{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,5,14]],"date-time":"2025-05-14T22:27:50Z","timestamp":1747261670994,"version":"3.37.3"},"reference-count":20,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2018,9,8]],"date-time":"2018-09-08T00:00:00Z","timestamp":1536364800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Math Imaging Vis"],"published-print":{"date-parts":[[2019,2]]},"DOI":"10.1007\/s10851-018-0846-5","type":"journal-article","created":{"date-parts":[[2018,9,8]],"date-time":"2018-09-08T05:18:35Z","timestamp":1536383915000},"page":"224-236","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Combinatorics of the Gauss Digitization Under Translation in 2D"],"prefix":"10.1007","volume":"61","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2038-9434","authenticated-orcid":false,"given":"\u00c9tienne","family":"Baudrier","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Lo\u00efc","family":"Mazo","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2018,9,8]]},"reference":[{"key":"846_CR1","doi-asserted-by":"publisher","unstructured":"Baudrier, \u00c9., Mazo, L.: Curve digitization variability. In: Normand, N, Gu\u00e9don, J, Autrusseau, F (eds.) Discrete Geometry for Computer Imagery. DGCI 2016, Lecture Notes in Computer Science, vol. 9647, pp. 59\u201370. Springer, Heidelberg, IAPR (2016) \n                    https:\/\/doi.org\/10.1007\/978-3-319-32360-2_5","DOI":"10.1007\/978-3-319-32360-2_5"},{"key":"846_CR2","doi-asserted-by":"publisher","unstructured":"Berger, M.: Geometry I. Universitext. Springer-Verlag Berlin Heidelberg (1987). \n                    https:\/\/doi.org\/10.1007\/978-3-540-93815-6","DOI":"10.1007\/978-3-540-93815-6"},{"key":"846_CR3","unstructured":"Dorst, L., Smeulders, A.W.M.: Discrete representation of straight lines. IEEE Trans. Pattern Anal. Mach. Intell. 6(4), 450\u2013463 (1984), \n                    http:\/\/ieeexplore.ieee.org\/lpdocs\/epic03\/wrapper.htm?arnumber=4767550"},{"issue":"1\u20133","key":"846_CR4","doi-asserted-by":"publisher","first-page":"51","DOI":"10.1016\/j.dam.2002.11.009","volume":"139","author":"F Feschet","year":"2004","unstructured":"Feschet, F., Tougne, L.: An approach for the estimation of the precision of a real object from its digitization. Discret. Appl. Math. 139(1\u20133), 51\u201363 (2004). \n                    https:\/\/doi.org\/10.1016\/j.dam.2002.11.009","journal-title":"Discret. Appl. Math."},{"key":"846_CR5","first-page":"883","volume":"2","author":"D Heath-Brown","year":"1997","unstructured":"Heath-Brown, D.: Lattice points in the sphere. Number Theory Prog. 2, 883\u2013892 (1997)","journal-title":"Number Theory Prog."},{"issue":"1","key":"846_CR6","doi-asserted-by":"publisher","first-page":"127","DOI":"10.1515\/forum.2010.007","volume":"22","author":"MN Huxley","year":"2010","unstructured":"Huxley, M.N.: The number of configurations in lattice point counting I. Forum Math. 22(1), 127\u2013152 (2010). \n                    https:\/\/doi.org\/10.1112\/plms\/pdt011","journal-title":"Forum Math."},{"key":"846_CR7","doi-asserted-by":"publisher","unstructured":"Huxley, M.N., \u017duni\u0107, J.D.: On the number of digitizations of a disc depending on its position. In: Combinatorial Image Analysis, 10th Int Workshop, IWCIA 2004, New Zealand. pp. 219\u2013231 (2004) \n                    https:\/\/doi.org\/10.1007\/978-3-540-30503-3_17","DOI":"10.1007\/978-3-540-30503-3_17"},{"issue":"2","key":"846_CR8","doi-asserted-by":"publisher","first-page":"255","DOI":"10.1007\/s10208-005-0177-y","volume":"6","author":"MN Huxley","year":"2006","unstructured":"Huxley, M.N., \u017duni\u0107, J.D.: Different digitisations of displaced discs. Found Comput. Math. 6(2), 255\u2013268 (2006). \n                    https:\/\/doi.org\/10.1007\/s10208-005-0177-y","journal-title":"Found Comput. Math."},{"issue":"1","key":"846_CR9","doi-asserted-by":"publisher","first-page":"159","DOI":"10.1109\/TPAMI.2007.250606","volume":"29","author":"MN Huxley","year":"2007","unstructured":"Huxley, M.N., \u017duni\u0107, J.D.: The number of \n                    \n                      \n                    \n                    $$N$$\n                    \n                      \n                        N\n                      \n                    \n                  -point digital discs. IEEE Trans. Pattern Anal. Mach. Intell. 29(1), 159\u2013161 (2007). \n                    https:\/\/doi.org\/10.1109\/TPAMI.2007.250606","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"issue":"3","key":"846_CR10","doi-asserted-by":"publisher","first-page":"403","DOI":"10.1007\/s10851-016-0643-y","volume":"56","author":"MN Huxley","year":"2016","unstructured":"Huxley, M.N., \u017duni\u0107, J.D.: The number of different digital \n                    \n                      \n                    \n                    $$N$$\n                    \n                      \n                        N\n                      \n                    \n                  -discs. J. Math. Imaging Vision 56(3), 403\u2013408 (2016). \n                    https:\/\/doi.org\/10.1007\/s10851-016-0643-y","journal-title":"J. Math. Imaging Vision"},{"issue":"1","key":"846_CR11","doi-asserted-by":"publisher","first-page":"47","DOI":"10.1007\/BF01571276","volume":"110","author":"JE Mazo","year":"1990","unstructured":"Mazo, J.E., Odlyzko, A.M.: Lattice points in high-dimensional spheres. Monatshefte f\u00fcr Mathematik 110(1), 47\u201361 (1990). \n                    https:\/\/doi.org\/10.1007\/BF01571276","journal-title":"Monatshefte f\u00fcr Mathematik"},{"key":"846_CR12","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcss.2017.08.001","author":"L Mazo","year":"2017","unstructured":"Mazo, L., Baudrier, \u00c9.: Object digitization up to a translation. J. Comput. Syst. Sci. (2017). \n                    https:\/\/doi.org\/10.1016\/j.jcss.2017.08.001","journal-title":"J. Comput. Syst. Sci."},{"key":"846_CR13","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"363","DOI":"10.1007\/978-3-319-66272-5_29","volume-title":"Discrete Geometry for Computer Imagery DGCI","author":"L Mazo","year":"2017","unstructured":"Mazo, L., Baudrier, \u00c9.: Study on the digitization dual combinatorics and convex case. In: Kropatsch, W.G., Artner, N.M., Janush, I. (eds.) Discrete Geometry for Computer Imagery DGCI. Lecture Notes in Computer Science, vol. 10502, pp. 363\u2013374. Springer, Heidelberg (2017). \n                    https:\/\/doi.org\/10.1007\/978-3-319-66272-5_29"},{"key":"846_CR14","doi-asserted-by":"publisher","first-page":"607","DOI":"10.1016\/j.endm.2005.04.006","volume":"20","author":"B Nagy","year":"2005","unstructured":"Nagy, B.: An algorithm to find the number of the digitizations of discs with a fixed radius. Electron. Notes Discret. Math. 20, 607\u2013622 (2005). \n                    https:\/\/doi.org\/10.1016\/j.endm.2005.04.006","journal-title":"Electron. Notes Discret. Math."},{"issue":"4","key":"846_CR15","doi-asserted-by":"publisher","first-page":"393","DOI":"10.1016\/j.cviu.2012.08.014","volume":"117","author":"P Ngo","year":"2013","unstructured":"Ngo, P., Kenmochi, Y., Passat, N., Talbot, H.: Combinatorial structure of rigid transformations in 2D digital images. Comput. Vision Image Underst. 117(4), 393\u2013408 (2013). \n                    https:\/\/doi.org\/10.1016\/j.cviu.2012.08.014","journal-title":"Comput. Vision Image Underst."},{"issue":"2","key":"846_CR16","doi-asserted-by":"publisher","first-page":"325","DOI":"10.1016\/j.dam.2004.09.018","volume":"147","author":"B Nouvel","year":"2005","unstructured":"Nouvel, B., R\u00e9mila, \u00c9.: Configurations induced by discrete rotations: periodicity and quasi-periodicity properties. Discret. Appl. Math. 147(2), 325\u2013343 (2005). \n                    https:\/\/doi.org\/10.1016\/j.dam.2004.09.018","journal-title":"Discret. Appl. Math."},{"issue":"1","key":"846_CR17","doi-asserted-by":"publisher","first-page":"84","DOI":"10.1007\/s10851-017-0706-8","volume":"59","author":"K Pluta","year":"2017","unstructured":"Pluta, K., Romon, P., Kenmochi, Y., Passat, N.: J. Math. Imaging Vision 59(1), 84\u2013105 (2017). \n                    https:\/\/doi.org\/10.1007\/s10851-017-0706-8","journal-title":"J. Math. Imaging Vision"},{"issue":"3","key":"846_CR18","doi-asserted-by":"publisher","first-page":"313","DOI":"10.1007\/BF01475864","volume":"77","author":"H Weyl","year":"1916","unstructured":"Weyl, H.: \u00dcber die gleichverteilung von zahlen mod. Eins [on the distribution of numbers modulo one]. Math. Ann. 77(3), 313\u2013352 (1916). \n                    https:\/\/doi.org\/10.1007\/BF01475864\n                    \n                  . (in German)","journal-title":"Math. Ann."},{"issue":"3","key":"846_CR19","doi-asserted-by":"publisher","first-page":"199","DOI":"10.1023\/B:JMIV.0000043736.15525.ed","volume":"21","author":"JD \u017duni\u0107","year":"2004","unstructured":"\u017duni\u0107, J.D.: On the number of digital discs. J. Math. Imaging Vision 21(3), 199\u2013204 (2004). \n                    https:\/\/doi.org\/10.1023\/B:JMIV.0000043736.15525.ed","journal-title":"J. Math. Imaging Vision"},{"issue":"2","key":"846_CR20","doi-asserted-by":"publisher","first-page":"396","DOI":"10.1016\/j.jnt.2004.08.004","volume":"110","author":"JD \u017duni\u0107","year":"2005","unstructured":"\u017duni\u0107, J.D.: On the number of ways to occupy \n                    \n                      \n                    \n                    $$n$$\n                    \n                      \n                        n\n                      \n                    \n                   lattice points by balls in \n                    \n                      \n                    \n                    $$d$$\n                    \n                      \n                        d\n                      \n                    \n                  -dimensional space. J. Number Theory 110(2), 396\u2013402 (2005). \n                    https:\/\/doi.org\/10.1016\/j.jnt.2004.08.004","journal-title":"J. Number Theory"}],"container-title":["Journal of Mathematical Imaging and Vision"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10851-018-0846-5\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10851-018-0846-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10851-018-0846-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,9,7]],"date-time":"2019-09-07T19:08:28Z","timestamp":1567883308000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10851-018-0846-5"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,9,8]]},"references-count":20,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2019,2]]}},"alternative-id":["846"],"URL":"https:\/\/doi.org\/10.1007\/s10851-018-0846-5","relation":{},"ISSN":["0924-9907","1573-7683"],"issn-type":[{"type":"print","value":"0924-9907"},{"type":"electronic","value":"1573-7683"}],"subject":[],"published":{"date-parts":[[2018,9,8]]},"assertion":[{"value":"12 January 2018","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"3 September 2018","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"8 September 2018","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}