{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,25]],"date-time":"2026-04-25T11:42:51Z","timestamp":1777117371862,"version":"3.51.4"},"reference-count":20,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2021,12,23]],"date-time":"2021-12-23T00:00:00Z","timestamp":1640217600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2021,12,23]],"date-time":"2021-12-23T00:00:00Z","timestamp":1640217600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/100014440","name":"Ministerio de Ciencia, Innovaci\u00f3n y Universidades","doi-asserted-by":"publisher","award":["PID2019-107339GB-I00"],"award-info":[{"award-number":["PID2019-107339GB-I00"]}],"id":[{"id":"10.13039\/100014440","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100006461","name":"Agencia de Innovaci\u00f3n y Desarrollo de Andaluc\u00eda","doi-asserted-by":"publisher","award":["PY20-01145"],"award-info":[{"award-number":["PY20-01145"]}],"id":[{"id":"10.13039\/501100006461","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Comb Optim"],"published-print":{"date-parts":[[2022,11]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>In this paper, we define a new flavour of well-composedness, called strong Euler well-composedness. In the general setting of regular cell complexes, a regular cell complex of dimension <jats:italic>n<\/jats:italic> is strongly Euler well-composed if the Euler characteristic of the link of each boundary cell is 1, which is the Euler characteristic of an <jats:inline-formula><jats:alternatives><jats:tex-math>$$(n-1)$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mrow>\n                    <mml:mo>(<\/mml:mo>\n                    <mml:mi>n<\/mml:mi>\n                    <mml:mo>-<\/mml:mo>\n                    <mml:mn>1<\/mml:mn>\n                    <mml:mo>)<\/mml:mo>\n                  <\/mml:mrow>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula>-dimensional ball. Working in the particular setting of cubical complexes canonically associated with <jats:inline-formula><jats:alternatives><jats:tex-math>$$n$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mi>n<\/mml:mi>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula>D pictures, we formally prove in this paper that strong Euler well-composedness implies digital well-composedness in any dimension <jats:inline-formula><jats:alternatives><jats:tex-math>$$n\\ge 2$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mrow>\n                    <mml:mi>n<\/mml:mi>\n                    <mml:mo>\u2265<\/mml:mo>\n                    <mml:mn>2<\/mml:mn>\n                  <\/mml:mrow>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula> and that the converse is not true when <jats:inline-formula><jats:alternatives><jats:tex-math>$$n\\ge 4$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mrow>\n                    <mml:mi>n<\/mml:mi>\n                    <mml:mo>\u2265<\/mml:mo>\n                    <mml:mn>4<\/mml:mn>\n                  <\/mml:mrow>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula>.<\/jats:p>","DOI":"10.1007\/s10878-021-00837-8","type":"journal-article","created":{"date-parts":[[2021,12,23]],"date-time":"2021-12-23T06:04:46Z","timestamp":1640239486000},"page":"3038-3055","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Strong Euler well-composedness"],"prefix":"10.1007","volume":"44","author":[{"given":"Nicolas","family":"Boutry","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9937-0033","authenticated-orcid":false,"given":"Rocio","family":"Gonzalez-Diaz","sequence":"additional","affiliation":[]},{"given":"Maria-Jose","family":"Jimenez","sequence":"additional","affiliation":[]},{"given":"Eduardo","family":"Paluzo-Hildago","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2021,12,23]]},"reference":[{"key":"837_CR1","doi-asserted-by":"crossref","unstructured":"Boutry N, G\u00e9raud T, Najman L (2015) How to make $$n$$D images well-composed without interpolation. In: 2015 IEEE international conference on image processing (ICIP). IEEE, pp 2149\u20132153","DOI":"10.1109\/ICIP.2015.7351181"},{"key":"837_CR2","doi-asserted-by":"crossref","unstructured":"Boutry N, G\u00e9raud T, Najman L (2015) How to make $$n$$D functions digitally well-composed in a self-dual way. In: International symposium on mathematical morphology and its applications to signal and image processing, lecture notes in computer science, vol 9082. Springer, pp 561\u2013572","DOI":"10.1007\/978-3-319-18720-4_47"},{"issue":"3","key":"837_CR3","doi-asserted-by":"publisher","first-page":"443","DOI":"10.1007\/s10851-017-0769-6","volume":"60","author":"N Boutry","year":"2018","unstructured":"Boutry N, G\u00e9raud T, Najman L (2018) A tutorial on well-composedness. J Math Imaging Vis 60(3):443\u2013478","journal-title":"J Math Imaging Vis"},{"key":"837_CR4","doi-asserted-by":"publisher","first-page":"62","DOI":"10.1016\/j.ins.2018.06.005","volume":"499","author":"N Boutry","year":"2019","unstructured":"Boutry N, Gonzalez-Diaz R, Jimenez MJ (2019) Weakly well-composed cell complexes over $$n$$D pictures. Inf Sci 499:62\u201383","journal-title":"Inf Sci"},{"key":"837_CR5","doi-asserted-by":"crossref","unstructured":"Boutry N, Gonzalez-Diaz R, Jimenez MJ, Paluzo-Hildago E (2020) Euler well-composedness. In: Lukic T, Barneva RP, Brimkov V, Comic L, Sladoje N (eds) Combinatorial image analysis: proceedings of the 20th international workshop, IWCIA 2020, Novi Sad, Serbia, July 16\u201318, 2020, lecture notes in computer science, vol 12148. Springer, pp 3\u201319","DOI":"10.1007\/978-3-030-51002-2_1"},{"key":"837_CR6","doi-asserted-by":"crossref","unstructured":"Boutry N, Gonzalez-Diaz R, Najman L, G\u00e9raud T (2020) A 4d counter-example showing that DWCness does not imply CWCness in $$n$$D. In: Lukic T, Barneva RP, Brimkov V, Comic L, Sladoje N (eds) Combinatorial image analysis: proceedings of the 20th international workshop, IWCIA 2020, Novi Sad, Serbia, July 16\u201318, 2020, lecture notes in computer science, vol 12148. Springer, pp 73\u201387","DOI":"10.1007\/978-3-030-51002-2_6"},{"key":"837_CR7","doi-asserted-by":"publisher","first-page":"1285","DOI":"10.1007\/s10851-020-00988-z","volume":"62","author":"N Boutry","year":"2020","unstructured":"Boutry N, Najman L, G\u00e9raud T (2020) Equivalence between digital well-composedness and well-composedness in the sense of Alexandrov on n-d cubical grids. J Math Imaging Vis 62:1285\u20131333","journal-title":"J Math Imaging Vis"},{"key":"837_CR8","volume-title":"Computational topology: an introduction","author":"H Edelsbrunner","year":"2010","unstructured":"Edelsbrunner H, Harer J (2010) Computational topology: an introduction. American Mathematical Society, Providence"},{"key":"837_CR9","doi-asserted-by":"crossref","unstructured":"G\u00e9raud T, Carlinet E, Crozet S, Najman L (2013) A quasi-linear algorithm to compute the tree of shapes of $$n$$D images. In: International symposium on mathematical morphology and its applications to signal and image processing. Springer, pp 98\u2013110","DOI":"10.1007\/978-3-642-38294-9_9"},{"key":"837_CR10","doi-asserted-by":"publisher","first-page":"59","DOI":"10.1016\/j.dam.2014.08.036","volume":"183","author":"R Gonzalez-Diaz","year":"2015","unstructured":"Gonzalez-Diaz R, Jimenez MJ, Medrano B (2015) 3D well-composed polyhedral complexes. Discrete Appl Math 183:59\u201377","journal-title":"Discrete Appl Math"},{"issue":"1","key":"837_CR11","doi-asserted-by":"publisher","first-page":"106","DOI":"10.1007\/s10851-017-0722-8","volume":"59","author":"R Gonzalez-Diaz","year":"2017","unstructured":"Gonzalez-Diaz R, Jimenez MJ, Medrano B (2017) Efficiently storing well-composed polyhedral complexes computed over 3D binary images. J Math Imaging Vis 59(1):106\u2013122","journal-title":"J Math Imaging Vis"},{"key":"837_CR12","volume-title":"Algebraic topology","author":"A Hatcher","year":"2002","unstructured":"Hatcher A (2002) Algebraic topology. Cambridge University Press, Cambridge"},{"issue":"3","key":"837_CR13","doi-asserted-by":"publisher","first-page":"129","DOI":"10.1006\/gmod.2000.0522","volume":"62","author":"JO Lachaud","year":"2000","unstructured":"Lachaud JO, Montanvert A (2000) Continuous analogs of digital boundaries: a topological approach to iso-surfaces. Graph Models 62(3):129\u2013164","journal-title":"Graph Models"},{"issue":"3","key":"837_CR14","doi-asserted-by":"publisher","first-page":"164","DOI":"10.1006\/gmip.1997.0422","volume":"59","author":"LJ Latecki","year":"1997","unstructured":"Latecki LJ (1997) 3D well-composed pictures. Graph Models Image Process 59(3):164\u2013172","journal-title":"Graph Models Image Process"},{"key":"837_CR15","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-015-9002-0","volume-title":"Discrete representation of spatial objects in computer vision","author":"LJ Latecki","year":"1998","unstructured":"Latecki LJ (1998) Discrete representation of spatial objects in computer vision. Kluwer Academic, Dordrecht"},{"issue":"1","key":"837_CR16","first-page":"70","volume":"61","author":"L Latecki","year":"1995","unstructured":"Latecki L, Eckhardt U, Rosenfeld A (1995) Well-composed sets. CVIU 61(1):70\u201383","journal-title":"CVIU"},{"issue":"5","key":"837_CR17","doi-asserted-by":"publisher","first-page":"581","DOI":"10.1016\/j.patrec.2003.12.005","volume":"25","author":"J Marchadier","year":"2004","unstructured":"Marchadier J, Arqu\u00e8s D, Michelin S (2004) Thinning grayscale well-composed images. Pattern Recognit Lett 25(5):581\u2013590","journal-title":"Pattern Recognit Lett"},{"key":"837_CR18","unstructured":"Siqueira M, Latecki LJ, Gallier J (2005) Making 3d binary digital images well-composed. In: SPIE, vision geometry XIII, vol 5675. International Society for Optics and Photonics, pp 150\u2013164"},{"key":"837_CR19","doi-asserted-by":"publisher","first-page":"249","DOI":"10.1007\/s10851-007-0054-1","volume":"30","author":"M Siqueira","year":"2008","unstructured":"Siqueira M, Latecki L, Tustison N, Gallier J, Gee J (2008) Topological repairing of $$3$$D digital images. J Math Imaging Vis 30:249\u2013274","journal-title":"J Math Imaging Vis"},{"key":"837_CR20","doi-asserted-by":"crossref","unstructured":"Stelldinger P, Latecki LJ (2006) 3D object digitization: majority interpolation and marching cubes. In: 18th international conference on pattern recognition, vol 2. IEEE, pp 1173\u20131176","DOI":"10.1109\/ICPR.2006.29"}],"container-title":["Journal of Combinatorial Optimization"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10878-021-00837-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10878-021-00837-8\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10878-021-00837-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,10,14]],"date-time":"2022-10-14T20:25:50Z","timestamp":1665779150000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10878-021-00837-8"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,12,23]]},"references-count":20,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2022,11]]}},"alternative-id":["837"],"URL":"https:\/\/doi.org\/10.1007\/s10878-021-00837-8","relation":{},"ISSN":["1382-6905","1573-2886"],"issn-type":[{"value":"1382-6905","type":"print"},{"value":"1573-2886","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,12,23]]},"assertion":[{"value":"23 November 2021","order":1,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"23 December 2021","order":2,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare that they have no conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}]}}