{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,11]],"date-time":"2026-06-11T22:34:39Z","timestamp":1781217279089,"version":"3.54.1"},"publisher-location":"Berlin, Heidelberg","reference-count":26,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"value":"9783540708223","type":"print"},{"value":"9783540708230","type":"electronic"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2007]]},"DOI":"10.1007\/978-3-540-70823-0_11","type":"book-chapter","created":{"date-parts":[[2007,5,24]],"date-time":"2007-05-24T00:52:26Z","timestamp":1179967946000},"page":"151-169","source":"Crossref","is-referenced-by-count":9,"title":["A Practical Approach to Two-Dimensional Scalar Topology"],"prefix":"10.1007","author":[{"given":"Peer-Timo","family":"Bremer","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Valerio","family":"Pascucci","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","reference":[{"key":"11_CR1_Ref","first-page":"51","volume-title":"Proc. IEEE Visualization \u201998","author":"C. L. Bajaj","year":"1998","unstructured":"C. L. Bajaj, V. Pascucci, and D. R. Schikore. Visualization of scalar topology for structural enhancement. In D. Ebert, H. Hagen, H. Rushmeier, , editors, Proc. IEEE Visualization \u201998, pages 51-58, Los Alamitos California, 1998. IEEE, IEEE Computer Society Press."},{"issue":"1","key":"11_CR2_Ref","doi-asserted-by":"publisher","first-page":"3","DOI":"10.1016\/S0097-8493(97)00079-4","volume":"22","author":"C. L. Bajaj","year":"1998","unstructured":"C. L. Bajaj and D. R. Schikore. Topology preserving data simplification with error bounds. Computers and Graphics, 22(1):3-12, 1998.","journal-title":"Computers and Graphics"},{"issue":"4","key":"11_CR3_Ref","doi-asserted-by":"publisher","first-page":"385","DOI":"10.1109\/TVCG.2004.3","volume":"10","author":"P.-T. Bremer","year":"2004","unstructured":"P.-T. Bremer, H. Edelsbrunner, B. Hamann, and V. Pascucci. A topological hierarchy for functions on triangulated surfaces. IEEE Trans. on Visualization and Computer Graphics, 10(4):385-396, 2004.","journal-title":"IEEE Trans. on Visualization and Computer Graphics"},{"key":"11_CR4_Ref","doi-asserted-by":"crossref","unstructured":"H. Carr, J. Snoeyink, and M. van de Panne. Simplifying flexible isosurfaces using local geometric measures. In IEEE Visualization \u201904, pages 497-504. IEEE Computer Society, 2004.","DOI":"10.1109\/VISUAL.2004.96"},{"key":"11_CR5_Ref","doi-asserted-by":"crossref","first-page":"264","DOI":"10.1080\/14786445908642760","volume":"XVIII","author":"A. Cayley","year":"1859","unstructured":"A. Cayley. On contour and slope lines. The London, Edinburgh and Dublin Philosophical Magazine and Journal of Science, XVIII:264-268, 1859.","journal-title":"The London, Edinburgh and Dublin Philosophical Magazine and Journal of Science"},{"key":"11_CR6_Ref","doi-asserted-by":"publisher","first-page":"333","DOI":"10.1017\/S0022112004009681","volume":"511","author":"A.W. Cook","year":"2004","unstructured":"A.W. Cook, W. Cabot, and P.L. Miller. The mixing transition in RayleighTaylor instability. J. Fluid Mech., 511:333-362, 2004.","journal-title":"J. Fluid Mech."},{"issue":"3","key":"11_CR7_Ref","doi-asserted-by":"publisher","first-page":"1057","DOI":"10.1145\/1141911.1141993","volume":"25","author":"S. Dong","year":"2006","unstructured":"S. Dong, P.-T. Bremer, M. Garland, V. Pascucci, and J. C. Hart. Spectral surface quadrangulation. ACM Trans. on Graphics (TOG) \/ Proc.of ACM SIGGRAPH, 25(3):1057-1066, 2006.","journal-title":"ACM Trans. on Graphics (TOG) \/ Proc.of ACM SIGGRAPH"},{"key":"11_CR8_Ref","doi-asserted-by":"crossref","unstructured":"H. Edelsbrunner, J. Harer, V. Natarajan, and V. Pascucci. Morse-Smale complexes for piecewise linear 3-manifolds. In Proc. 19th Sympos. Comput. Geom., pages 361-370, 2003.","DOI":"10.1145\/777792.777846"},{"key":"11_CR9_Ref","doi-asserted-by":"crossref","first-page":"87","DOI":"10.1007\/s00454-003-2926-5","volume":"30","author":"H. Edelsbrunner","year":"2003","unstructured":"H. Edelsbrunner, J. Harer, and A. Zomorodian. Hierarchical Morse-Smale complexes for piecewise linear 2-manifolds. Discrete Comput. Geom., 30:87-107, 2003.","journal-title":"Discrete Comput. Geom"},{"key":"11_CR10_Ref","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-71714-7","volume-title":"Stratified Morse Theory","author":"M. Goresky","year":"1988","unstructured":"M. Goresky and R. MacPherson. Stratified Morse Theory. Springer-Verlag, Heidelberg, Germany, 1988."},{"key":"11_CR11_Ref","doi-asserted-by":"crossref","unstructured":"A. Gyulassy, V. Natarajan, V. Pascucci, P.-T. Bremer, and B. Hamann. Topology-based simplification for feature extraction from 3D scalar fields. In Proceedings of the IEEE Visualization 2005 (VIS\u201905), pages 535-542. IEEE Computer Society, 2005.","DOI":"10.1109\/VISUAL.2005.1532839"},{"issue":"1","key":"11_CR12_Ref","first-page":"100","volume":"29","author":"R. M. Haralick","year":"1985","unstructured":"R. M. Haralick and L. G. Shapiro. Image segmentation techniques. CVGIP, 29(1):100-132, January 1985.","journal-title":"CVGIP"},{"issue":"3","key":"11_CR13_Ref","doi-asserted-by":"publisher","first-page":"36","DOI":"10.1109\/38.79452","volume":"11","author":"J. L. Helman","year":"1991","unstructured":"J. L. Helman and L. Hesselink. Visualizing vector field topology in fluid flows. IEEE Computer Graphics and Applications, 11(3):36-46, May\/Jun. 1991.","journal-title":"IEEE Computer Graphics and Applications"},{"key":"11_CR14_Ref","first-page":"203","volume-title":"Proceedings of ACM SIGGRAPH 2001","author":"M. Hilaga","year":"2001","unstructured":"M. Hilaga, Y. Shinagawa, T. Kohmura, and T. L. Kunii. Topology matching for fully automatic similarity estimation of 3D shapes. In E. Fiume, editor, Proceedings of ACM SIGGRAPH 2001, pages 203-212, New York, NY, USA, 2001. ACM."},{"issue":"4","key":"11_CR15_Ref","first-page":"99","volume":"30","author":"H. Hoppe","year":"1996","unstructured":"H. Hoppe. Progressive meshes. Computer Graphics (Proc. SIGGRAPH \u201996), 30(4):99-108, Aug. 1996.","journal-title":"Computer Graphics (Proc. SIGGRAPH \u201996)"},{"key":"11_CR16_Ref","doi-asserted-by":"crossref","unstructured":"Y. Matsumoto. An Introduction to Morse Theory. American Mathematical Society, 2002.","DOI":"10.1090\/mmono\/208"},{"key":"11_CR17_Ref","doi-asserted-by":"crossref","first-page":"421","DOI":"10.1080\/14786447008640422","volume":"XL","author":"J. C. Maxwell","year":"1870","unstructured":"J. C. Maxwell. On hills and dales. The London, Edinburgh and Dublin Philosophical Magazine and Journal of Science, XL:421-427, 1870.","journal-title":"The London, Edinburgh and Dublin Philosophical Magazine and Journal of Science"},{"key":"11_CR18_Ref","doi-asserted-by":"crossref","DOI":"10.1515\/9781400881802","volume-title":"Morse Theory","author":"J. Milnor","year":"1963","unstructured":"J. Milnor. Morse Theory. Princeton University Press, New Jersey, 1963."},{"issue":"4","key":"11_CR19_Ref","doi-asserted-by":"publisher","first-page":"442","DOI":"10.1109\/TPAMI.1984.4767549","volume":"6","author":"L. R. Nackman","year":"1984","unstructured":"L. R. Nackman. Two-dimensional critical point configuration graphs. IEEE Transactions on Pattern Analysis and Machine Intelligence, 6(4):442-450, July 1984.","journal-title":"IEEE Transactions on Pattern Analysis and Machine Intelligence"},{"key":"11_CR20_Ref","doi-asserted-by":"crossref","first-page":"77","DOI":"10.1111\/j.1538-4632.1976.tb00530.x","volume":"8","author":"J. Pfaltz","year":"1976","unstructured":"J. Pfaltz. Surface networks. Geographical Analysis, 8:77-93, 1976.","journal-title":"Geographical Analysis"},{"key":"11_CR21_Ref","doi-asserted-by":"crossref","unstructured":"J. Pfaltz. A graph grammar that describes the set of two-dimensional surface networks. Graph-Grammars and Their Application to Computer Science and Biology (Lecture Notes in Computer Science, no. 73, 1979.","DOI":"10.1007\/BFb0025734"},{"key":"11_CR22_Ref","doi-asserted-by":"publisher","first-page":"66","DOI":"10.1109\/38.90568","volume":"11","author":"Y. Shinagawa","year":"1991","unstructured":"Y. Shinagawa, T. Kunii, and Y. L. Kergosien. Surface coding based on Morse theory. IEEE Computer Graphics and Applications, 11:66-78, 1991.","journal-title":"IEEE Computer Graphics and Applications"},{"key":"11_CR23_Ref","doi-asserted-by":"crossref","unstructured":"S. Takahashi, T. Ikeda, Y. Shinigawa, T. L. Kunii, and M. Ueda. Algorithms for extracting correct critical points and constructing topological graphs from discrete geographical elevation data. In Proc. Eurographics \u201995, pages C-181-C-192, Sep. 1995.","DOI":"10.1111\/j.1467-8659.1995.cgf143_0181.x"},{"key":"11_CR24_Ref","doi-asserted-by":"crossref","unstructured":"S. Takahashi, Y. Shinagawa, and T. L. Kunii. A feature-based approach for smooth surfaces. In Proc. of the Fourth Symp on Solid Modeling and Applications, SMA \u201997, pages 97-110. ACM, May 1997.","DOI":"10.1145\/267734.267760"},{"key":"11_CR25_Ref","doi-asserted-by":"crossref","unstructured":"M. J. van Kreveld, R. van Oostrum, C. L. Bajaj, V. Pascucci, and D. Schikore. Contour trees and small seed sets for isosurface traversal. In Symposium on Computational Geometry, pages 212-220, 1997.","DOI":"10.1145\/262839.269238"},{"key":"11_CR26_Ref","doi-asserted-by":"publisher","first-page":"47","DOI":"10.1007\/BF01982509","volume":"17","author":"W. Warntz","year":"1966","unstructured":"W. Warntz. The topology of a socio-economic terrain and spatial flows. Regional Scientific Associations, 17:47-61, 1966.","journal-title":"Regional Scientific Associations"}],"container-title":["Mathematics and Visualization","Topology-based Methods in Visualization"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-540-70823-0_11.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,11,19]],"date-time":"2020-11-19T05:10:34Z","timestamp":1605762634000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-540-70823-0_11"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2007]]},"ISBN":["9783540708223","9783540708230"],"references-count":26,"URL":"https:\/\/doi.org\/10.1007\/978-3-540-70823-0_11","relation":{},"ISSN":["1612-3786"],"issn-type":[{"value":"1612-3786","type":"print"}],"subject":[],"published":{"date-parts":[[2007]]}}}