{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,21]],"date-time":"2025-10-21T14:52:51Z","timestamp":1761058371120},"publisher-location":"Berlin, Heidelberg","reference-count":27,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"type":"print","value":"9783540298366"},{"type":"electronic","value":"9783540320975"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2005]]},"DOI":"10.1007\/11577812_12","type":"book-chapter","created":{"date-parts":[[2005,11,22]],"date-time":"2005-11-22T06:28:13Z","timestamp":1132640893000},"page":"135-145","source":"Crossref","is-referenced-by-count":3,"title":["Deep Structure from a Geometric Point of View"],"prefix":"10.1007","author":[{"given":"Luc","family":"Florack","sequence":"first","affiliation":[]}],"member":"297","reference":[{"key":"12_CR1","doi-asserted-by":"publisher","first-page":"363","DOI":"10.1007\/BF00336961","volume":"50","author":"J.J. Koenderink","year":"1984","unstructured":"Koenderink, J.J.: The structure of images. Biological Cybernetics\u00a050, 363\u2013370 (1984)","journal-title":"Biological Cybernetics"},{"key":"12_CR2","volume-title":"Partial Differential Equations","author":"D. Colton","year":"1988","unstructured":"Colton, D.: Partial Differential Equations. Random House, New York (1988)"},{"key":"12_CR3","doi-asserted-by":"publisher","first-page":"1222","DOI":"10.1109\/34.42861","volume":"11","author":"J.J. Koenderink","year":"1989","unstructured":"Koenderink, J.J.: A hitherto unnoticed singularity of scale-space. IEEE Transactions on Pattern Analysis and Machine Intelligence\u00a011, 1222\u20131224 (1989)","journal-title":"IEEE Transactions on Pattern Analysis and Machine Intelligence"},{"key":"12_CR4","doi-asserted-by":"publisher","first-page":"368","DOI":"10.1006\/jdeq.1995.1019","volume":"115","author":"J. Damon","year":"1995","unstructured":"Damon, J.: Local Morse theory for solutions to the heat equation and Gaussian blurring. Journal of Differential Equations\u00a0115, 368\u2013401 (1995)","journal-title":"Journal of Differential Equations"},{"key":"12_CR5","doi-asserted-by":"publisher","first-page":"65","DOI":"10.1023\/A:1008304909717","volume":"12","author":"L. Florack","year":"2000","unstructured":"Florack, L., Kuijper, A.: The topological structure of scale-space images. Journal of Mathematical Imaging and Vision\u00a012, 65\u201379 (2000)","journal-title":"Journal of Mathematical Imaging and Vision"},{"key":"12_CR6","doi-asserted-by":"publisher","first-page":"169","DOI":"10.1023\/A:1022168617945","volume":"18","author":"A. Kuijper","year":"2003","unstructured":"Kuijper, A., Florack, L.M.J., Viergever, M.A.: Scale space hierarchy. Journal of Mathematical Imaging and Vision\u00a018, 169\u2013189 (2003)","journal-title":"Journal of Mathematical Imaging and Vision"},{"key":"12_CR7","doi-asserted-by":"publisher","first-page":"1067","DOI":"10.1109\/TIP.2003.815252","volume":"12","author":"A. Kuijper","year":"2003","unstructured":"Kuijper, A., Florack, L.M.J.: The hierarchical structure of images. IEEE Transactions on Image Processing\u00a012, 1067\u20131079 (2003)","journal-title":"IEEE Transactions on Image Processing"},{"key":"12_CR8","doi-asserted-by":"publisher","first-page":"67","DOI":"10.1023\/B:VISI.0000013091.14851.24","volume":"57","author":"A. Kuijper","year":"2004","unstructured":"Kuijper, A., Florack, L.M.J.: The relevance of non-generic events in scale space models. International Journal of Computer Vision\u00a057, 67\u201384 (2004)","journal-title":"International Journal of Computer Vision"},{"key":"12_CR9","doi-asserted-by":"crossref","unstructured":"Eberly, D.: A differential geometric approach to anisotropic diffusion. [24], 371\u2013392","DOI":"10.1007\/978-94-017-1699-4_14"},{"key":"12_CR10","series-title":"Computational Imaging and Vision Series","doi-asserted-by":"crossref","DOI":"10.1007\/978-94-015-8765-5","volume-title":"Ridges in Image and Data Analysis","author":"D. Eberly","year":"1996","unstructured":"Eberly, D.: Ridges in Image and Data Analysis. Computational Imaging and Vision Series, vol.\u00a07. Kluwer Academic Publishers, Dordrecht (1996)"},{"key":"12_CR11","first-page":"15","volume-title":"Proceedings of the IEEE Symposium on Information Visualization (InfoVis 2003)","author":"J.J. Wijk","year":"2003","unstructured":"Wijk, J.J., Nuij, W.A.A.: Smooth and efficient zooming and panning. In: Munzner, T., North, S. (eds.) Proceedings of the IEEE Symposium on Information Visualization (InfoVis 2003), pp. 15\u201322. IEEE Computer Society Press, Los Alamitos (2003) Best paper award"},{"key":"12_CR12","volume-title":"Gravitation","author":"C.W. Misner","year":"1973","unstructured":"Misner, C.W., Thorne, K.S., Wheeler, J.A.: Gravitation. Freeman, San Francisco (1973)"},{"key":"12_CR13","doi-asserted-by":"crossref","first-page":"325","DOI":"10.24033\/asens.751","volume":"40","author":"\u00c9. Cartan","year":"1923","unstructured":"Cartan, \u00c9.: Sur les vari\u00e9t\u00e9s \u00e0 connexion affine et la th\u00e9orie de la relativit\u00e9 generalis\u00e9e (premi\u00e8re partie). Ann. \u00c9cole Norm. Sup.\u00a040, 325\u2013412 (1923)","journal-title":"Ann. \u00c9cole Norm. Sup."},{"key":"12_CR14","volume-title":"Differential Geometry","author":"M. Spivak","year":"1975","unstructured":"Spivak, M.: Differential Geometry, vol.\u00a01\u20135. Publish or Perish, Berkeley (1975)"},{"key":"12_CR15","volume-title":"Solid Shape","author":"J.J. Koenderink","year":"1990","unstructured":"Koenderink, J.J.: Solid Shape. MIT Press, Cambridge (1990)"},{"key":"12_CR16","volume-title":"Foundations of Space-Time Theories: Relativistic Physics and Philosophy of Science","author":"M. Friedman","year":"1983","unstructured":"Friedman, M.: Foundations of Space-Time Theories: Relativistic Physics and Philosophy of Science. Princeton University Press, Princeton (1983)"},{"key":"12_CR17","first-page":"485","volume-title":"The Philosophy of Science","author":"C. Glymour","year":"1991","unstructured":"Glymour, C.: The epistemology of geometry. In: Boyd, R., Gasper, P., Trout, J.D. (eds.) The Philosophy of Science, pp. 485\u2013500. MIT Press, Cambridge (1991)"},{"key":"12_CR18","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"294","DOI":"10.1007\/3-540-48236-9_26","volume-title":"Scale-Space Theories in Computer Vision","author":"R. Kimmel","year":"1999","unstructured":"Kimmel, R., Sochen, N.A.: Geometric-variational approach for color image enhancement and segmentation. In: Nielsen, M., Johansen, P., Fogh Olsen, O., Weickert, J. (eds.) Scale-Space 1999. LNCS, vol.\u00a01682, pp. 294\u2013305. Springer, Heidelberg (1999)"},{"key":"12_CR19","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"236","DOI":"10.1007\/3-540-63167-4_54","volume-title":"Scale-Space Theory in Computer Vision","author":"R. Kimmel","year":"1997","unstructured":"Kimmel, R., Sochen, N.A., Malladi, R.: From high energy physics to low level vision. In: ter Haar Romeny, B.M., Florack, L.M.J., Viergever, M.A. (eds.) Scale-Space 1997. LNCS, vol.\u00a01252, pp. 236\u2013247. Springer, Heidelberg (1997)"},{"key":"12_CR20","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"127","DOI":"10.1007\/978-3-540-24673-2_11","volume-title":"Computer Vision - ECCV 2004","author":"C. Lenglet","year":"2004","unstructured":"Lenglet, C., Deriche, R., Faugeras, O.: Inferring white matter geometry from diffusion tensor MRI: Application to connectivity mapping. In: Pajdla, T., Matas, J(G.) (eds.) ECCV 2004. LNCS, vol.\u00a03021-3024 , pp. 127\u2013140. Springer, Heidelberg (2004)"},{"key":"12_CR21","first-page":"288","volume-title":"Proceedings of the 8th International Conference on Computer Vision","author":"N.A. Sochen","year":"2001","unstructured":"Sochen, N.A.: Stochastic processes in vision: From Langevin to Beltrami. In: Proceedings of the 8th International Conference on Computer Vision, Vancouver, Canada, July 9-12, pp. 288\u2013293. IEEE Computer Society Press, Los Alamitos (2001)"},{"key":"12_CR22","series-title":"ECMI Series","volume-title":"Anisotropic Diffusion in Image Processing","author":"J.A. Weickert","year":"1998","unstructured":"Weickert, J.A.: Anisotropic Diffusion in Image Processing. ECMI Series. Teubner, Stuttgart (1998)"},{"key":"12_CR23","doi-asserted-by":"publisher","first-page":"111","DOI":"10.1023\/A:1008009714131","volume":"31","author":"J.A. Weickert","year":"1999","unstructured":"Weickert, J.A.: Coherence-enhancing diffusion filtering. International Journal of Computer Vision\u00a031, 111\u2013127 (1999)","journal-title":"International Journal of Computer Vision"},{"key":"12_CR24","series-title":"Computational Imaging and Vision Series","doi-asserted-by":"crossref","DOI":"10.1007\/978-94-017-1699-4","volume-title":"Geometry-Driven Diffusion in Computer Vision","author":"B.M.t. Haar Romeny","year":"1994","unstructured":"Haar Romeny, B.M.t.: Geometry-Driven Diffusion in Computer Vision. Computational Imaging and Vision Series, vol.\u00a01. Kluwer Academic Publishers, Dordrecht (1994)"},{"key":"12_CR25","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"574","DOI":"10.1007\/3-540-45482-9_58","volume-title":"Biologically Motivated Computer Vision","author":"L.M.J. Florack","year":"2000","unstructured":"Florack, L.M.J.: A geometric model for cortical magnification. In: B\u00fclthoff, H.H., Poggio, T.A., Lee, S.-W. (eds.) BMCV 2000. LNCS, vol.\u00a01811, pp. 574\u2013583. Springer, Heidelberg (2000)"},{"key":"12_CR26","volume-title":"Lectures on Hyperbolic Geometry","author":"R. Benedetti","year":"1987","unstructured":"Benedetti, R., Petronio, C.: Lectures on Hyperbolic Geometry. Springer, Berlin (1987)"},{"key":"12_CR27","series-title":"Studies in Mathematics","doi-asserted-by":"crossref","DOI":"10.1515\/9783110849455","volume-title":"Elementary Geometry in Hyperbolic Space","author":"W. Fenchel","year":"1989","unstructured":"Fenchel, W.: Elementary Geometry in Hyperbolic Space. Studies in Mathematics, vol.\u00a011. Walter de Gruyter, Berlin (1989)"}],"container-title":["Lecture Notes in Computer Science","Deep Structure, Singularities, and Computer Vision"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/11577812_12.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,11,17]],"date-time":"2020-11-17T19:59:41Z","timestamp":1605643181000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/11577812_12"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2005]]},"ISBN":["9783540298366","9783540320975"],"references-count":27,"URL":"https:\/\/doi.org\/10.1007\/11577812_12","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2005]]}}}