826_CR14","unstructured":"D. Bar-Natan, \u201cPerturbative aspects of the topological quantum field theory, \u201d Ph.D. thesis, Princeton University, 1991."},{"key":"356826_CR15","doi-asserted-by":"crossref","first-page":"423","DOI":"10.1016\/0040-9383(95)93237-2","volume":"34","author":"D. Bar-Natan","year":"1995","unstructured":"D. Bar-Natan, \u201cOn the Vassiliev knot invariants, \u201d Topology, Vol. 34, pp. 423\u2013472, 1995.","journal-title":"Topology"},{"key":"356826_CR16","doi-asserted-by":"crossref","first-page":"209","DOI":"10.1007\/978-94-011-1040-2_27","volume-title":"Mathematical Morphology and Its Applications to Image Processing","author":"E. Bertin","year":"1994","unstructured":"E. Bertin, S. Marchand-Maillet, and J.-M. Chassery, \u201cOptimisation in Voronoi diagrams, \u201d in Mathematical Morphology and Its Applications to Image Processing. Kluwer Academic Publishers: London, 1994, pp. 209\u2013216."},{"key":"356826_CR17","volume-title":"Segmentation d'images et morphologie math\u00e9matique","author":"S. Beucher","year":"1990","unstructured":"S. Beucher, \u201cSegmentation d'images et morphologie math\u00e9matique, \u201d Ph.D. thesis, \u00c9cole des Mines, France, 1990."},{"key":"356826_CR18","doi-asserted-by":"crossref","first-page":"69","DOI":"10.1007\/978-94-011-1040-2_10","volume-title":"Mathematical Morphology and Its Applications to Image Processing","author":"S. Beucher","year":"1994","unstructured":"S. Beucher, \u201cWatershed, hierarchical segmentation and waterfall algorithm, \u201d in Mathematical Morphology and Its Applications to Image Processing, Kluwer Academic Publishers: Dordrecht, 1994, pp. 69\u201376."},{"key":"356826_CR19","doi-asserted-by":"crossref","first-page":"251","DOI":"10.1006\/jdeq.1998.3426","volume":"146","author":"F. Beukers","year":"1998","unstructured":"F. Beukers, J. Sanders, and J. Wang, \u201cOne symmetry does not imply integrability, \u201d Journal of Differential Equations, Vol. 146, pp. 251\u2013260, 1998.","journal-title":"Journal of Differential Equations"},{"key":"356826_CR20","volume-title":"Topological and geometrical aspects of image structure","author":"J. Blom","year":"1992","unstructured":"J. Blom, \u201cTopological and geometrical aspects of image structure, \u201d Ph.D. thesis, Utrecht University, The Netherlands, 1992."},{"key":"356826_CR21","doi-asserted-by":"crossref","first-page":"1019","DOI":"10.1063\/1.524550","volume":"21","author":"G. Bluman","year":"1979","unstructured":"G. Bluman and S. Kumei, \u201cA remarkable nonlinear diffusion equation, \u201d Journal of Mathematical Physics,Vol. 21, pp. 1019\u20131023, 1979.","journal-title":"Journal of Mathematical Physics"},{"key":"356826_CR22","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4757-4307-4","volume-title":"Symmetries and Differential Equations","author":"G. Bluman","year":"1989","unstructured":"G. Bluman and S. Kumei, Symmetries and Differential Equations, Springer-Verlag: New York, 1989."},{"key":"356826_CR23","series-title":"Technical Report DELiA","volume-title":"DELiA: A system for exact analysis of differential equations using S. lie approach","author":"A.V. Bocharov","year":"1991","unstructured":"A.V. Bocharov, \u201cDELiA: A system for exact analysis of differential equations using S. lie approach, \u201d Technical Report DELiA 1.5.1, Beaver Soft Programming Team, New York, 1991."},{"key":"356826_CR24","doi-asserted-by":"crossref","first-page":"5247","DOI":"10.1063\/1.530750","volume":"35","author":"R. Bott","year":"1994","unstructured":"R. Bott and C. Taubes, \u201cOn the self-linking of knots, \u201d Journal of Mathematical Physics, Vol. 35, pp. 5247\u20135287, 1994.","journal-title":"Journal of Mathematical Physics"},{"key":"356826_CR25","unstructured":"A.M. Bruckstein and A.N. Netravali, \u201cOn differential invariants of planar curves and recognising partially occluded planar shapes, \u201d in Proc. of Visual Form Workshop, Capri, Italy, 1990."},{"key":"356826_CR26","doi-asserted-by":"crossref","first-page":"991","DOI":"10.1142\/S0218001495000407","volume":"9","author":"A.M. Bruckstein","year":"1995","unstructured":"A.M. Bruckstein, G. Sapiro, and D. Shaked, \u201cEvolutions of planar polygons, \u201d International Journal of Pattern Recognition and Artificial Intelligence, Vol. 9, pp. 991\u20131014, 1995.","journal-title":"International Journal of Pattern Recognition and Artificial Intelligence"},{"key":"356826_CR27","doi-asserted-by":"crossref","first-page":"225","DOI":"10.1023\/A:1008226427785","volume":"7","author":"A.M. Bruckstein","year":"1997","unstructured":"A.M. Bruckstein and D. Shaked, \u201cOn projective invariant smoothing and evolutions of planar curves and polygons, \u201d Journal of Mathematical Imaging and Vision, Vol. 7, pp. 225\u2013240, 1997.","journal-title":"Journal of Mathematical Imaging and Vision"},{"key":"356826_CR28","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4613-9714-4","volume-title":"Exterior Differential Systems","author":"R.L. Bryant","year":"1991","unstructured":"R.L. Bryant, S.S. Chern, R.B. Gardner, H.L. Goldschmidt, and P.A. Griffiths, Exterior Differential Systems, Springer-Verlag: New York, 1991."},{"key":"356826_CR29","doi-asserted-by":"crossref","first-page":"532","DOI":"10.1109\/TCOM.1983.1095851","volume":"9","author":"P.J. Burt","year":"1983","unstructured":"P.J. Burt and E.H. Adelson, \u201cThe Laplacian pyramid as a compact image code, \u201d IEEE Trans. Communications, Vol. 9, pp. 532\u2013540, 1983.","journal-title":"IEEE Trans. Communications"},{"key":"356826_CR30","doi-asserted-by":"crossref","first-page":"107","DOI":"10.1023\/A:1007992709392","volume":"26","author":"E. Calabi","year":"1998","unstructured":"E. Calabi, P.J. Olver, C. Shakiban, A. Tannenbaum, and S. Haker, \u201cDifferential and numerically invariant signature curves applied to object recognition, \u201d International Journal of Computer Vision, Vol. 26, pp. 107\u2013135, 1998.","journal-title":"International Journal of Computer Vision"},{"key":"356826_CR31","doi-asserted-by":"crossref","first-page":"154","DOI":"10.1006\/aima.1996.0081","volume":"124","author":"E. Calabi","year":"1996","unstructured":"E. Calabi, P.J. Olver, and A. Tannenbaum, \u201cAffine geometry, curve flows, and invariant numerical approximations, \u201d Adv. in Math., Vol. 124, pp. 154\u2013196, 1996.","journal-title":"Adv. in Math."},{"key":"356826_CR32","doi-asserted-by":"crossref","first-page":"588","DOI":"10.21136\/CMJ.1961.100486","volume":"11","author":"G. Calugareanu","year":"1961","unstructured":"G. Calugareanu, \u201cSur les classes d'isotopie des noeuds tridimensionels et leurs invariants, \u201d Czechoslovak Math. J., Vol. 11, pp. 588\u2013625, 1961.","journal-title":"Czechoslovak Math. J."},{"key":"356826_CR33","first-page":"171","volume":"2","author":"E. Cartan","year":"1923","unstructured":"E. Cartan, \u201cLes \u00e9spaces \u00e0 connexion conforme, \u201d Ann. Soc. Plon. Math., Vol. 2, pp. 171\u2013221, 1923.","journal-title":"Ann. Soc. Plon. Math."},{"key":"356826_CR34","volume-title":"G\u00e9om\u00e9trie des \u00c8spaces de Riemann","author":"E. Cartan","year":"1928","unstructured":"E. Cartan, G\u00e9om\u00e9trie des \u00c8spaces de Riemann, Gauthiers-Villars: Paris, 1928."},{"key":"356826_CR35","volume-title":"Lec\u00b8ons sur la Th\u00e9orie des \u00c8spaces \u00e0 Connexion Projective","author":"E. Cartan","year":"1937","unstructured":"E. Cartan, Lec\u00b8ons sur la Th\u00e9orie des \u00c8spaces \u00e0 Connexion Projective, Gauthiers-Villars: Paris, 1937."},{"key":"356826_CR36","volume-title":"La Th\u00e9orie des Groupes Finis et Continus et la G\u00e9ometrie Diff\u00e9rentielle trait\u00e9es par la M\u00e9thode du R\u00e9p\u00e8re Mobile","author":"E. Cartan","year":"1937","unstructured":"E. Cartan, La Th\u00e9orie des Groupes Finis et Continus et la G\u00e9ometrie Diff\u00e9rentielle trait\u00e9es par la M\u00e9thode du R\u00e9p\u00e8re Mobile, Gauthiers-Villars: Paris, 1937."},{"key":"356826_CR37","volume-title":"Oeuvres Compl\u00e8tes","author":"E. Cartan","year":"1952","unstructured":"E. Cartan, \u201cLes probl\u00e8mes d'\u00e9quivalence, \u201d in Oeuvres Compl\u00e8tes, Gauthiers-Villars: Paris, 1952, Vol. 2, pp. 1311\u20131334."},{"key":"356826_CR38","volume-title":"Sur les vari\u00e9t\u00e9s \u00e0 connexion affine et la th\u00e9orie de la relativit\u00e9 g\u00e9n\u00e9ralis\u00e9e","author":"E. Cartan","year":"1955","unstructured":"E. Cartan, Sur les vari\u00e9t\u00e9s \u00e0 connexion affine et la th\u00e9orie de la relativit\u00e9 g\u00e9n\u00e9ralis\u00e9e, Gauthiers-Villars: Paris, 1955."},{"key":"356826_CR39","volume-title":"Lec\u00b8ons sur la G\u00e9om\u00e9trie des Espaces de Riemann","author":"E. Cartan","year":"1963","unstructured":"E. Cartan, Lec\u00b8ons sur la G\u00e9om\u00e9trie des Espaces de Riemann, Gauthier-Villars: Paris, 1963."},{"key":"356826_CR40","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/BF01385685","volume":"66","author":"V. Caselles","year":"1993","unstructured":"V. Caselles, F. Catt\u00e9, T. Coll, and F. Dibos, \u201cA geometric model for active contours, \u201d Numerische Mathematik, Vol. 66, pp. 1\u201331, 1993.","journal-title":"Numerische Mathematik"},{"key":"356826_CR41","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, and T. Coll, \u201cImage selective smoothing and edge detection by nonlinear diffusion, \u201d SIAM J. Num. Anal., Vol. 29, pp. 182\u2013193, 1992.","journal-title":"SIAM J. Num. Anal."},{"key":"356826_CR42","first-page":"662","volume":"1","author":"R. Claypoole","year":"1997","unstructured":"R. Claypoole, G. Davis, W. Sweldens, and R. Baraniuk, \u201cNonlinear wavelet transform for image coding, \u201d in Proceedings of the 31-st Asilomar Conference on Singals, Systems, and Computers, Vol. 1, 1997, pp. 662\u2013667.","journal-title":"Proceedings of the 31-st Asilomar Conference on Singals, Systems, and Computers"},{"key":"356826_CR43","volume-title":"G\u00e9om\u00e9trie non commutative","author":"A. Connes","year":"1990","unstructured":"A. Connes, G\u00e9om\u00e9trie non commutative, InterEditions: Paris, 1990."},{"key":"356826_CR44","volume-title":"A representation for visual information","author":"J.L. Crowley","year":"1981","unstructured":"J.L. Crowley, \u201cA representation for visual information, \u201d Ph.D. thesis, Carnegie-Mellon University, Robotics Institute, Pittsburgh, Pennsylvania, 1981."},{"key":"356826_CR45","unstructured":"J. Damon, \u201cLocal Morse theory for solutions to the heat equation and Gaussian blurring, \u201d Jour. Diff. Eqtns., 1993."},{"key":"356826_CR46","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9780511805110","volume-title":"Differential Forms and Connections","author":"R.W.R. Darling","year":"1994","unstructured":"R.W.R. Darling, Differential Forms and Connections, Cambridge University Press: New York, 1994."},{"key":"356826_CR47","series-title":"Lecture Notes in Computer Science","volume-title":"Scale-Space Theories in Computer Vision","author":"D.L. Donoho","year":"1999","unstructured":"D.L. Donoho, \u201cAnisotropy scaling and discontinuities along curves, \u201d in Scale-Space Theories in Computer Vision, Lecture Notes in Computer Science, Springer: Berlin, Vol. 1682, 1999."},{"volume-title":"First International Conference on Computing Anticipatory Systems: CASYS'97","year":"1998","key":"356826_CR48","unstructured":"D.M. Dubois (Ed.), First International Conference on Computing Anticipatory Systems: CASYS'97, AIP Conference ProceedingsVol. 437, American Institute of Physics, College Park, MD, 1998."},{"key":"356826_CR49","series-title":"AIP Conference Proceedings","volume-title":"Second International Conference on Computing Anticipatory Systems: CASYS'98","year":"1999","unstructured":"D.M. Dubois (Ed.), Second International Conference on Computing Anticipatory Systems: CASYS'98, AIP Conference Proceedings Vol.465, American Institute of Physics, College Park, MD, 1999."},{"key":"356826_CR50","unstructured":"C.N. de Graaf, S.M. Pizer, A.Toet, J.J.Koenderink, P. Zuidema, and P.P. van Rijk, \u201cPyramid segmentation of medical 3D images, \u201d in Medical Computer Graphics and Image Communications, 1984, pp. 71\u201377."},{"key":"356826_CR51","volume-title":"Geometric methods for analysis of ridges in ndimensional images","author":"D.H. Eberly","year":"1994","unstructured":"D.H. Eberly, \u201cGeometric methods for analysis of ridges in ndimensional images, \u201d Ph.D. Thesis, Department of Computer Vision, The University of North Carolina, Chapel Hill, North Carolina, 1994."},{"key":"356826_CR52","volume-title":"Parabolic Systems","author":"S.D. Eidel'Man","year":"1962","unstructured":"S.D. Eidel'Man, Parabolic Systems, North-Holland Publishing Company andWolters-Noordhoff Publishing: Amsterdam, 1962."},{"key":"356826_CR53","unstructured":"EUMETSAT, User Handbook, meteorological archive and retrieval facilities edition, issue 2, 1998."},{"key":"356826_CR54","doi-asserted-by":"crossref","first-page":"109","DOI":"10.1007\/BF00119834","volume":"6","author":"A.V. Evako","year":"1996","unstructured":"A.V. Evako, R. Kopperman, and Y.V. Mukhin, \u201cDimensional properties of graphs and digital spaces, \u201c Journal of Mathematical Imaging and Vision, Vol. 6, pp. 109\u2013119, 1996.","journal-title":"Journal of Mathematical Imaging and Vision"},{"key":"356826_CR55","series-title":"Lecture Notes in Computer Science","first-page":"11","volume-title":"Applications of Invariance in Computer Vision","author":"O. Faugeras","year":"1994","unstructured":"O. Faugeras, \u201cCartan's moving frame method and its applications to the geometry and evolution of curves in the Euclidean, affine and projective planes, \u201d in Applications of Invariance in Computer Vision, Lecture Notes in Computer Science, Springer-Verlag: Berlin, 1994, Vol. 825, pp. 11\u201346, 1994."},{"key":"356826_CR56","unstructured":"O. Faugeras and R. Keriven, \u201cScale-spaces and affine curvature, \u201d in Proceedings Europe-China Workshop on Geometric Modelling and Invariants for Computer Vision, 1995, pp. 17\u201324."},{"key":"356826_CR57","doi-asserted-by":"crossref","first-page":"13","DOI":"10.1109\/ICIP.1995.537568","volume":"III","author":"O. Faugeras","year":"1995","unstructured":"O. Faugeras and R. Keriven, \u201cSome recent results on the projective evolution of 2-D curves, \u201d in Proceedings of the International Conference on Image Processing, Lausanne, Switzerland, 1995, Vol. III, pp. 13\u201316.","journal-title":"Proceedings of the International Conference on Image Processing"},{"key":"356826_CR58","volume-title":"Cours de G\u00e9om\u00e9trie Diff\u00e9rentielle Locale","author":"J. Favard","year":"1957","unstructured":"J. Favard, Cours de G\u00e9om\u00e9trie Diff\u00e9rentielle Locale, Gauthier-Villars: Paris, 1957."},{"key":"356826_CR59","doi-asserted-by":"crossref","first-page":"161","DOI":"10.1023\/A:1005878210297","volume":"51","author":"M. Fels","year":"1998","unstructured":"M. Fels and P. Olver, \u201cMoving co-frames, I: A practical algorithm, \u201d Acta Appl. Math., Vol. 51, pp. 161\u2013213, 1998.","journal-title":"Acta Appl. Math."},{"key":"356826_CR60","doi-asserted-by":"crossref","first-page":"127","DOI":"10.1023\/A:1006195823000","volume":"55","author":"M. Fels","year":"1999","unstructured":"M. Fels and P. Olver, \u201cMoving co-frames, II: Regularisation and theoretical foundations, \u201d Acta Appl. Math., Vol. 55, pp. 127\u2013208, 1999.","journal-title":"Acta Appl. Math."},{"key":"356826_CR61","doi-asserted-by":"crossref","unstructured":"L.M.J. Florack, B.M. ter Haar Romeny, J.J. Koenderink, and M.A. Viergever, \u201cFamilies of tuned scale-space kernels, \u201d in Proceedings of the European Conference on Computer Vision, 1992, pp. 19\u201323.","DOI":"10.1007\/3-540-55426-2_2"},{"key":"356826_CR62","doi-asserted-by":"crossref","first-page":"327","DOI":"10.1007\/BF01664793","volume":"3","author":"L.M.J. Florack","year":"1993","unstructured":"L.M.J. Florack, B.M. ter Haar Romeny, J.J. Koenderink, and M.A. Viergever, \u201cCartesian differential invariants in scale-space, \u201d Journal of Mathematical Imaging and Vision, Vol. 3, pp. 327\u2013348, 1993.","journal-title":"Journal of Mathematical Imaging and Vision"},{"key":"356826_CR63","volume-title":"The syntactical structure of scalar images","author":"L.M.J. Florack","year":"1993","unstructured":"L.M.J. Florack, \u201cThe syntactical structure of scalar images, \u201d Ph.D. thesis, Utrecht University, The Netherlands, 1993."},{"key":"356826_CR64","doi-asserted-by":"crossref","first-page":"339","DOI":"10.1007\/978-94-017-1699-4_13","volume-title":"Geometry-Driven Diffusion in Computer Vision","author":"L.M.J. Florack","year":"1994","unstructured":"L.M.J. Florack, A.H. Salden, B.M. ter Haar Romeny, J.J. Koenderink, and M.A. Viergever, \u201cNonlinear scale-space, \u201d in Geometry-Driven Diffusion in Computer Vision, Kluwer Academic Publishers: Dordrecht, 1994, pp. 339\u2013370."},{"key":"356826_CR65","doi-asserted-by":"crossref","first-page":"279","DOI":"10.1016\/0262-8856(95)99716-E","volume":"13","author":"L.M.J. Florack","year":"1995","unstructured":"L.M.J. Florack, A.H. Salden, B.M. ter Haar Romeny, J.J. Koenderink, and M.A.Viergever, \u201cNonlinear scale-space, \u201d Image and Vision Computing, Vol. 13, pp. 279\u2013294, 1995.","journal-title":"Image and Vision Computing"},{"key":"356826_CR66","volume-title":"Image Structure, Vol. 10 of Computational Imaging and Vision Series","author":"L.M.J. Florack","year":"1996","unstructured":"L.M.J. Florack, Image Structure, Vol. 10 of Computational Imaging and Vision Series, Kluwer Academic Publishers: Dordrecht, 1996."},{"key":"356826_CR67","doi-asserted-by":"crossref","first-page":"263","DOI":"10.1023\/A:1007922215235","volume":"27","author":"L.M.J. Florack","year":"1998","unstructured":"L.M.J. Florack and M. Nielsen, \u201cThe intrinsic structure of the optic flow field, \u201d International Journal of Computer Vision, Vol. 27, pp. 263\u2013286, 1998.","journal-title":"International Journal of Computer Vision"},{"key":"356826_CR68","doi-asserted-by":"crossref","first-page":"65","DOI":"10.1023\/A:1008304909717","volume":"12","author":"L.M.J. Florack","year":"2000","unstructured":"L.M.J. Florack and A. Kuijper\u201d, \u201cThe topological structure of scale-space images, \u201d Journal of Mathematical Imaging and Vision, Vol. 12, pp. 65\u201379, 2000.","journal-title":"Journal of Mathematical Imaging and Vision"},{"key":"356826_CR69","doi-asserted-by":"crossref","first-page":"1","DOI":"10.2307\/2946626","volume":"139","author":"M. Freedman","year":"1994","unstructured":"M. Freedman, Z.-X. He, and Z. Wang, \u201cM\u00f6bius energies of knots and unknots, \u201d Ann. Math., Vol. 139, pp. 1\u201350, 1994.","journal-title":"Ann. Math."},{"key":"356826_CR70","doi-asserted-by":"crossref","first-page":"329","DOI":"10.1007\/BF00121877","volume":"2","author":"J. G\u00e5rding","year":"1992","unstructured":"J. G\u00e5rding, \u201cShape from texture for smooth curved surfaces in perspective projection, \u201d Journal of Mathematical Imaging and Vision, Vol. 2, pp. 329\u2013352, 1992.","journal-title":"Journal of Mathematical Imaging and Vision"},{"key":"356826_CR71","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"365","DOI":"10.1007\/3-540-57956-7_40","volume-title":"Proceedings European Conference on Computer Vision","author":"J. G\u00e5rding","year":"1994","unstructured":"J.G\u00e5rding and T. Lindeberg, \u201cDirect estimation of local surface shape in a fixating binocular vision system, \u201d in Proceedings European Conference on Computer Vision, Lecture Notes in Computer Science, Springer-Verlag: Berlin, 1994, Vol. 800, pp. 365\u2013376."},{"key":"356826_CR72","series-title":"CBMS-NSF Regional Conference Series in Applied Mathematics","doi-asserted-by":"crossref","DOI":"10.1137\/1.9781611970135","volume-title":"The Method of Equivalence and Its Applications","author":"R.B. Gardner","year":"1989","unstructured":"R.B. Gardner, The Method of Equivalence and Its Applications, CBMS-NSF Regional Conference Series in Applied Mathematics, Society for Industrial and Applied Mathematics, Philadelphia, Pennsylvania, 1989."},{"key":"356826_CR73","doi-asserted-by":"crossref","first-page":"721","DOI":"10.1109\/TPAMI.1984.4767596","volume":"6","author":"S. Geman","year":"1984","unstructured":"S. Geman and D. Geman, \u201cStochastic relaxation, Gibbs distributions, and the Bayesian restoration of images, \u201d IEEE Trans. Pattern Analysis and Machine Intelligence, Vol. 6, pp. 721\u2013741, 1984.","journal-title":"IEEE Trans. Pattern Analysis and Machine Intelligence"},{"key":"356826_CR74","doi-asserted-by":"crossref","unstructured":"V.P. Gerdt and A.Y. Zharkov, in Proc. ISSAC'90, 1990, pp. 250\u2013254.","DOI":"10.1145\/96877.96939"},{"key":"356826_CR75","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, and F.A. Jolesz. \u201dNonlinear anisotropic filtering of MRI data, \u201d IEEE Transactions on Medical Imaging, Vol. 11, pp. 221\u2013232, 1992.","journal-title":"IEEE Transactions on Medical Imaging"},{"key":"356826_CR76","unstructured":"C.R. Giardina and E.R. Dougherty (Eds.), Morphological Methods in Image and Signal Processing, Prentice-Hall: Englewood Cliffs, 1988."},{"key":"356826_CR77","doi-asserted-by":"crossref","first-page":"30","DOI":"10.1016\/S0375-9601(97)00750-0","volume":"236","author":"\u00d1. G\u00f6ktas","year":"1997","unstructured":"\u00d1. G\u00f6ktas, H.W. Hereman, and G. Erdmann, \u201cComputation of conserved densities for systems of nonlinear differentialdifference equations, \u201d Physics Letters A, Vol. 236, pp. 30\u201338, 1997.","journal-title":"Physics Letters A"},{"key":"356826_CR78","doi-asserted-by":"crossref","first-page":"591","DOI":"10.1006\/jsco.1997.0154","volume":"24","author":"\u00d1 G\u00f6ktas","year":"1997","unstructured":"\u00d1, G\u00f6ktas and W. Hereman, \u201cComputation of conserved densities for systems of nonlinear differential-difference equations, \u201d Journal of Symbolic Computation, Vol. 24, pp. 591\u2013621, 1997.","journal-title":"Journal of Symbolic Computation"},{"key":"356826_CR79","doi-asserted-by":"crossref","first-page":"425","DOI":"10.1016\/S0167-2789(98)00140-7","volume":"123","author":"\u00d1 G\u00f6ktas","year":"1998","unstructured":"\u00d1, G\u00f6ktas and W. Hereman, \u201cComputation of conserved densities for nonlinear lattices, \u201d Physica D, Vol. 123, pp. 425\u2013436, 1998.","journal-title":"Physica D"},{"key":"356826_CR80","doi-asserted-by":"crossref","first-page":"735","DOI":"10.1215\/S0012-7094-78-04535-0","volume":"45","author":"M.L. Green","year":"1978","unstructured":"M.L. Green, \u201cThe moving frame, differential invariants and rigidity theorems for curves in homogeneous spaces, \u201d Duke Mathematical Journal, Vol. 45, pp. 735\u2013779, 1978.","journal-title":"Duke Mathematical Journal"},{"key":"356826_CR81","volume-title":"Lectures in Pattern Theory I, II and III: Pattern Analysis, Pattern Synthesis and Regular Structures","author":"U. Grenander","year":"1976","unstructured":"U. Grenander, Lectures in Pattern Theory I, II and III: Pattern Analysis, Pattern Synthesis and Regular Structures, Springer-Verlag: Berlin, 1976\u201381."},{"volume-title":"Physics-based Vision: Principles and Practice; Colour","year":"1992","key":"356826_CR82","unstructured":"G.E. Healey and S.A. Shafer (Eds.), Physics-based Vision: Principles and Practice; Colour, Jones and Bartlett Publishers: Boston, London, 1992."},{"key":"356826_CR83","unstructured":"F.W. Hehl, J. Dermott McCrea, and E.W. Mielke, Weyl Spacetimes, The Dilation Current, And Creation Of Gravitating Mass By Symmetry Breaking, Verlag Peter Lang: Frankfurt, 1988, pp. 241\u2013311."},{"key":"356826_CR84","first-page":"237","volume":"10","author":"H.J.A.M. Heijmans","year":"1992","unstructured":"H.J.A.M. Heijmans, \u201cMathematical morphology: A geometrical approach in image processing, \u201d Nieuw Archief voor Wiskunde, Vol. 10, pp. 237\u2013276, 1992.","journal-title":"Nieuw Archief voor Wiskunde"},{"key":"356826_CR85","doi-asserted-by":"crossref","unstructured":"H.J.A.M. Heijmans, \u201cMathematical morphology as a tool for shape description, \u201d in Proc. of the NATO Advanced Research Workshop Shape in Picture-Mathematical Description of Shape in Grey-Level Images, Vol. 126 of NATO ASI Series F, pp. 147\u2013176, 1994.","DOI":"10.1007\/978-3-662-03039-4_11"},{"volume-title":"Morphological Image Operators","year":"1994","key":"356826_CR86","unstructured":"H.J.A.M. Heijmans (Ed.), Morphological Image Operators, Academic Press: San Diego, 1994."},{"key":"356826_CR87","doi-asserted-by":"crossref","first-page":"297","DOI":"10.1016\/1049-9660(91)90017-J","volume":"53","author":"Y. Hel-Or","year":"1991","unstructured":"Y. Hel-Or, S. Peleg, and D. Avnir, \u201cCharaterization of righthanded and left-handed shapes, \u201d in Proceedings CVGIP:IU, 1991, Vol. 53, pp. 297\u2013302.","journal-title":"Proceedings CVGIP:IU"},{"key":"356826_CR88","doi-asserted-by":"crossref","first-page":"83","DOI":"10.1023\/A:1008274211102","volume":"9","author":"Y. Hel-Or","year":"1998","unstructured":"Y. Hel-Or and P. Teo, \u201cCanonical decomposition of steerable filters, \u201d Journal of Mathematical Imaging and Vision, Vol. 9, pp. 83\u201395, 1998.","journal-title":"Journal of Mathematical Imaging and Vision"},{"key":"356826_CR89","doi-asserted-by":"crossref","first-page":"428","DOI":"10.1016\/S0010-4655(98)00121-0","volume":"115","author":"W. Hereman","year":"1998","unstructured":"W. Hereman, \u00d1. G\u00f6ktas, and A. Miller, \u201cAlgorithmic integrability tests for nonlinear differential and lattice equations, \u201d Computer Physics Communications, Vol. 115, pp. 428\u2013446, 1998.","journal-title":"Computer Physics Communications"},{"key":"356826_CR90","doi-asserted-by":"crossref","first-page":"121","DOI":"10.1007\/BF00119835","volume":"6","author":"G.T. Herman","year":"1996","unstructured":"G.T. Herman and Z. Enping, \u201cJordan surfaces in simply connected digital spaces, \u201d Journal of Mathematical Imaging and Vision, Vol. 6, pp. 121\u2013138, 1996.","journal-title":"Journal of Mathematical Imaging and Vision"},{"key":"356826_CR91","volume-title":"Theory of Algebraic Invariants","author":"D. Hilbert","year":"1993","unstructured":"D. Hilbert, Theory of Algebraic Invariants, Cambridge University Press: New York, 1993."},{"key":"356826_CR92","doi-asserted-by":"crossref","first-page":"106","DOI":"10.1113\/jphysiol.1962.sp006837","volume":"160","author":"D.H. Hubel","year":"1962","unstructured":"D.H. Hubel and T.N. Wiesel, \u201cReceptive fields, binocular interaction, and functional architecture in the cat's visual cortex, \u201d Journal of Physiology, Vol. 160, pp. 106\u2013154, 1962.","journal-title":"Journal of Physiology"},{"key":"356826_CR93","first-page":"187","volume-title":"Parallel Computer Vision","author":"R.A. Hummel","year":"1987","unstructured":"R.A. Hummel, \u201cThe scale-space formulation of pyramid data structures, \u201d in Parallel Computer Vision, Academic Press: New York, 1987, pp. 187\u2013123."},{"key":"356826_CR94","first-page":"368","volume":"26","author":"T. Iijima","year":"1962","unstructured":"T. Iijima, \u201cBasic theory on the normalisation of a pattern, \u201d Bulletin of Electrical Laboratory, Vol. 26, pp. 368\u2013388, 1962.","journal-title":"Bulletin of Electrical Laboratory"},{"issue":"11","key":"356826_CR95","first-page":"37","volume":"54-C","author":"T. Iijima","year":"1971","unstructured":"T. Iijima, \u201cBasic equation of figure and observational transformation, \u201d Transactions of the Institute of Electronics and Communication Engineers of Japan, Vol.54-C(11), pp. 37\u201338, 1971.","journal-title":"Transactions of the Institute of Electronics and Communication Engineers of Japan"},{"issue":"8","key":"356826_CR96","first-page":"35","volume":"54-C","author":"T. Iijima","year":"1971","unstructured":"T. Iijima, \u201cBasic theory on the construction of figure space, \u201d Transactions of the Institute of Electronics and Communication Engineers of Japan, Vol. 54-C(8), pp. 35\u201336, 1971.","journal-title":"Transactions of the Institute of Electronics and Communication Engineers of Japan"},{"issue":"9","key":"356826_CR97","first-page":"30","volume":"54-C","author":"T. Iijima","year":"1971","unstructured":"T. Iijima, \u201cAsuppression kernel of a figure and its mathematical characteristics, \u201d Transactions of the Institute of Electronics and Communication Engineers of Japan, Vol. 54-C(9), pp. 30\u201331, 1971.","journal-title":"Transactions of the Institute of Electronics and Communication Engineers of Japan"},{"issue":"11","key":"356826_CR98","first-page":"24","volume":"54-C","author":"T. Iijima","year":"1971","unstructured":"T. Iijima, \u201cBasic theory on normalisation of figure, \u201d Transactions of the Institute of Electronics and Communication Engineers of Japan, Vol. 54-C(11), pp. 24\u201325, 1971.","journal-title":"Transactions of the Institute of Electronics and Communication Engineers of Japan"},{"issue":"11","key":"356826_CR99","first-page":"26","volume":"54-C","author":"T. Iijima","year":"1971","unstructured":"T. Iijima, \u201cA system of fundamental functions in an abstract figure space, \u201d Transactions of the Institute of Electronics and Communication Engineers of Japan, Vol. 54-C(11), pp. 26\u201327, 1971.","journal-title":"Transactions of the Institute of Electronics and Communication Engineers of Japan"},{"issue":"12","key":"356826_CR100","first-page":"35","volume":"54-C","author":"T. Iijima","year":"1971","unstructured":"T. Iijima, \u201cBasic theory on feature extraction of figures, \u201d Transactions of the Institute of Electronics and Communication Engineers of Japan, Vol. 54-C(12), pp. 35\u201336, 1971.","journal-title":"Transactions of the Institute of Electronics and Communication Engineers of Japan"},{"issue":"8","key":"356826_CR101","first-page":"28","volume":"55-D","author":"T. Iijima","year":"1972","unstructured":"T. Iijima, \u201cBasic theory on the structural recognition of a figure, \u201d Transactions of the Institute of Electronics and Communication Engineers of Japan, Vol. 55-D(8), pp. 28\u201329, 1972.","journal-title":"Transactions of the Institute of Electronics and Communication Engineers of Japan"},{"issue":"8","key":"356826_CR102","first-page":"29","volume":"54-D","author":"T. Iijima","year":"1972","unstructured":"T. Iijima, \u201cTheoretical studies on the figure identification by pattern matching, \u201d Transactions of the Institute of Electronics and Communication Engineers of Japan, Vol. 54-D(8), pp. 29\u201330, 1972.","journal-title":"Transactions of the Institute of Electronics and Communication Engineers of Japan"},{"key":"356826_CR103","doi-asserted-by":"crossref","unstructured":"B. Jawerth and W. Sweldens, \u201cAn overview of the theory and applications of wavelets, \u201d in Proc. of the NATO Advanced ResearchWorkshop Shape in Picture-Mathematical Description of Shape in Grey-Level Images, Vol. 126 of NATO ASI Series F, 1994, pp. 249\u2013274.","DOI":"10.1007\/978-3-662-03039-4_16"},{"key":"356826_CR104","doi-asserted-by":"crossref","DOI":"10.1007\/BFb0068415","volume-title":"Higher Order Contact of Submanifolds of Homogeneous Spaces","author":"G.R. Jensen","year":"1977","unstructured":"G.R. Jensen, Higher Order Contact of Submanifolds of Homogeneous Spaces, Springer-Verlag: Berlin, 1977."},{"key":"356826_CR105","unstructured":"P. Johansen, S. Skelboe, K. Grue, and J.D. Andersen, \u201cRepresenting signals by their top-points in scale-space, \u201d in Proceedings of the 8-th International Conference on Pattern Recognition, 1986, pp. 215\u2013217."},{"key":"356826_CR106","doi-asserted-by":"crossref","first-page":"57","DOI":"10.1007\/BF01250004","volume":"4","author":"P. Johansen","year":"1994","unstructured":"P. Johansen, \u201cOn the classification of top-points in scale-space, \u201d Journal of Mathematical Imaging and Vision, Vol. 4, pp. 57\u201368, 1994.","journal-title":"Journal of Mathematical Imaging and Vision"},{"key":"356826_CR107","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4615-2792-3","volume-title":"A Pyramid Framework for Early Vision","author":"J.-J. Jolion","year":"1994","unstructured":"J.-J. Jolion and A. Rozenfeld, A Pyramid Framework for Early Vision, Kluwer Academic Publishers: Dordrecht, The Netherlands, 1994."},{"key":"356826_CR108","doi-asserted-by":"crossref","DOI":"10.1007\/3-540-11977-9","volume-title":"A Gauge Theory of Dislocations and Disclinations","author":"A. Kadi","year":"1983","unstructured":"A. Kadi and D.G.B. Edelen, A Gauge Theory of Dislocations and Disclinations, Springer-Verlag: Berlin, 1983."},{"key":"356826_CR109","doi-asserted-by":"crossref","first-page":"253","DOI":"10.1023\/A:1008376504545","volume":"9","author":"S.N. Kalitzin","year":"1998","unstructured":"S.N. Kalitzin, B.M. ter Haar Romeny, A.H. Salden, P.F.M. Nacken and M.A. Viergever, \u201cTopological numbers and singularities in scalar images; scale-space evolution properties, \u201d Journal of Mathematical Imaging and Vision, Vol. 9, pp. 253\u2013269, 1998.","journal-title":"Journal of Mathematical Imaging and Vision"},{"key":"356826_CR110","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"77","DOI":"10.1007\/3-540-63167-4_41","volume-title":"Scale-Space Theories in ComputerVision","author":"S.N. Kalitzin","year":"1997","unstructured":"S.N. Kalitzin, B.M. ter Haar Romeny, and M.A. Viergever, \u201cInvertible orientation bundles on 2D scalar images, \u201d in Scale-Space Theories in ComputerVision, Lecture Notes in Computer Science, Springer-Verlag: Berlin, 1997, Vol. 1252, pp. 77\u201388."},{"key":"356826_CR111","doi-asserted-by":"crossref","unstructured":"S.N. Kalitzin, B.M. ter Haar Romeny, and M.A. Viergever, \u201cOn topological deep-structure segmentation, \u201d in Proceedings International Conference on Image Processing, pp. 863\u2013866, 1997.","DOI":"10.1109\/ICIP.1997.638633"},{"key":"356826_CR112","doi-asserted-by":"crossref","first-page":"145","DOI":"10.1023\/A:1008013815039","volume":"31","author":"S.N. Kalitzin","year":"1999","unstructured":"S.N. Kalitzin, B.M. ter Haar Romeny, and M.A. Viergever, \u201cInvertible apertured orientation filters in image image analysis, \u201d International Journal of Computer Vision, Vol. 31, pp. 145\u2013158, 1999.","journal-title":"International Journal of Computer Vision"},{"key":"356826_CR113","unstructured":"S.N. Kalitzin, J. Staal, B.M. ter Haar Romeny, and M.A. Viergever, \u201cFrame-relative critical point-sets in image analysis, \u201d in Proc. Conf. on Computer Analysis of Images and Patterns, CAIP99, Lecture Notes in Computer Science, Vol. 1354, Springer-Verlag, Lijubljana, Slovenia, in press."},{"key":"356826_CR114","unstructured":"N. Kamran, R. Milson, and P.J. Olver, \u201cInvariant modules and the reduction of nonlinear partial differential equations to dynamical systems, \u201d Adv. in Math., to appear."},{"key":"356826_CR115","unstructured":"M. Kass, A.Witkin, and D. Terzopoulos, \u201cSnakes: Active contour models, \u201d in Proc. IEEEFirst Int. Comp.Vision Conf., 1987, pp. 259\u2013268."},{"key":"356826_CR116","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9780511809187","volume-title":"Introduction to the Modern Theory of Dynamical Systems","author":"A. Katok","year":"1995","unstructured":"A. Katok and B. Hasselblatt, Introduction to the Modern Theory of Dynamical Systems, Cambridge University Press: NewYork, 1995."},{"key":"356826_CR117","doi-asserted-by":"crossref","unstructured":"L.H. Kauffman, \u201cNoncommutativity and discrete physics, \u201d Physica D, pp. 125\u2013138, 1998.","DOI":"10.1016\/S0167-2789(98)00049-9"},{"key":"356826_CR118","series-title":"Report IMSc-98\/04\/15","volume-title":"Frontiers of Field Theory, Quantum Gravity and Strings","author":"R.K. Kaul","year":"1996","unstructured":"R.K. Kaul, \u201cChern-Simons theory, knot invariants, vertex models and three-manifold invariants, \u201d in Frontiers of Field Theory, Quantum Gravity and Strings, Puri, India, 1996. Report IMSc-98\/04\/15, Institute of Mathematical Sciences, Taramani, Madras, India."},{"key":"356826_CR119","volume-title":"Mathematical Foundations of Information Theory","author":"A. Khinchine","year":"1957","unstructured":"A. Khinchine, Mathematical Foundations of Information Theory, Dover Publications: New York, 1957."},{"key":"356826_CR120","doi-asserted-by":"crossref","first-page":"275","DOI":"10.1007\/BF00379537","volume":"134","author":"S. Kichenassamy","year":"1996","unstructured":"S. Kichenassamy, A. Kumar, P.J. Olver, A. Tannenbaum, and A. Yezzi, \u201cConformal curvature flows: From phase transitions to active vision, \u201d Arch. Rat. Mech. Anal.,Vol. 134, pp. 275\u2013301, 1996.","journal-title":"Arch. Rat. Mech. Anal."},{"key":"356826_CR121","volume-title":"Towards a computational theory of Shape","author":"B.B. Kimia","year":"1990","unstructured":"B.B. Kimia, \u201cTowards a computational theory of Shape, \u201d Ph.D. thesis, Department of Electrical Enginering, McGill University, Montreal, Canada, 1990."},{"key":"356826_CR122","doi-asserted-by":"crossref","unstructured":"B. Kimia, A. Tannenbaum, and S. Zucker, \u201cOn optimal control methods in computer vision and image processing, \u201d in Geometry-Driven Diffusion in ComputerVision, 1994, pp. 307\u2013338.","DOI":"10.1007\/978-94-017-1699-4_12"},{"key":"356826_CR123","doi-asserted-by":"crossref","first-page":"189","DOI":"10.1007\/BF01451741","volume":"15","author":"B.B. Kimia","year":"1994","unstructured":"B.B. Kimia, A. Tannenbaum, and S.W. Zucker, \u201cShapes, shocks, and deformations, I, \u201d International Journal of Computer Vision, Vol. 15, pp. 189\u2013224, 1994.","journal-title":"International Journal of Computer Vision"},{"key":"356826_CR124","doi-asserted-by":"crossref","first-page":"107","DOI":"10.1007\/BF01539551","volume":"16","author":"R. Kimmel","year":"1995","unstructured":"R. Kimmel, K. Siddiqi, B.B. Kimia, and A. Bruckstein, \u201cShape from shading: Level set propagation and viscosity solutions, \u201d International Journal of Computer Vision, Vol. 16, pp. 107\u2013133, 1995.","journal-title":"International Journal of Computer Vision"},{"key":"356826_CR125","doi-asserted-by":"crossref","DOI":"10.1142\/0356","volume-title":"Gauge Fields in Condensed Matter","author":"H. Kleinert","year":"1989","unstructured":"H. Kleinert, Gauge Fields in Condensed Matter, Vol. 1\u20132. World Scientific Publishing: Singapore, 1989."},{"key":"356826_CR126","doi-asserted-by":"crossref","first-page":"1222","DOI":"10.1109\/34.42861","volume":"11","author":"J. J. Koenderink","year":"1989","unstructured":"Jan J. Koenderink, \u201cA hitherto unnoticed singularity of scale-space, \u201d IEEE Trans. Pattern Analysis and Machine Intelligence, Vol. 11, pp. 1222\u20131224, 1989.","journal-title":"IEEE Trans. Pattern Analysis and Machine Intelligence"},{"key":"356826_CR127","doi-asserted-by":"crossref","first-page":"363","DOI":"10.1007\/BF00336961","volume":"50","author":"J.J. Koenderink","year":"1984","unstructured":"J.J. Koenderink, \u201cThe structure of images, \u201d Biol. Cybern., Vol. 50, pp. 363\u2013370, 1984.","journal-title":"Biol. Cybern."},{"key":"356826_CR128","doi-asserted-by":"crossref","first-page":"159","DOI":"10.1007\/BF00364135","volume":"58","author":"J.J. Koenderink","year":"1988","unstructured":"J.J. Koenderink, \u201cScale-time, \u201d Biol. Cybern., Vol. 58, pp. 159\u2013162, 1988.","journal-title":"Biol. Cybern."},{"key":"356826_CR129","doi-asserted-by":"crossref","first-page":"1136","DOI":"10.1364\/JOSAA.5.001136","volume":"5","author":"J.J. Koenderink","year":"1988","unstructured":"J.J. Koenderink and W. Richards, \u201cTwo-dimensional curvature operators, \u201d Journal of the Optical Society of America-A, Vol. 5, pp. 1136\u20131141, 1988.","journal-title":"Journal of the Optical Society of America-A"},{"key":"356826_CR130","unstructured":"J.J. Koenderink and A.J. van Doorn, \u201cA description of the structure of visual images in terms of an ordered hierarchy of light and dark blobs, \u201d in Second Int. Visual Psychophysics and Medical Imaging Conf., IEEE Cat. No. 81 CH 1676\u20136, 1981."},{"key":"356826_CR131","doi-asserted-by":"crossref","first-page":"383","DOI":"10.1007\/BF00318204","volume":"53","author":"J.J. Koenderink","year":"1986","unstructured":"J.J. Koenderink and A.J. van Doorn, \u201cDynamic shape, \u201d Biol. Cybern., Vol. 53, pp. 383\u2013396, 1986.","journal-title":"Biol. Cybern."},{"key":"356826_CR132","first-page":"2","volume":"2031","author":"J.J. Koenderink","year":"1993","unstructured":"J.J. Koenderink and A.J. van Doorn, \u201cLocal features of smooth shapes: Ridges and courses, \u201d in Proc. SPIE Geometric Methods in Computer Vision II, Vol. 2031, pp. 2\u201313, 1993.","journal-title":"Proc. SPIE Geometric Methods in Computer Vision II"},{"key":"356826_CR133","volume-title":"Probability Methods for Approximations In Stochastic Control and For Elliptic Equations, Vol. 129 of Mathematics In Science And Engineering","author":"H.J. Kushner","year":"1977","unstructured":"H.J. Kushner, Probability Methods for Approximations In Stochastic Control and For Elliptic Equations, Vol. 129 of Mathematics In Science And Engineering, Academic Press: New York, 1977."},{"key":"356826_CR134","series-title":"Lecture Notes in Physics","volume-title":"Time-Harmonic Electromagnetic Fields in Chiral Media","author":"A. Lakhtakia","year":"1989","unstructured":"A. Lakhtakia, V.K.Varadan, and V.V.Varadan, Time-Harmonic Electromagnetic Fields in Chiral Media, Lecture Notes in Physics, Springer-Verlag: Berlin, 1989, Vol. 335."},{"key":"356826_CR135","doi-asserted-by":"crossref","first-page":"85","DOI":"10.1023\/A:1005857402634","volume":"49","author":"C. Landi","year":"1997","unstructured":"C. Landi and P. Frosini, \u201cSize functions and morphological transformations, \u201d Acta Applicandae Mathematicae,Vol. 49, pp. 85\u2013104, 1997.","journal-title":"Acta Applicandae Mathematicae"},{"key":"356826_CR136","doi-asserted-by":"crossref","unstructured":"T. Lindeberg, \u201cScale-space for discrete signals, \u201d IEEE Trans. Pattern Analysis and Machine Intelligence, Vol. 12, pp. 234\u2013245, 1990.","DOI":"10.1109\/34.49051"},{"key":"356826_CR137","doi-asserted-by":"crossref","unstructured":"T. Lindeberg and J. G\u00e5rding, \u201cShape from texture from a multiscale perspective, \u201d in Proceedings 4th International Conference on Computer Vision, 1993, pp. 683\u2013691.","DOI":"10.1109\/ICCV.1993.378146"},{"key":"356826_CR138","series-title":"The Kluwer International Series in Engineering and Computer Science","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, The Kluwer International Series in Engineering and Computer Science., Kluwer Academic Publishers: Dordrecht, The Netherlands, 1994."},{"key":"356826_CR139","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"389","DOI":"10.1007\/3-540-57956-7_42","volume-title":"Proceedings European Conference on Computer Vision","author":"T. Lindeberg","year":"1994","unstructured":"T. Lindeberg and J. G\u00e5rding, \u201cShape-adapted smoothing in estimation of 3-D depth cues from affine distortions of local 2-D structure, \u201d in Proceedings European Conference on Computer Vision, Lecture Notes in Computer Science, Springer-Verlag: Berlin, 1994, Vol. 800, pp. 389\u2013400."},{"key":"356826_CR140","doi-asserted-by":"crossref","unstructured":"T. Lindeberg, \u201cDirect estimation of affine deformations of brightness patterns using visual front-end operators with automatic scale selection, \u201d in Proc. 5th International Conference on Computer Vision, 1995, pp. 134\u2013141. I","DOI":"10.1109\/ICCV.1995.466795"},{"key":"356826_CR141","volume-title":"Equivalence transformations for classes of differential equations","author":"I. Lisle","year":"1992","unstructured":"I. Lisle, \u201cEquivalence transformations for classes of differential equations, \u201d Ph.D. thesis, University of British Columbia, Vancouver, Canada, 1992."},{"key":"356826_CR142","doi-asserted-by":"crossref","first-page":"103","DOI":"10.1023\/A:1008330904886","volume":"10","author":"M. Nielsen","year":"1999","unstructured":"M. Nielsen, R. Maas, W.J. Niessen, L.M.J. Florack, and B.M. ter Haar Romeny, \u201cBinocular stereo from grey-scale image, \u201d Journal of Mathematical Imaging and Vision, Vol. 10, pp. 103\u2013122, 1999.","journal-title":"Journal of Mathematical Imaging and Vision"},{"key":"356826_CR143","doi-asserted-by":"crossref","first-page":"269","DOI":"10.1007\/BF00119843","volume":"6","author":"R. Malladi","year":"1996","unstructured":"R. Malladi, J.A. Sethian, and B.C. Vemuri, \u201cA fast level set based algorithm for topology-independent shape modelling, \u201d Journal of Mathematical Imaging and Vision, Vol. 6, pp. 269\u2013289, 1996.","journal-title":"Journal of Mathematical Imaging and Vision"},{"key":"356826_CR144","doi-asserted-by":"crossref","first-page":"674","DOI":"10.1109\/34.192463","volume":"11","author":"S.G. Mallat","year":"1989","unstructured":"S.G. Mallat, \u201cA theory for multiresolution signal decomposition: Thewavelet representation, \u201d IEEE Trans.Pattern Analysis and Machine Intelligence, Vol. 11, pp. 674\u2013694, 1989.","journal-title":"IEEE Trans.Pattern Analysis and Machine Intelligence"},{"key":"356826_CR145","volume-title":"Random Sets and Integral Geometry","author":"G. Matheron","year":"1975","unstructured":"G. Matheron, Random Sets and Integral Geometry, Wiley: New York, 1975."},{"key":"356826_CR146","doi-asserted-by":"crossref","first-page":"139","DOI":"10.1007\/BF00119836","volume":"6","author":"M.H. McAndrew","year":"1996","unstructured":"M.H. McAndrew and C.A. Osborne, \u201cA survey of algebraic methods in digital topology, \u201d Journal of Mathematical Imaging and Vision, Vol. 6, pp. 139\u2013159, 1996.","journal-title":"Journal of Mathematical Imaging and Vision"},{"key":"356826_CR147","doi-asserted-by":"crossref","first-page":"1087","DOI":"10.1063\/1.1699114","volume":"21","author":"N. Metropolis","year":"1953","unstructured":"N. Metropolis, A.W. Rosenbluth, M.N. Rosenbluth, A.H. Teller, and E. Teller, \u201cEquation of the state calculations by fast computing machine, \u201d Journal of Chemical Physics, Vol. 21, pp. 1087\u20131091, 1953.","journal-title":"Journal of Chemical Physics"},{"key":"356826_CR148","doi-asserted-by":"crossref","first-page":"77","DOI":"10.1007\/978-94-011-1040-2_11","volume-title":"Mathematical Morphology and Its Applications to Image Processing","author":"F. Meyer","year":"1994","unstructured":"F. Meyer, \u201cMinimum spanning forests for morphological segmentation, \u201d Mathematical Morphology and Its Applications to Image Processing, Kluwer Academic Publishers: Dordrecht, The Netherlands, 1994, pp. 77\u201384."},{"key":"356826_CR149","doi-asserted-by":"crossref","first-page":"34","DOI":"10.1109\/TPAMI.1986.4767750","volume":"8","author":"F. Mokhtarian","year":"1986","unstructured":"F. Mokhtarian and A. Mackworth, \u201cScale-based description of planar curves and two-dimensional shapes, \u201d IEEE Trans. Pattern Analysis and Machine Intelligence, Vol. 8, pp. 34\u201343, 1986.","journal-title":"IEEE Trans. Pattern Analysis and Machine Intelligence"},{"key":"356826_CR150","first-page":"25","volume":"14","author":"T. Moons","year":"1995","unstructured":"T. Moons, E. Pauwels, L. Van Gool, and A. Oosterlinck, \u201cFoundations of semi-differential invariants, \u201d Journal of Mathematical Imaging and Vision, Vol. 14, pp. 25\u201347, 1995.","journal-title":"Journal of Mathematical Imaging and Vision"},{"key":"356826_CR151","unstructured":"D. Mumford and J. Shah, \u201cBoundary detection by minimising functionals, \u201d in Proceedings IEEE Conference on Computer Vision and Pattern Recognition, 1985, pp. 22\u201326."},{"key":"356826_CR152","doi-asserted-by":"crossref","first-page":"577","DOI":"10.1002\/cpa.3160420503","volume":"XLII","author":"D. Mumford","year":"1989","unstructured":"D. Mumford and J. Shah, \u201cOptimal approximations by piecewise smooth functions and associated variational problems, \u201d Communications on Pure and Applied Mathematics,Vol. XLII, pp. 577\u2013685, 1989.","journal-title":"Communications on Pure and Applied Mathematics"},{"key":"356826_CR153","doi-asserted-by":"crossref","first-page":"135","DOI":"10.1007\/978-94-017-1699-4_5","volume-title":"Geometry-Driven Diffusion in Computer Vision","author":"D. Mumford","year":"1994","unstructured":"D. Mumford, \u201cBayesian rationale for the variational formulation, \u201d in Geometry-Driven Diffusion in Computer Vision, Computational Imaging and Vision, Kluwer Academic Publishers: Dordrecht, The Netherlands, 1994, pp. 135\u2013146."},{"key":"356826_CR154","volume-title":"ICIAM","author":"D. Mumford","year":"1996","unstructured":"D. Mumford, \u201cThe statistical description of visual signals, \u201d in ICIAM 95, Akademie Verlag: Berlin, 1996."},{"key":"356826_CR155","doi-asserted-by":"crossref","first-page":"25","DOI":"10.1017\/CBO9780511984037.003","volume-title":"Perception as Bayesian Inference","author":"D. Mumford","year":"1996","unstructured":"D. Mumford, \u201cPattern Theory: A unifying perspective, \u201d in Perception as Bayesian Inference, Cambridge University Press: New York, 1996, pp. 25\u201362."},{"key":"356826_CR156","volume-title":"Differential Topology and Quantum Field Theory","author":"C. Nash","year":"1990","unstructured":"C. Nash, Differential Topology and Quantum Field Theory, Academic Press: London, 1990."},{"key":"356826_CR157","doi-asserted-by":"crossref","first-page":"139","DOI":"10.1007\/BF00119837","volume":"6","author":"M. Newman","year":"1996","unstructured":"M. Newman, \u201cA fundamental group for grey-scale digital images, \u201d Journal of Mathematical Imaging and Vision, Vol. 6, pp. 139\u2013159, 1996.","journal-title":"Journal of Mathematical Imaging and Vision"},{"key":"356826_CR158","doi-asserted-by":"crossref","unstructured":"W.J. Niessen, J.S. Duncan, L.M.J. Florack, B.M. ter Haar Romeny, and M.A. Viergever, \u201cSpatiotemporal operators and optic flow, \u201d in Physics-Based Modeling in Computer Vision, pp. 78\u201384, 1995.","DOI":"10.1109\/PBMCV.1995.514671"},{"key":"356826_CR159","doi-asserted-by":"crossref","first-page":"826","DOI":"10.1109\/34.149593","volume":"14","author":"M. Nitzberg","year":"1992","unstructured":"M. Nitzberg and T. Shiota, \u201cNonlinear image filtering with edge and corner enhancement, \u201d IEEE Trans. Pattern Analysis and Machine Intelligence, Vol. 14, pp. 826\u2013833, 1992.","journal-title":"IEEE Trans. Pattern Analysis and Machine Intelligence"},{"key":"356826_CR160","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, \u201cBiased anisotropic diffusion-a unified regularisation and diffusion approach to edge detection, \u201d Image and Vision Computing, Vol. 8, pp. 318\u2013327, 1990.","journal-title":"Image and Vision Computing"},{"key":"356826_CR161","unstructured":"N. Nordstr\u00f6m, Variational Edge Detection, Ph.D. thesis, University of California at Berkeley, May 1990."},{"key":"356826_CR162","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4684-0274-2","volume-title":"Applications of Lie Groups to Differential Equations, Vol. 107 of Graduate Texts in Mathematics","author":"P.J. Olver","year":"1986","unstructured":"P.J. Olver, Applications of Lie Groups to Differential Equations, Vol. 107 of Graduate Texts in Mathematics, Springer-Verlag: Berlin, 1986."},{"key":"356826_CR163","first-page":"59","volume-title":"Invariant Theory and Tableaux, IMA Volumes in Mathematics and Its Applications","author":"P.J. Olver","year":"1990","unstructured":"P.J. Olver, \u201cInvariant theory, equivalence problems and the calculus of variations, \u201d in Invariant Theory and Tableaux, IMA Volumes in Mathematics and Its Applications, Springer-Verlag: Berlin, 1990, Vol. 19, pp. 59\u201381."},{"key":"356826_CR164","first-page":"339","volume":"319","author":"P.J. Olver","year":"1994","unstructured":"P.J. Olver, G. Sapiro, and A. Tannenbaum, \u201cClassification and uniqueness of invariant geometric flows, \u201d Comptes Rendus Acad. Sci. (Paris), Serie I, Vol. 319, pp. 339\u2013344, 1994.","journal-title":"Comptes Rendus Acad. Sci. (Paris), Serie I"},{"key":"356826_CR165","doi-asserted-by":"crossref","first-page":"255","DOI":"10.1007\/978-94-017-1699-4_11","volume-title":"Geometry-Driven Diffusion in Computer Vision","author":"P. Olver","year":"1994","unstructured":"P. Olver, G. Sapiro, and A. Tannenbaum, \u201cDifferential invariant signatures and flows in computer vision:A symmetry group approach, \u201d in Geometry-Driven Diffusion in Computer Vision, Computational Imaging and Vision, Kluwer Academic Publishers: Dordrecht, The Netherlands, 1994, pp. 255\u2013306."},{"key":"356826_CR166","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9780511609565","volume-title":"Equivalence, Invariants, and Symmetry","author":"P. Olver","year":"1995","unstructured":"P. Olver, Equivalence, Invariants, and Symmetry, Cambridge University Press: New York, 1995."},{"key":"356826_CR167","doi-asserted-by":"crossref","first-page":"176","DOI":"10.1137\/S0036139994266311","volume":"57","author":"P.J. Olver","year":"1997","unstructured":"P.J. Olver, G. Sapiro, and A. Tannenbaum, \u201cInvariant geometric evolutions of surfaces and volumetric smoothing, \u201d SIAM J. Appl. Math., Vol. 57, pp. 176\u2013194, 1997.","journal-title":"SIAM J. Appl. Math."},{"key":"356826_CR168","unstructured":"P.J. Olver, G. Sapiro, and A. Tannenbaum, \u201cAffine invariant edge maps and active contours, \u201d Acta Appli. Math., to appear."},{"key":"356826_CR169","doi-asserted-by":"crossref","first-page":"12","DOI":"10.1016\/0021-9991(88)90002-2","volume":"79","author":"S. Osher","year":"1988","unstructured":"S. Osher and J.A. Sethian, \u201cFronts propagating with curvature dependent speed: Algorithms based on the Hamilton-Jacobi formalism, \u201d J. Computational Physics, Vol. 79, pp. 12\u201349, 1988.","journal-title":"J. Computational Physics"},{"key":"356826_CR170","volume-title":"Group Analysis of Differential Equations","author":"L.V. Ovsiannikov","year":"1982","unstructured":"L.V. Ovsiannikov, Group Analysis of Differential Equations, Academic Press: New York, 1982."},{"key":"356826_CR171","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, \u201cScale-space and edge detection using anisotropic diffusion, \u201d IEEE Trans. Pattern Analysis and Machine Intelligence, Vol. 12, pp. 629\u2013639, 1990.","journal-title":"IEEE Trans. Pattern Analysis and Machine Intelligence"},{"key":"356826_CR172","volume-title":"Meso-scale Meteorological Modeling","author":"R.A. Pielke","year":"1984","unstructured":"R.A. Pielke. Meso-scale Meteorological Modeling, Academic Press: New York, 1984."},{"key":"356826_CR173","doi-asserted-by":"crossref","first-page":"163","DOI":"10.1142\/S0218216595000089","volume":"4","author":"S. Piunikhin","year":"1995","unstructured":"S. Piunikhin, \u201cWeights of Feynman diagrams, link polynomials and Vassiliev knot invariants, \u201d Journal of Knot Theory and its Ramifications, Vol. 4, pp. 163\u2013188, 1995.","journal-title":"Journal of Knot Theory and its Ramifications"},{"key":"356826_CR174","first-page":"975","volume":"17","author":"W.F. Pohl","year":"1968","unstructured":"W.F. Pohl. \u201cThe self-linking number of a closed space curve, \u201d Journal of Mathematics and Mechanics, Vol. 17, pp. 975\u2013985, 1968.","journal-title":"Journal of Mathematics and Mechanics"},{"key":"356826_CR175","volume-title":"Systems of Partial Differential Equations and Lie Pseudogroups","author":"J.F. Pommaret","year":"1978","unstructured":"J.F. Pommaret, Systems of Partial Differential Equations and Lie Pseudogroups, Gordon and Breach: New York, 1978."},{"key":"356826_CR176","volume-title":"Differential Galois Theory","author":"J.F. Pommaret","year":"1983","unstructured":"J.F. Pommaret, Differential Galois Theory, Gordon and Breach: New York, 1983."},{"key":"356826_CR177","volume-title":"Lie Pseudogroups and Mechanics","author":"J.F. Pommaret","year":"1988","unstructured":"J.F. Pommaret, Lie Pseudogroups and Mechanics, Gordon and Breach: New York, 1988."},{"key":"356826_CR178","volume-title":"Topological Groups","author":"L. Pontryagin","year":"1946","unstructured":"L. Pontryagin, Topological Groups, Princeton University Press: Princeton, N.J., 1946."},{"key":"356826_CR179","doi-asserted-by":"crossref","first-page":"239","DOI":"10.1007\/BF00129878","volume":"1","author":"F. Preteux","year":"1992","unstructured":"F. Preteux, \u201cWatershed and skeleton by influence zones: A distance-based approach, \u201d Journal of Mathematical Imaging and Vision, Vol. 1, pp. 239\u2013256, 1992.","journal-title":"Journal of Mathematical Imaging and Vision"},{"key":"356826_CR180","doi-asserted-by":"crossref","first-page":"191","DOI":"10.1007\/978-94-017-1699-4_9","volume-title":"Geometry-Driven Diffusion in Computer Vision","author":"M. Proesmans","year":"1994","unstructured":"M. Proesmans, E. Pauwels, and L. Van Gool, \u201cCoupled geometry-driven diffusion equations for low level vision, \u201d in Geometry-Driven Diffusion in Computer Vision, Computational Imaging and Vision, Kluwer Academic Publishers: Dordrecht, The Netherlands, 1994, pp. 191\u2013228."},{"key":"356826_CR181","doi-asserted-by":"crossref","first-page":"169","DOI":"10.1007\/978-94-017-1699-4_8","volume-title":"Geometry-Driven Diffusion in Computer Vision","author":"T. Richardson","year":"1994","unstructured":"T. Richardson and S. Mitter, \u201cApproximation, computation, and distortion in the variational formulation, \u201d in Geometry-Driven Diffusion in Computer Vision, Computational Imaging and Vision, Kluwer Academic Publishers: Dordrecht, The Netherlands, 1994, pp. 169\u2013190."},{"key":"356826_CR182","doi-asserted-by":"crossref","first-page":"207","DOI":"10.1007\/BF01248372","volume":"5","author":"J.H. Rieger","year":"1995","unstructured":"J.H. Rieger, \u201cGeneric evolutions of edges on families of diffused grey-value surfaces, \u201d Journal of Mathematical Imaging and Vision, Vol. 5, pp. 207\u2013217, 1995.","journal-title":"Journal of Mathematical Imaging and Vision"},{"key":"356826_CR183","volume-title":"Anticipatory Systems","author":"R. Rosen","year":"1985","unstructured":"R. Rosen, Anticipatory Systems, Pergamon, New York, 1985."},{"key":"356826_CR184","first-page":"51","volume":"14","author":"R. Rothe","year":"1915","unstructured":"R. Rothe, \u201cZum problem des talwegs, \u201d Sitz. ber. d. Berliner Math. Gesellschaft, Vol. 14, pp. 51\u201369, 1915.","journal-title":"Sitz. ber. d. Berliner Math. Gesellschaft"},{"key":"356826_CR185","first-page":"78","volume":"1568","author":"N. Rougon","year":"1991","unstructured":"N. Rougon and F. Preteux, \u201cDeformable markers: Mathematical morphology for active contour models control, \u201d in Proceedings SPIE's International Symposium on Optical Applied Science and Engineering-Image Algebra and Morphological Image Processing II, Vol. 1568, pp. 78\u201389, 1991.","journal-title":"Proceedings SPIE's International Symposium on Optical Applied Science and Engineering-Image Algebra and Morphological Image Processing II"},{"key":"356826_CR186","volume-title":"\u00c9lements pour la r\u00e9connaissance des formes tridimensionnelles d\u00e9formables. Applications \u00e0 l'imagerie biom\u00e9dicale","author":"N. Rougon","year":"1993","unstructured":"N. Rougon, \u201c \u00c9lements pour la r\u00e9connaissance des formes tridimensionnelles d\u00e9formables. Applications \u00e0 l'imagerie biom\u00e9dicale, \u201d Ph.D. thesis, Telecom Paris-Department Images, Paris: France, 1993."},{"key":"356826_CR187","first-page":"2","volume":"2035","author":"N. Rougon","year":"1993","unstructured":"N. Rougon, \u201cOn mathematical foundations of local deformation analysis, \u201d in Proceedings SPIE's International Symposium on Optical Applied Science and Engineering-Mathematical Methods in Medical Imaging II, Vol. 2035, pp. 2\u201313, 1993.","journal-title":"Proceedings SPIE's International Symposium on Optical Applied Science and Engineering-Mathematical Methods in Medical Imaging II"},{"key":"356826_CR188","first-page":"151","volume":"2568","author":"N. Rougon","year":"1995","unstructured":"N. Rougon, \u201cGeometric Maxwell equations and the structure of diffusive scale-spaces, \u201d in Proceedings SPIE Conference on Morphological Image Processing and Random Image Modeling-SPIE's 1995 International Symposium on Optical Science, Engineering and Instrumentation,Vol. 2568, pp. 151\u2013165, 1995.","journal-title":"Proceedings SPIE Conference on Morphological Image Processing and Random Image Modeling-SPIE's 1995 International Symposium on Optical Science, Engineering and Instrumentation"},{"key":"356826_CR189","unstructured":"L. Rudin, S. Osher, and E. Fatemi, \u201cNonlinear total variation based noise removal algorithms, \u201d in Modelisations Matematiques pour le traitement d'images, 149\u2013179. INRIA, 1992."},{"key":"356826_CR190","unstructured":"L.I. Rudin and S. Osher, \u201cTotal variation based image restoration with free local constraints, \u201d in Proc. First IEEE Internat. Conf. on Image Processing, 1994, pp. 13\u201316."},{"key":"356826_CR191","doi-asserted-by":"crossref","unstructured":"A.H. Salden, B.M. ter Haar Romeny, and M.A. Viergever, \u201cLocal and multilocal scale-space description, \u201d in Proc. of the NATO Advanced Research Workshop Shape in Picture-Mathematical Description of Shape in Grey-Level Iimages,Vol. 126 of NATO ASI Series F, Berlin, 1994, pp. 661\u2013670.","DOI":"10.1007\/978-3-662-03039-4_49"},{"key":"356826_CR192","first-page":"309","volume":"10","author":"A.H. Salden","year":"1992","unstructured":"A.H. Salden, L.M.J. Florack, B.M. ter Haar Romeny, J.J.Koenderink, and M.A. Viergever, \u201cMulti-scale analysis and description of image structure, \u201d Nieuw Archief voor Wiskunde, Vol. 10, pp. 309\u2013326, 1992.","journal-title":"Nieuw Archief voor Wiskunde"},{"key":"356826_CR193","doi-asserted-by":"crossref","unstructured":"A.H. Salden, B.M. ter Haar Romeny, L.M.J. Florack, J.J.Koenderink, and M.A. Viergever, \u201cA complete and irreducible set of local orthogonally invariant features of 2-dimensional images, \u201d in Proceedings 11th IAPR Internat. Conf. on Pattern Recognition, The Hague, The Netherlands, 1992, pp. 180\u2013184.","DOI":"10.1109\/ICPR.1992.201956"},{"key":"356826_CR194","unstructured":"A.H. Salden, B.M. ter Haar Romeny, and M.A. Viergever, \u201cImage structure generating normalised geometric scale spaces, \u201d in Volume Image Processing '93, pp. 141\u2013143, Utrecht, The Netherlands, 1993."},{"key":"356826_CR195","unstructured":"A.H. Salden, B.M. ter Haar Romeny, and M.A. Viergever, \u201cModern geometry and dynamic scale-space theories, \u201d in Proc. Conf. on Differential Geometry and Computer Vision: From Pure over Applicable to Applied Differential Geometry, Nordfjordeid, Norway, 1995, in press."},{"key":"356826_CR196","volume-title":"Dynamic Scale-Space Paradigms","author":"A.H. Salden","year":"1996","unstructured":"A.H. Salden, \u201cDynamic Scale-Space Paradigms, \u201d Ph.D. thesis, Utrecht University: The Netherlands, 1996."},{"key":"356826_CR197","volume-title":"Gaussian Scale-Space Theory","author":"A.H. Salden","year":"1996","unstructured":"A.H. Salden, \u201cInvariant theory, \u201d in Gaussian Scale-Space Theory, Kluwer Academic Publishers: Dordrecht, The Netherlands, 1996."},{"key":"356826_CR198","doi-asserted-by":"crossref","unstructured":"A.H. Salden, B.M. ter Haar Romeny, and M.A.Viergever, \u201cDynamic scale-space theories, \u201d in Scale-Space 97, First International Conference on Scale-Space Theory in Computer Vision, Utrecht, the Netherlands, 1997, pp. 248\u2013259.","DOI":"10.1007\/3-540-63167-4_55"},{"key":"356826_CR199","doi-asserted-by":"crossref","first-page":"5","DOI":"10.1023\/A:1008253609285","volume":"9","author":"A.H. Salden","year":"1996","unstructured":"A.H. Salden, B.M. ter Haar Romeny, and M.A.Viergever, \u201cDifferential and integral geometry of linear scale spaces, \u201d Journal of Mathematical Imaging and Vision, Vol. 9, pp. 5\u201327, 1996.","journal-title":"Journal of Mathematical Imaging and Vision"},{"key":"356826_CR200","doi-asserted-by":"crossref","first-page":"103","DOI":"10.1023\/A:1008300826001","volume":"9","author":"A.H. Salden","year":"1998","unstructured":"A.H. Salden, B.M. ter Haar Romeny, and M.A.Viergever, \u201cLinear scale-space theory from physical principles, \u201d Journal of Mathematical Imaging and Vision, Vol. 9, pp. 103\u2013139, 1998.","journal-title":"Journal of Mathematical Imaging and Vision"},{"key":"356826_CR201","series-title":"Lecture Notes in Computer Science","first-page":"65","volume-title":"Asian Conference on Computer Vision","author":"A.H. Salden","year":"1998","unstructured":"A.H. Salden, \u201cAlgebraic invariants of linear scale-spaces, \u201d in Asian Conference on Computer Vision, Lecture Notes in Computer Science, Springer-Verlag: Berlin, 1998, Vol. 1352, pp. 65\u201372."},{"key":"356826_CR202","first-page":"131","volume":"39","author":"A.H. Salden","year":"2000","unstructured":"A.H. Salden, \u201cSatellite image analysis and processing tools to be used in air-pollution forecast and simulation systems, \u201d System Analysis Modelling Simulation, 4-th ERCIM Environmental Modelling Group Workshop, Vol. 39, pp. 131\u2013168, 2000.","journal-title":"System Analysis Modelling Simulation, 4-th ERCIM Environmental Modelling Group Workshop"},{"key":"356826_CR203","unstructured":"A.H. Salden, J.Weickert, and B.M. ter Haar Romeny, \u201cBluman and Kumei's nonlinear scale-space theory, \u201d Technical Report ERCIM-02\/99-R057, February 1999."},{"key":"356826_CR204","doi-asserted-by":"crossref","first-page":"29","DOI":"10.1023\/A:1008172320786","volume":"34","author":"A.H. Salden","year":"1999","unstructured":"A.H. Salden, B.M. ter Haar Romeny, and M.A.Viergever, \u201cLinearised Euclidean shortening flow of curve geometry, \u201d International Journal of Computer Vision, Vol. 34, pp. 29\u201367, 1999.","journal-title":"International Journal of Computer Vision"},{"key":"356826_CR205","doi-asserted-by":"crossref","unstructured":"A.H. Salden, \u201cDynamic scale-space paradigm versus mathematical morphology?, \u201d in AeroSense'99, SPIE's 13-th Annual Symposium on Aerospace\/Defence Sensing, Simulation, and Control, Orlando, Florida, USA, pp. 155\u2013166, 1999.","DOI":"10.1117\/12.354703"},{"key":"356826_CR206","unstructured":"A.H. Salden, \u201cModeling and analysis of sustainable systems, \u201d ERCIM, 1999, in press."},{"key":"356826_CR207","unstructured":"A.H. Salden and S. Iacob, \u201cDynamic multi-scale image classification, \u201d in SPIE's International Symposium on Electronic Imaging 2001, Internet Imaging EI24, 2001, in press."},{"key":"356826_CR208","doi-asserted-by":"crossref","first-page":"447","DOI":"10.1016\/S0010-4655(98)00122-2","volume":"115","author":"J. Sanders","year":"1998","unstructured":"J. Sanders and J. Wang, \u201cCombining maple and form to decide on integrability questions, \u201d Computer Physics Communications, Vol. 115, pp. 447\u2013459, 1998.","journal-title":"Computer Physics Communications"},{"key":"356826_CR209","doi-asserted-by":"crossref","first-page":"410","DOI":"10.1006\/jdeq.1998.3452","volume":"147","author":"J. Sanders","year":"1998","unstructured":"J. Sanders and J. Wang, \u201cOn the integrability of homogeneous scalar evolution equations, \u201d Journal of Differential Equations, Vol. 147, pp. 410\u2013434, 1998.","journal-title":"Journal of Differential Equations"},{"key":"356826_CR210","doi-asserted-by":"crossref","first-page":"471","DOI":"10.1016\/S0378-4754(97)00076-1","volume":"44","author":"J.A. Sanders","year":"1997","unstructured":"J.A. Sanders and J. Wang, \u201cClassification of conservation laws for KdV-like equations, \u201d Math. Comput. Simulation, Vol. 44, pp. 471\u2013481, 1997.","journal-title":"Math. Comput. Simulation"},{"key":"356826_CR211","first-page":"483","volume":"1","author":"L.A. Santalo","year":"1950","unstructured":"L.A. Santalo, \u201cIntegral geometry in general spaces, \u201d in Proceedings International Congress of Mathematics, Vol. 1, Cambridge, 1950, pp. 483\u2013489.","journal-title":"Proceedings International Congress of Mathematics"},{"key":"356826_CR212","doi-asserted-by":"crossref","first-page":"25","DOI":"10.1007\/BF01420591","volume":"11","author":"G. Sapiro","year":"1993","unstructured":"G. Sapiro and A. Tannenbaum, \u201cAffine invariant scale-space, \u201d International Journal of Computer Vision, Vol. 11, pp. 25\u201344, 1993.","journal-title":"International Journal of Computer Vision"},{"key":"356826_CR213","doi-asserted-by":"crossref","first-page":"1363","DOI":"10.1016\/0031-3203(93)90142-J","volume":"26","author":"G. Sapiro","year":"1993","unstructured":"G. Sapiro, R. Kimmel, D. Shaked, B.B. Kimia, and A.M. Bruckstein, \u201cImplementing continuous-scale morphology via curve evolution, \u201d Pattern Recognition, Vol. 26, pp. 1363\u20131372, 1993.","journal-title":"Pattern Recognition"},{"key":"356826_CR214","unstructured":"G. Sapiro and A. Tannenbaum, \u201cImage smoothing based on an affine invariant flow, \u201d in Conference on Information Sciences and Systems, Johns Hopkins University, 1993, pp. 196\u2013201."},{"key":"356826_CR215","first-page":"234","volume":"2031","author":"G. Sapiro","year":"1993","unstructured":"G. Sapiro and A. Tannenbaum, \u201cFormulating invariant heattype curve flows, \u201d in SPIE Conference on Geometric Methods in Computer Vision II, Vol. 2031, pp. 234\u2013245, 1993.","journal-title":"SPIE Conference on Geometric Methods in Computer Vision II"},{"key":"356826_CR216","doi-asserted-by":"crossref","first-page":"985","DOI":"10.1512\/iumj.1993.42.42046","volume":"42","author":"G. Sapiro","year":"1993","unstructured":"G. Sapiro and A. Tannenbaum, \u201cOn invariant curve evolution and image analysis, \u201d Indiana Journal of Mathematics, Vol. 42, pp. 985\u20131009, 1993.","journal-title":"Indiana Journal of Mathematics"},{"key":"356826_CR217","doi-asserted-by":"crossref","first-page":"67","DOI":"10.1109\/34.368150","volume":"17","author":"G. Sapiro","year":"1995","unstructured":"G. Sapiro and A. Tannenbaum, \u201cArea and length preserving geometric invariant scale-spaces, \u201d IEEE Trans. Pattern Analysis and Machine Intelligence, Vol. 17, pp. 67\u201372, 1995.","journal-title":"IEEE Trans. Pattern Analysis and Machine Intelligence"},{"issue":"1","key":"356826_CR218","doi-asserted-by":"crossref","first-page":"79","DOI":"10.1006\/jfan.1994.1004","volume":"119","author":"G. Sapiro","year":"1994","unstructured":"G. Sapiro and A. Tannenbaum, \u201cOn affine plane curve evolution, \u201d Journal of Functional Analysis, Vol. 119(1), pp. 79\u2013120, 1994.","journal-title":"Journal of Functional Analysis"},{"key":"356826_CR219","series-title":"Technical Report DIKU-98\/23","volume-title":"Relations between regularization and diffusion filtering","author":"O. Scherzer","year":"1998","unstructured":"O. Scherzer and J.Weickert, \u201cRelations between regularization and diffusion filtering, \u201d Technical Report DIKU-98\/23, Dept. of Computer Science, University of Copenhagen, Denmark, 1998."},{"key":"356826_CR220","doi-asserted-by":"crossref","unstructured":"C. Schmidt and R. Mohr, \u201cCombining grey-value invariants with local constraints for object recognition, \u201d in Proc. Intern. Conf. on Computer Vision and Pattern Recognition, San Francisco, USA, 1996.","DOI":"10.1109\/CVPR.1996.517174"},{"key":"356826_CR221","doi-asserted-by":"crossref","first-page":"79","DOI":"10.1007\/BF01248404","volume":"3","author":"J. Segman","year":"1993","unstructured":"J. Segman and W. Schempp, \u201cTwo ways to incorporate scale in the Heisenberg group with an intertwining operator, \u201d Journal of Mathematical Imaging and Vision, Vol. 3, pp. 79\u201394, 1993.","journal-title":"Journal of Mathematical Imaging and Vision"},{"key":"356826_CR222","doi-asserted-by":"crossref","first-page":"51","DOI":"10.1007\/BF01248403","volume":"3","author":"J. Segman","year":"1993","unstructured":"J. Segman and Y.Y. Zeevi, \u201cImage analysis by wavelet-type transforms: Group theoretic approach, \u201d Journal of Mathematical Imaging and Vision, Vol. 3, pp. 51\u201377, 1993.","journal-title":"Journal of Mathematical Imaging and Vision"},{"key":"356826_CR223","volume-title":"Image Analysis and Mathematical Morphology","author":"J. Serra","year":"1982","unstructured":"J. Serra, Image Analysis and Mathematical Morphology. Academic Press: New York, 1982."},{"key":"356826_CR224","doi-asserted-by":"crossref","unstructured":"J. Shah, \u201cSegmentation by nonlinear diffusion, \u201d in Conference on Computer Vision and Pattern Recognition, pp. 202\u2013207, 1991.","DOI":"10.1109\/CVPR.1991.139688"},{"key":"356826_CR225","doi-asserted-by":"crossref","first-page":"99","DOI":"10.1137\/0330007","volume":"30","author":"J. Shah","year":"1992","unstructured":"J. Shah, \u201cSegmentation by minimising functionals: Smoothing properties, \u201d SIAM J. Control and Optimisation, Vol. 30, pp. 99\u2013111, 1992.","journal-title":"SIAM J. Control and Optimisation"},{"key":"356826_CR226","doi-asserted-by":"crossref","unstructured":"J. Shah, \u201cA nonlinear model for discontinuous disparity and half-occlusions in stereo, \u201d in Proc. Computer Vision and Pattern Recognition, pp. 34\u201340, 1993.","DOI":"10.1109\/CVPR.1993.341004"},{"key":"356826_CR227","unstructured":"K. Sivakumar and J. Goutsias (Eds.), Mathematical Morphology and Its Applications to Image Processing, Kluwer Academic Publishers: London, 1994."},{"key":"356826_CR228","series-title":"Causal Productions, CD-ROM, paper","volume-title":"1997 IEEE\/EURASIP Workshop on Nonlinear Signal and Image Processing","author":"K. Sivakumar","year":"1997","unstructured":"K. Sivakumar and J. Goutsias, \u201cMorphological size densities: Applications to optimal texture classification and noise filtering, \u201d in 1997 IEEE\/EURASIP Workshop on Nonlinear Signal and Image Processing, Causal Productions, CD-ROM, paper 113, Mackinac Island, Michigan, USA, 1997."},{"key":"356826_CR229","volume-title":"Algebraic Topology","author":"E.H. Spanier","year":"1966","unstructured":"E.H. Spanier, Algebraic Topology, McGraw-Hill: New York, 1966."},{"key":"356826_CR230","doi-asserted-by":"crossref","unstructured":"J. Sporring, \u201cThe entropy of scale-space, \u201d in Proceedings of 13th International Conference on Pattern Recognition, Vienna, Austria, 1996.","DOI":"10.1109\/ICPR.1996.546154"},{"key":"356826_CR231","doi-asserted-by":"crossref","unstructured":"J. Sporring, M. Nielsen, J. Weickert, and O.F. Olsen, \u201cA note on differential corner measures, \u201d in Proceedings International Conference on Pattern Recognition, Brisbane, Australia, 1996, pp. 652\u2013654.","DOI":"10.1109\/ICPR.1998.711228"},{"key":"356826_CR232","doi-asserted-by":"crossref","first-page":"1051","DOI":"10.1109\/18.761342","volume":"45","author":"J. Sporring","year":"1999","unstructured":"J. Sporring and J. Weickert, \u201cInformation measures in scale-spaces, \u201d IEEE Trans. Information Theory, Vol. 45, pp. 1051\u20131058, 1999.","journal-title":"IEEE Trans. Information Theory"},{"key":"356826_CR233","first-page":"105","volume-title":"Scale-space theories in computer vision, Lecture Notes in Computer Science","author":"J. Staal","year":"1999","unstructured":"J. Staal, S.N. Kalitzin, B.M. ter Haar Romeny, and M.A. Viergever, \u201cDetection of critical structures in scale-space, \u201d in Scale-space theories in computer vision, Lecture Notes in Computer Science, Vol. 1682, Springer, Berlin, pp. 105\u2013116, 1999."},{"volume-title":"Structured Computer Vision","year":"1980","key":"356826_CR234","unstructured":"S. Tanimoto and A. Klinger (Eds.), Structured Computer Vision, Academic Press: New York, 1980."},{"key":"356826_CR235","doi-asserted-by":"crossref","first-page":"133","DOI":"10.1006\/cviu.1997.0612","volume":"66","author":"S. Tari","year":"1997","unstructured":"S. Tari, J. Shah, and H. Pien, \u201cExtraction of shape skeletons from grey-scale images, \u201d Computer Vision and Image Understanding, Vol. 66, pp. 133\u2013146, 1997.","journal-title":"Computer Vision and Image Understanding"},{"key":"356826_CR236","first-page":"105","volume":"3716","author":"S. Tari","year":"1999","unstructured":"S. Tari, \u201cColouring 3D symmetry set: Perceptual meaning and significance in 3D, \u201d in AeroSense'99, SPIE's 13-th Annual International Symposium on Aerospace\/Defence Sensing, Simulation, and Control, Vol. 3716, pp. 105\u2013111, 1999.","journal-title":"AeroSense'99, SPIE's 13-th Annual International Symposium on Aerospace\/Defence Sensing, Simulation, and Control"},{"volume-title":"Geometry-Driven Diffusion in Computer Vision","year":"1994","key":"356826_CR237","unstructured":"B.M. ter Haar Romeny (Ed.), Geometry-Driven Diffusion in Computer Vision, Kluwer Academic Publishers: Dordrecht, 1994."},{"key":"356826_CR238","volume-title":"The Differential Invariants of Generalised Spaces","author":"T.Y. Thomas","year":"1934","unstructured":"T.Y. Thomas, The Differential Invariants of Generalised Spaces, Cambridge University Press: New York, 1934."},{"key":"356826_CR239","volume-title":"Integral Expressions for the Vassiliev Knot Invariants","author":"D. Thurston","year":"1995","unstructured":"D. Thurston, Integral Expressions for the Vassiliev Knot Invariants, Harvard University, U.S.A. Senior Thesis, 1995."},{"key":"356826_CR240","doi-asserted-by":"crossref","first-page":"1959","DOI":"10.1142\/S0217751X88000825","volume":"3","author":"C.-H. Tze","year":"1988","unstructured":"C.-H. Tze, \u201cManifold-splitting regularization, self-linking, twisting, writhing numbers of space-time ribbins and polyakov's proof of Fermi-Bose transmutations, \u201d International Journal of Modern Physics A, Vol. 3, pp. 1959\u20131979, 1988.","journal-title":"International Journal of Modern Physics A"},{"key":"356826_CR241","volume-title":"Mathematical morphology: extensions towards computer Vision","author":"R. van den Boomgaard","year":"1992","unstructured":"R. van den Boomgaard, \u201cMathematical morphology: extensions towards computer Vision, \u201d Ph.D. thesis, University of Amsterdam, Amsterdam, The Netherlands, 1992."},{"key":"356826_CR242","first-page":"219","volume":"10","author":"R. van den Boomgaard","year":"1992","unstructured":"R. van den Boomgaard, \u201cThe morphological equivalent of the Gauss convolution, \u201d Nieuw Archief voorWiskunde, Vol. 10, pp. 219\u2013236, 1992.","journal-title":"Nieuw Archief voorWiskunde"},{"key":"356826_CR243","unstructured":"R. van den Boomgaard and A.W.M. Smeulders, \u201cMorphological multi-scale image analysis, \u201d in Mathematical Morphology and its Applications to Signal Processing, Barcelona, Spain, May 1993, pp. 180\u2013185."},{"key":"356826_CR244","doi-asserted-by":"crossref","first-page":"1101","DOI":"10.1109\/34.334389","volume":"16","author":"R. van den Boomgaard","year":"1994","unstructured":"R. van den Boomgaard and A.W.M. Smeulders, \u201cThe morphological structure of images, the differential equations of morphological scale-space, \u201d IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 16, pp. 1101\u20131113, 1994.","journal-title":"IEEE Transactions on Pattern Analysis and Machine Intelligence"},{"key":"356826_CR245","unstructured":"R. van den Boomgaard and J. Schavemaker, \u201cImage segmentation in morphological scale-space, \u201d in ISMM'94: Mathematical Morphology and Its Application to Signal Processing 2- Poster Contribution-, pp. 15\u201316, 1994."},{"key":"356826_CR246","first-page":"203","volume-title":"Gaussian Scale-Space Theory","author":"R. van den Boomgaard","year":"1996","unstructured":"R. van den Boomgaard and L. Dorst, \u201cThe morphological equivalent of Gaussian scale-space, \u201d in Gaussian Scale-Space Theory, Kluwer Academic Publishers: Dordrecht, 1996, pp. 203\u2013220."},{"key":"356826_CR247","first-page":"23","volume":"1","author":"V.A. Vassiliev","year":"1990","unstructured":"V.A. Vassiliev, \u201cCohomology of knot spaces, \u201d Advances in Soviet Mathematics, Vol. 1, pp. 23\u201369, 1990.","journal-title":"Advances in Soviet Mathematics"},{"key":"356826_CR248","first-page":"9","volume":"1","author":"V.A. Vassiliev","year":"1990","unstructured":"V.A.Vassiliev, \u201cTopology of complements to discriminants and loop spaces, \u201d Advances in Soviet Mathematics,Vol. 1, pp. 9\u201321, 1990.","journal-title":"Advances in Soviet Mathematics"},{"key":"356826_CR249","doi-asserted-by":"crossref","unstructured":"L. Vincent and P. Soille, \u201cWatersheds in digital spaces: An efficient algorithm based on immersion simulations, \u201d IEEE Trans. Pattern Analysis and Machine Intelligence, Vol. 13, pp. 583\u2013598, 1991.","DOI":"10.1109\/34.87344"},{"key":"356826_CR250","volume-title":"Symmetries and Conservation Laws of Evolution Equations","author":"J.P. Wang","year":"1998","unstructured":"J.P. Wang, Symmetries and Conservation Laws of Evolution Equations, Ph.D. thesis, Thomas Stieltjes Institute for Mathematics, Vrije Universiteit, Amsterdam, The Netherlands, 1998."},{"key":"356826_CR251","volume-title":"Anisotropic Diffusion in Image Processing","author":"J. Weickert","year":"1996","unstructured":"J. Weickert, Anisotropic Diffusion in Image Processing, Ph.D. thesis, Dept. of Mathematics, University of Kaiserslautern, Germany, 1996."},{"key":"356826_CR252","first-page":"283","volume-title":"Numerical Analysis, Scientific Computing, Computer Science","author":"J. Weickert","year":"1996","unstructured":"J. Weickert, \u201cFoundations and applications of nonlinear anisotropic diffusion filtering, \u201d in Numerical Analysis, Scientific Computing, Computer Science, Akademie Verlag, Berlin, 1996, pp. 283\u2013286."},{"key":"356826_CR253","series-title":"Lecture Notes in Control and Information Sciences","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, \u201cNonlinear diffusion scale-spaces: From the continuous to the discrete setting, \u201d in ICAOS '96: Images,Wavelets and PDEs, Lecture Notes in Control and Information Sciences, Springer-Verlag: London, 1996, Vol. 219, pp. 111\u2013118."},{"key":"356826_CR254","volume-title":"Anisotropic Diffusion in Image Processing","author":"J. Weickert","year":"1998","unstructured":"J. Weickert, Anisotropic Diffusion in Image Processing, Teubner-Verlag: Stuttgart, Germany, 1998."},{"key":"356826_CR255","unstructured":"J.Weickert, \u201cOn discontinuity-preserving optic flow, \u201d in Proc. Computer Vision and Mobile Robotics Workshop, Santorini, Greece, 1998, pp. 115\u2013122."},{"key":"356826_CR256","doi-asserted-by":"crossref","first-page":"93","DOI":"10.1007\/978-3-642-72282-0_8","volume-title":"Mustererkennung 1998","author":"J. Weickert","year":"1998","unstructured":"J. Weickert, \u201cFast segmentation methods based on partial differential equations and the watershed transformation, \u201d in Mustererkennung 1998, Springer-Verlag, Berlin, Germany, 1998, pp. 93\u2013100."},{"key":"356826_CR257","first-page":"45","volume-title":"Gaussian Scale-Space Theory","author":"J. Weickert","year":"1996","unstructured":"J. Weickert, S. Ishikawa, and A. Imiya, \u201cOn the history of gaussian scale-space axiomatics, \u201d in Gaussian Scale-Space Theory, Kluwer: Dordrecht, 1996, pp. 45\u201359."},{"key":"356826_CR258","doi-asserted-by":"crossref","first-page":"237","DOI":"10.1023\/A:1008344623873","volume":"10","author":"J. Weickert","year":"1999","unstructured":"J. Weickert and S. Ishikawa, \u201cLinear scale-space has first been proposed in Japan, \u201d Journal of Mathematical Imaging and Vision, Vol. 10, pp. 237\u2013252, 1999.","journal-title":"Journal of Mathematical Imaging and Vision"},{"key":"356826_CR259","volume-title":"L'integration dans les groupes topologiques et ses applications","author":"A. Weil","year":"1938","unstructured":"A. Weil, L'integration dans les groupes topologiques et ses applications, Gauthiers Villars: Paris, 1938."},{"key":"356826_CR260","doi-asserted-by":"crossref","first-page":"99","DOI":"10.1006\/cviu.1993.1006","volume":"57","author":"R.T. Whitaker","year":"1993","unstructured":"R.T. Whitaker and S.M. Pizer, \u201cA multi-scale approach to nonuniform diffusion, \u201d Computer Vision, Graphics, and Image Processing: Image Understanding, Vol. 57, pp. 99\u2013110, 1993.","journal-title":"Computer Vision, Graphics, and Image Processing: Image Understanding"},{"key":"356826_CR261","series-title":"Computational Imaging and Vision","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.T. Whitaker","year":"1994","unstructured":"R.T. Whitaker and G. Gerig, \u201cVector-valued diffusion, \u201d in Geometry-Driven Diffusion in Computer Vision, Computational Imaging and Vision, Kluwer Academic Publishers: Dordrecht, The Netherlands, 1994, pp. 93\u2013134."},{"key":"356826_CR262","doi-asserted-by":"crossref","first-page":"693","DOI":"10.2307\/2373348","volume":"91","author":"J.H. White","year":"1969","unstructured":"J.H. White, \u201cSelf-linking and the Gauss integral in higher dimensions, \u201d American Journal of Mathematics, Vol. 91, pp. 693\u2013728, 1969.","journal-title":"American Journal of Mathematics"},{"key":"356826_CR263","unstructured":"A.P. Witkin, \u201cScale-space filtering, \u201d in Proc. International Joint Conference on Artificial Intelligence, Karlsruhe, Germany, 1983, pp. 1019\u20131023."},{"volume-title":"Physics-based Vision: Principles and Practice; Radiometry","year":"1992","key":"356826_CR264","unstructured":"L.B. Wolff, S.A. Shafer, and G.E. Healey (Eds.), Physics-based Vision: Principles and Practice; Radiometry, Jones and Bartlett Publishers: London, 1992."},{"key":"356826_CR265","doi-asserted-by":"crossref","first-page":"199","DOI":"10.1109\/42.563665","volume":"16","author":"A. Yezzi","year":"1997","unstructured":"A. Yezzi, S. Kichenassamy, A. Kumar, P.J. Olver, and A. Tannenbaum, \u201cA geometric snake model for segmentation of medical imagery, \u201d Medical Imaging, Vol. 16, pp. 199\u2013209, 1997.","journal-title":"Medical Imaging"},{"key":"356826_CR266","doi-asserted-by":"crossref","unstructured":"A. Yuille, L. Vincent, and D. Geiger, \u201cStatistical morphology and Bayesian reconstruction, \u201d Journal of Mathematical Imaging and Vision, Special Issue: Image Algebra and Morphological Image Processing, Vol. 1, pp. 223\u2013238, 1992.","DOI":"10.1007\/BF00129877"},{"key":"356826_CR267","doi-asserted-by":"crossref","first-page":"15","DOI":"10.1109\/TPAMI.1986.4767748","volume":"8","author":"A.L. Yuille","year":"1986","unstructured":"A.L. Yuille and T.A. Poggio, \u201cScaling theorems for zerocrossings, \u201d IEEE Trans. Pattern Analysis and Machine Intelligence, Vol. 8, pp. 15\u201325, 1986.","journal-title":"IEEE Trans. Pattern Analysis and Machine Intelligence"},{"key":"356826_CR268","volume-title":"Renormalised Quantum Field Theory","author":"O.I. Zavialov","year":"1990","unstructured":"O.I. Zavialov, Renormalised Quantum Field Theory, Kluwer Academic Publishers: Dordrecht, 1990."}],"container-title":["Journal of Mathematical Imaging and Vision"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1023\/A:1012282305022.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1023\/A:1012282305022\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1023\/A:1012282305022.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,12]],"date-time":"2025-06-12T10:31:27Z","timestamp":1749724287000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1023\/A:1012282305022"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2001,11]]},"references-count":268,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2001,11]]}},"alternative-id":["356826"],"URL":"https:\/\/doi.org\/10.1023\/a:1012282305022","relation":{},"ISSN":["0924-9907","1573-7683"],"issn-type":[{"type":"print","value":"0924-9907"},{"type":"electronic","value":"1573-7683"}],"subject":[],"published":{"date-parts":[[2001,11]]}}}