{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,9,4]],"date-time":"2024-09-04T13:13:43Z","timestamp":1725455623499},"publisher-location":"Berlin, Heidelberg","reference-count":20,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"type":"print","value":"9783540638841"},{"type":"electronic","value":"9783540696605"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[1997]]},"DOI":"10.1007\/bfb0024838","type":"book-chapter","created":{"date-parts":[[2005,11,19]],"date-time":"2005-11-19T07:33:57Z","timestamp":1132385637000},"page":"161-174","source":"Crossref","is-referenced-by-count":2,"title":["The Euler characteristic of discrete object"],"prefix":"10.1007","author":[{"given":"Atsushi","family":"Imiya","sequence":"first","affiliation":[]},{"given":"Ulrich","family":"Eckhardt","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2005,6,10]]},"reference":[{"key":"13_CR1","first-page":"2153","volume":"34","author":"A. Imiya","year":"1993","unstructured":"Imiya, A.: Geometry of three-dimensional neighborhood and its applications, Transactions of Information Processing Society of Japan, Vol. 34, pp. 2153\u20132164, 1993 (in Japanese).","journal-title":"Transactions of Information Processing Society of Japan"},{"key":"13_CR2","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"127","DOI":"10.1007\/3-540-62005-2_11","volume-title":"Discrete Geometry for Computer Imagery","author":"Y. Kenmochi","year":"1996","unstructured":"Kenmochi, Y., Imiya, A., and Ezuquera, R.: Polyhedra generation from lattice points, Miguet, S., and Montanvert, A., and Ub\u00e9da, S. eds.: Discrete Geometry for Computer Imagery, pp.127\u2013138, Lecture Notes in Computer Science, Vol. 1176, Springer-Verlag: Berlin, 1996."},{"key":"13_CR3","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"146","DOI":"10.1007\/3-540-63460-6_111","volume-title":"Computer Analysis of Images and Patterns","author":"Y. Kenmochi","year":"1997","unstructured":"Kenmochi, Y. and Imiya, A.: Deformation of discrete object surfaces, Sommer, G., Daniilidis, K. and Pauli, J. eds.: Computer Analysis of Images and Patterns, pp. 146\u2013153, Lecture Notes in Computer Science, Vol. 1296, Springer-Verlag: Berlin, 1997."},{"key":"13_CR4","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"36","DOI":"10.1007\/3-540-62005-2_4","volume-title":"Discrete Geometry for Computer Imagery","author":"Z. Aktouf","year":"1996","unstructured":"Aktouf, Z., Bertrand, G., and Perrton, L.: A three-dimensional holes closing algorithm, pp. 36\u201338, Miguet, S., and Montanvert, A., and Ub\u00e9da, S. eds.: Discrete Geometry for Computer Imagery, Lecture Notes in Computer Science, Vol. 1176, Springer-Verlag: Berlin, 1996."},{"key":"13_CR5","volume-title":"Convex Polytopes","author":"B. Gr\u00fcnbaum","year":"1967","unstructured":"Gr\u00fcnbaum, B.:Convex Polytopes, Interscience: London, 1967."},{"key":"13_CR6","volume-title":"Spatial Tessellations Concepts and Applications of Voronoi Diagrams","author":"A. Okabe","year":"1992","unstructured":"Okabe, A., Boots, B., and Sugihara, K.: Spatial Tessellations Concepts and Applications of Voronoi Diagrams, John Wiley& Sons: Chichster, 1992."},{"key":"13_CR7","series-title":"Lecture Notes in Mathematics","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-662-21563-0","volume-title":"Diferential Geometry in the Large","author":"H. Hopf","year":"1983","unstructured":"Hopf, H.:Diferential Geometry in the Large, Lecture Notes in Mathematics, Vol. 1000, Springer-Verlag: Berlin, 1983."},{"key":"13_CR8","volume-title":"Image Analysis and Mathematical Morphology","author":"J. Serra","year":"1982","unstructured":"Serra, J.:Image Analysis and Mathematical Morphology, Academic Press: London, 1982."},{"key":"13_CR9","volume-title":"Digital Image processing for Image Understanding, Vols.1 and 2","author":"J.-I. Toriwaki","year":"1988","unstructured":"Toriwaki, J.-I.: Digital Image processing for Image Understanding, Vols.1 and 2, Syokodo: Tokyo, 1988 (in Japanese)."},{"key":"13_CR10","first-page":"815","volume":"E63","author":"T. Yonekura","year":"1980","unstructured":"Yonekura, T., Toriwaki, J.-I., and Fukumura, T., and Yokoi, S.: On connectivity and the Euler number of three-dimensional digitized binary picture, Transactions on IECE Japan, Vol. E63, pp. 815\u2013816, 1980.","journal-title":"Transactions on IECE Japan"},{"key":"13_CR11","unstructured":"Toriwaki, J.-I., Yokoi, S., Yonekura, T., and Fukumura, 'P.: Topological properties and topological preserving transformation of a three-dimensional binary picture, Proc. of the 6th ICPR, pp. 414\u2013419, 1982."},{"key":"13_CR12","doi-asserted-by":"crossref","first-page":"20","DOI":"10.1006\/cgip.1993.1002","volume":"55","author":"C.-N. Lee","year":"1993","unstructured":"Lee, C.-N., Poston, T., and Rosenfeld, A.: Holes and genus of 2D and 3D digital images, CVGIP Graphical Models and Image Processing, Vol. 55, pp. 20\u201347, 1993.","journal-title":"CVGIP Graphical Models and Image Processing"},{"key":"13_CR13","doi-asserted-by":"crossref","first-page":"159","DOI":"10.1016\/0304-3975(95)00059-3","volume":"156","author":"J. Fran\u00e7on","year":"1996","unstructured":"Fran\u00e7on, J.: Sur la topologie d'un plan arithm\u00e9tique, Theoretical Computer Sciences, Vol. 156, pp. 159\u2013176, 1996.","journal-title":"Theoretical Computer Sciences"},{"key":"13_CR14","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4612-2540-9","volume-title":"The Foundation, of Topological Graph Theory","author":"C. P. Bonnington","year":"1995","unstructured":"Bonnington, C. P. and Little, C.H.C.: The Foundation, of Topological Graph Theory Springer-Verlag:Berlin, 1995."},{"key":"13_CR15","doi-asserted-by":"crossref","first-page":"166","DOI":"10.1016\/S0734-189X(84)80019-5","volume":"28","author":"H. Bieri","year":"1984","unstructured":"Bieri, H. and Nef, W.: Algorithms for the Euler characteristic and related additive firnctionals of digital objects, Computer Vision, Graphics, and Image Processing Vol. 28, pp. 166\u2013175, 1984.","journal-title":"Computer Vision, Graphics, and Image Processing"},{"key":"13_CR16","doi-asserted-by":"crossref","first-page":"189","DOI":"10.1007\/BF02241747","volume":"28","author":"H. Bieri","year":"1982","unstructured":"Bieri, H. and Nef, W.: A recursive sweep-plane algorithm, determining all cells of a finite division of R\nd, Computing Vol. 28, pp. 189\u2013198, 1982.","journal-title":"Computing"},{"key":"13_CR17","doi-asserted-by":"crossref","first-page":"69","DOI":"10.1016\/0024-3795(83)80008-1","volume":"52\/53","author":"H. Bieri","year":"1983","unstructured":"Bieri, H. and Nef, W.: A sweep-plane algorithm for computing the volume of polyhedra represented in Boolean form, Linear Algebra and Its Applications, Vol. 52\/53, pp. 69\u201397, 1983.","journal-title":"Linear Algebra and Its Applications"},{"key":"13_CR18","doi-asserted-by":"crossref","first-page":"287","DOI":"10.1007\/BF02251831","volume":"34","author":"H. Bied","year":"1985","unstructured":"Bied, H. and Nef, W.: A sweep-plane algorithm for computing the Eulercharacteristic of polyhedra represented in Boolean form, Computing, Vol. 34, pp. 287\u2013304, 1985.","journal-title":"Computing"},{"key":"13_CR19","first-page":"184","volume":"1","author":"H. Stark","year":"1988","unstructured":"Stark, H. and Peng, H.: Shape estimation in computer tomography from minimal data, Proceedings of 9th ICPR, Vol. 1, pp. 184\u2013186, 1988.","journal-title":"Proceedings of 9th ICPR"},{"key":"13_CR20","doi-asserted-by":"crossref","first-page":"49","DOI":"10.1002\/cpa.3160190105","volume":"19","author":"D. Ludwing","year":"1966","unstructured":"Ludwing, D.: The Radon transform on Euclidean space, Comm. Pure and Applied Mathematics, Vol. 19, pp. 49\u201381, 1966.","journal-title":"Comm. Pure and Applied Mathematics"}],"container-title":["Lecture Notes in Computer Science","Discrete Geometry for Computer Imagery"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/BFb0024838","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,2,4]],"date-time":"2019-02-04T23:40:08Z","timestamp":1549323608000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/BFb0024838"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1997]]},"ISBN":["9783540638841","9783540696605"],"references-count":20,"URL":"https:\/\/doi.org\/10.1007\/bfb0024838","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[1997]]}}}