{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,20]],"date-time":"2026-04-20T10:49:00Z","timestamp":1776682140427,"version":"3.51.2"},"publisher-location":"Berlin, Heidelberg","reference-count":21,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"value":"9783642347313","type":"print"},{"value":"9783642347320","type":"electronic"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2012]]},"DOI":"10.1007\/978-3-642-34732-0_11","type":"book-chapter","created":{"date-parts":[[2012,11,14]],"date-time":"2012-11-14T14:32:34Z","timestamp":1352903554000},"page":"143-153","source":"Crossref","is-referenced-by-count":16,"title":["Cellular Topology on the Triangular Grid"],"prefix":"10.1007","author":[{"given":"Benedek","family":"Nagy","sequence":"first","affiliation":[]}],"member":"297","reference":[{"key":"11_CR1","doi-asserted-by":"crossref","unstructured":"Brimkov, V.E., Barneva, R.: \u201cHoneycomb\u201d vs square and cubic models. Electronic Notes in Theoretical Computer Science\u00a046 (2001)","DOI":"10.1016\/S1571-0661(04)80995-2"},{"key":"11_CR2","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"397","DOI":"10.1007\/978-3-642-10210-3_31","volume-title":"Combinatorial Image Analysis","author":"J. Cousty","year":"2009","unstructured":"Cousty, J., Bertrand, G., Couprie, M., Najman, L.: Collapses and Watersheds in Pseudomanifolds. In: Wiederhold, P., Barneva, R.P. (eds.) IWCIA 2009. LNCS, vol.\u00a05852, pp. 397\u2013410. Springer, Heidelberg (2009)"},{"issue":"5","key":"11_CR3","doi-asserted-by":"publisher","first-page":"925","DOI":"10.1109\/TPAMI.2009.71","volume":"32","author":"J. Cousty","year":"2010","unstructured":"Cousty, J., Bertrand, G., Najman, L., Couprie, M.: Watershed cuts: Thinnings, shortest path forests, and topological watersheds. IEEE Transactions on Pattern Analysis and Machine Intelligence\u00a032(5), 925\u2013939 (2010)","journal-title":"IEEE Transactions on Pattern Analysis and Machine Intelligence"},{"key":"11_CR4","volume-title":"Introduction to Geometry","author":"H.S.M. Coxeter","year":"1969","unstructured":"Coxeter, H.S.M.: Introduction to Geometry, 2nd edn. Wiley, New York (1969)","edition":"2"},{"key":"11_CR5","unstructured":"Hatcher, A.: Algebraic Topology. Cambridge University Press (2002)"},{"issue":"9","key":"11_CR6","doi-asserted-by":"publisher","first-page":"1213","DOI":"10.1109\/83.413166","volume":"4","author":"I. Her","year":"1995","unstructured":"Her, I.: Geometric transformations on the hexagonal grid. IEEE Transactions on Image Processing\u00a04(9), 1213\u20131222 (1995)","journal-title":"IEEE Transactions on Image Processing"},{"key":"11_CR7","unstructured":"Ito, K. (ed.): Encyclopedic Dictionary of Mathematics, vol. 2. MIT Press (1993, 2000) (original Japanese edition, 1954)"},{"issue":"5","key":"11_CR8","doi-asserted-by":"publisher","first-page":"532","DOI":"10.1109\/TC.1976.1674642","volume":"C-25","author":"E. Luczak","year":"1976","unstructured":"Luczak, E., Rosenfeld, A.: Distance on a hexagonal grid. Transactions on Computers\u00a0C-25(5), 532\u2013533 (1976)","journal-title":"Transactions on Computers"},{"key":"11_CR9","unstructured":"Klette, R., Rosenfeld, A.: Digital geometry. Geometric methods for digital picture analysis. Morgan Kaufmann Publishers, San Francisco; Elsevier Science B.V., Amsterdam (2004)"},{"issue":"3","key":"11_CR10","doi-asserted-by":"publisher","first-page":"357","DOI":"10.1016\/0734-189X(89)90147-3","volume":"48","author":"T. Kong","year":"1989","unstructured":"Kong, T., Rosenfeld, A.: Digital topology: Introduction and survey. Computer Vision, Graphics, and Image Processing\u00a048(3), 357\u2013393 (1989)","journal-title":"Computer Vision, Graphics, and Image Processing"},{"key":"11_CR11","doi-asserted-by":"publisher","first-page":"141","DOI":"10.1016\/0734-189X(89)90165-5","volume":"45","author":"V. Kovalevsky","year":"1989","unstructured":"Kovalevsky, V.: Finite topology as applied to image analysis. Computer Vision, Graphics and Image Processing\u00a045, 141\u2013161 (1989)","journal-title":"Computer Vision, Graphics and Image Processing"},{"key":"11_CR12","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"366","DOI":"10.1007\/978-3-540-30503-3_27","volume-title":"Combinatorial Image Analysis","author":"V. Kovalevsky","year":"2004","unstructured":"Kovalevsky, V.: Algorithms in Digital Geometry Based on Cellular Topology. In: Klette, R., \u017duni\u0107, J. (eds.) IWCIA 2004. LNCS, vol.\u00a03322, pp. 366\u2013393. Springer, Heidelberg (2004)"},{"key":"11_CR13","unstructured":"Kovalevsky, V.A.: Geometry of Locally Finite Spaces (Computer Agreeable Topology and Algorithms for Computer Imagery). Editing House Dr. B\u00e4rbel Kovalevski, Berlin (2008)"},{"key":"11_CR14","doi-asserted-by":"crossref","unstructured":"Nagy, B.: A family of triangular grids in digital geometry. In: ISPA 2003, 3rd International Symposium on Image and Signal Processing and Analysis, Rome, Italy, pp. 101\u2013106 (2003)","DOI":"10.1109\/ISPA.2003.1296876"},{"key":"11_CR15","first-page":"63","volume":"20","author":"B. Nagy","year":"2004","unstructured":"Nagy, B.: Generalized triangular grids in digital geometry. Acta Mathematica Academiae Paedagogicae Ny\u00edregyh\u00e1ziensis\u00a020, 63\u201378 (2004)","journal-title":"Acta Mathematica Academiae Paedagogicae Ny\u00edregyh\u00e1ziensis"},{"key":"11_CR16","unstructured":"Nagy, B.: A symmetric coordinate frame for hexagonal networks. In: Theoretical Computer Science - Information Society 2004, Ljubljana, Slovenia, pp. 193\u2013196 (2004)"},{"issue":"11","key":"11_CR17","doi-asserted-by":"publisher","first-page":"1231","DOI":"10.1016\/j.patrec.2004.04.001","volume":"25","author":"B. Nagy","year":"2004","unstructured":"Nagy, B.: Characterization of digital circles in triangular grid. Pattern Recognition Letters\u00a025(11), 1231\u20131242 (2004)","journal-title":"Pattern Recognition Letters"},{"key":"11_CR18","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"1157","DOI":"10.1007\/978-3-540-89646-3_115","volume-title":"Advances in Visual Computing","author":"B. Nagy","year":"2008","unstructured":"Nagy, B., Strand, R.: A Connection between \u2124 n and Generalized Triangular Grids. In: Bebis, G., Boyle, R., Parvin, B., Koracin, D., Remagnino, P., Porikli, F., Peters, J., Klosowski, J., Arns, L., Chun, Y.K., Rhyne, T.-M., Monroe, L. (eds.) ISVC 2008, Part II. LNCS, vol.\u00a05359, pp. 1157\u20131166. Springer, Heidelberg (2008)"},{"issue":"2","key":"11_CR19","doi-asserted-by":"publisher","first-page":"209","DOI":"10.1142\/S0218654308001154","volume":"14","author":"B. Nagy","year":"2008","unstructured":"Nagy, B., Strand, R.: Non-traditional grids embedded in \u2124 n . International Journal of Shape Modeling - IJSM\u00a014(2), 209\u2013228 (2008)","journal-title":"International Journal of Shape Modeling - IJSM"},{"issue":"1","key":"11_CR20","doi-asserted-by":"publisher","first-page":"21","DOI":"10.1111\/1467-8659.1210021","volume":"12","author":"L. Yong-Kui","year":"1993","unstructured":"Yong-Kui, L.: The generation of straight lines on hexagonal grids. Comput. Graph. Forum\u00a012(1), 21\u201325 (1993)","journal-title":"Comput. Graph. Forum"},{"issue":"4","key":"11_CR21","doi-asserted-by":"publisher","first-page":"324","DOI":"10.1016\/1049-9652(91)90036-J","volume":"53","author":"C.A. Wuthrich","year":"1991","unstructured":"Wuthrich, C.A., Stucki, P.: An algorithm comparison between square- and hexagonal-based grids. Graph. Model Im. Proc.\u00a053(4), 324\u2013339 (1991)","journal-title":"Graph. Model Im. Proc."}],"container-title":["Lecture Notes in Computer Science","Combinatorial Image Analaysis"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-642-34732-0_11.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,4,20]],"date-time":"2025-04-20T21:34:01Z","timestamp":1745184841000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-642-34732-0_11"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012]]},"ISBN":["9783642347313","9783642347320"],"references-count":21,"URL":"https:\/\/doi.org\/10.1007\/978-3-642-34732-0_11","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"value":"0302-9743","type":"print"},{"value":"1611-3349","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012]]}}}