{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,6,12]],"date-time":"2025-06-12T10:43:53Z","timestamp":1749725033129},"publisher-location":"Berlin, Heidelberg","reference-count":26,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"type":"print","value":"9783540631675"},{"type":"electronic","value":"9783540691969"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[1997]]},"DOI":"10.1007\/3-540-63167-4_49","type":"book-chapter","created":{"date-parts":[[2012,2,26]],"date-time":"2012-02-26T23:15:01Z","timestamp":1330298101000},"page":"176-187","source":"Crossref","is-referenced-by-count":7,"title":["Image loci are ridges in geometric spaces"],"prefix":"10.1007","author":[{"given":"Jacob D.","family":"Furst","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Robert S.","family":"Keller","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jason E.","family":"Miller","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Stephen M.","family":"Pizer","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2005,6,8]]},"reference":[{"issue":"6","key":"13_CR1","doi-asserted-by":"crossref","first-page":"726","DOI":"10.1109\/TPAMI.1987.4767980","volume":"PAMI-9","author":"F. Bergholm","year":"1987","unstructured":"F. Bergholm. Edge focusing. IEEE Transactions on Pattern Analysis and Machine Intelligence, PAMI-9(6):726\u2013741, November 1987.","journal-title":"IEEE Transactions on Pattern Analysis and Machine Intelligence"},{"key":"13_CR2","doi-asserted-by":"crossref","first-page":"167","DOI":"10.1016\/0031-3203(78)90025-0","volume":"10","author":"H. Blum","year":"1978","unstructured":"H. Blum and R. N. Nagel. Shape description using weighted symmetric axis features. Pattern Recognition, 10:167\u2013180, 1978.","journal-title":"Pattern Recognition"},{"issue":"6","key":"13_CR3","doi-asserted-by":"crossref","first-page":"679","DOI":"10.1109\/TPAMI.1986.4767851","volume":"PAMI-8","author":"J. Canny","year":"1986","unstructured":"J. Canny. A computational approach to edge detection. IEEE Transactions on Pattern Analysis and Machine Intelligence, PAMI-8(6):679\u2013698, November 1986.","journal-title":"IEEE Transactions on Pattern Analysis and Machine Intelligence"},{"key":"13_CR4","unstructured":"J. Damon. Generic structure of two dimensional images under Gaussian blurring. very preliminary version, 1996, preprint."},{"key":"13_CR5","doi-asserted-by":"crossref","unstructured":"J. Damon. Local morse theory for Gaussian blurred images. In L. Florak J. Sporring, M. Nielsen and P. Johansen, editors, Gaussian Scale Space Theory, chapter 12. Kluwer, 1996.","DOI":"10.1007\/978-94-015-8802-7_11"},{"key":"13_CR6","doi-asserted-by":"crossref","first-page":"695","DOI":"10.2307\/2374610","volume":"109","author":"J. Damon","year":"1987","unstructured":"J. Damon. Deformations of sections of singularities and Gorenstein surface singularities. Amer. J. Math., 109:695\u2013722, 1987.","journal-title":"Amer. J. Math."},{"key":"13_CR7","doi-asserted-by":"crossref","first-page":"93","DOI":"10.1007\/BFb0086377","volume":"1462","author":"J. Damon","year":"1991","unstructured":"J. Damon. A-equivalence and the equivalence of sections of images and discriminants. Springer Lecture Notes, 1462:93\u2013121, 1991.","journal-title":"Springer Lecture Notes"},{"key":"13_CR8","volume-title":"Computational Vision Series","author":"D. Eberly","year":"1996","unstructured":"D. Eberly. Ridges in Image Analysis. Computational Vision Series. Kluwer Academic Publishers, Dordrecht, NL, 1996. to appear."},{"key":"13_CR9","doi-asserted-by":"crossref","first-page":"351","DOI":"10.1007\/BF01262402","volume":"4","author":"D. Eberly","year":"1994","unstructured":"D. Eberly, R. Gardner, B. Morse, S. Pizer, and C. Scharlach. Ridges for image analysis. Journal of Mathematical Imaging and Vision, 4:351\u2013371, 1994.","journal-title":"Journal of Mathematical Imaging and Vision"},{"key":"13_CR10","doi-asserted-by":"crossref","unstructured":"M. Fidrich. Iso-surface extraction in 4d with applications related to scale space. Technical Report 2833, Institut National de Recherche en Informatique et en Automatique, March 1996.","DOI":"10.1007\/3-540-62005-2_22"},{"key":"13_CR11","unstructured":"D. S. Fritsch, D. Eberly, S. M. Pizer, and M. J. McAuliffe. Simulated cores and their application in medical imaging. Information Processing in Medical Imaging, Y. Bizais, C. Barillot, and R. Di Paola (eds.) Computational Imaging and Vision Series. pages 365\u2013368, 1995."},{"key":"13_CR12","doi-asserted-by":"crossref","first-page":"28","DOI":"10.1016\/0734-189X(83)90094-4","volume":"22","author":"R. M. Haralick","year":"1983","unstructured":"R. M. Haralick. Ridges and valleys on digital images. Computer Vision, Graphics, and Image Processing, 22:28\u201338, 1983.","journal-title":"Computer Vision, Graphics, and Image Processing"},{"key":"13_CR13","unstructured":"R. Katz. Ph. D. Thesis Computer Science Dept. University of North Carolina, in preparation, 1997."},{"key":"13_CR14","doi-asserted-by":"crossref","unstructured":"M. W. Hirsch. Differential Topology. Number 33 in Graduate texts in Mathematics. Springer-Verlag, 1976.","DOI":"10.1007\/978-1-4684-9449-5"},{"key":"13_CR15","unstructured":"R. Keller. Ph.D. Thesis. Mathematics Dept., University of North Carolina, in preparation, 1997."},{"key":"13_CR16","doi-asserted-by":"crossref","unstructured":"T. Lindeberg. Edge detection and ridge detection with automatic scale selection. Technical Report ISRN KTH\/NA\/P-96\/06-SE, KTH (Royal Institute of Technology), 1996.","DOI":"10.1109\/CVPR.1996.517113"},{"key":"13_CR17","doi-asserted-by":"crossref","first-page":"199","DOI":"10.1090\/pspum\/040.2\/713249","volume":"40","author":"J. N. Mather","year":"1983","unstructured":"J. N. Mather. Distance from a submanifold in Euclidean space. Proceedings of Symposia in Pure Mathematics, 40:199\u2013216, 1983.","journal-title":"Proceedings of Symposia in Pure Mathematics"},{"key":"13_CR18","unstructured":"J. Miller. Ph.D. Thesis. Mathematics Dept., University of North Carolina, in preparation, 1997."},{"key":"13_CR19","doi-asserted-by":"crossref","first-page":"112","DOI":"10.1007\/BFb0013784","volume":"687","author":"B. S. Morse","year":"1993","unstructured":"B. S. Morse, S. M. Pizer, and A. Liu. Multiscale medial analysis of medical images. Proceedings on Information Processing in Medical Images, 687:112\u2013131, 1993.","journal-title":"Proceedings on Information Processing in Medical Images"},{"key":"13_CR20","doi-asserted-by":"crossref","first-page":"43","DOI":"10.1016\/0146-664X(82)90072-7","volume":"20","author":"L. R. Nackman","year":"1982","unstructured":"L. R. Nackman. Curvature relations in three-dimensional symmetric axes. Computer Graphics and Image Processing, 20:43\u201357, 1982.","journal-title":"Computer Graphics and Image Processing"},{"issue":"2","key":"13_CR21","doi-asserted-by":"crossref","first-page":"187","DOI":"10.1109\/TPAMI.1985.4767643","volume":"6","author":"L. R. Nackman","year":"1985","unstructured":"L. R. Nackman and S. M. Pizer. Three-dimensional shape description using the symmetric axis transform, i: Theory. IEEE Transactions of Pattern Analysis and Machine Intelligence, 6(2):187\u2013202, 1985.","journal-title":"IEEE Transactions of Pattern Analysis and Machine Intelligence"},{"key":"13_CR22","unstructured":"S. M. Pizer, D. H. Eberly, B. S. Morse, and D. S. Fritsch. Zoom invariant vision of figurai shape: the mathematics of cores. Technical Report TR96-004, University of North Carolina, 1996. Accepted for publication in Computer Vision and Image Understanding."},{"issue":"1","key":"13_CR23","doi-asserted-by":"crossref","first-page":"147","DOI":"10.1006\/cviu.1996.0050","volume":"64","author":"X. Qu","year":"1996","unstructured":"X. Qu and X. Li. A 3d surface tracking algorithm. Computer Vision and Image Understanding, 64(1):147\u2013156, July 1996.","journal-title":"Computer Vision and Image Understanding"},{"key":"13_CR24","unstructured":"J. Thirion and A. Gourdon. The 3d marching lines algorithm and its application to crest lines extraction. Technical Report 1672, Institut National de Recherche en Informatique et en Automatique, May 1992."},{"key":"13_CR25","unstructured":"J. Thirion and A. Gourdon. The marching lines algorithm: new results and proofs. Technical Report 1881, Institut National de Recherche en Informatique et en Automatique, April 1993."},{"issue":"2","key":"13_CR26","first-page":"225","volume":"43","author":"Y. Yomdin","year":"1981","unstructured":"Y. Yomdin. On the local structure of a generic central set. Compositio Mathematica, 43(2):225\u2013238, 1981.","journal-title":"Compositio Mathematica"}],"container-title":["Lecture Notes in Computer Science","Scale-Space Theory in Computer Vision"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/3-540-63167-4_49.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,11,17]],"date-time":"2020-11-17T21:16:56Z","timestamp":1605647816000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/3-540-63167-4_49"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1997]]},"ISBN":["9783540631675","9783540691969"],"references-count":26,"URL":"https:\/\/doi.org\/10.1007\/3-540-63167-4_49","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[1997]]}}}