{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,5,14]],"date-time":"2025-05-14T02:38:09Z","timestamp":1747190289887,"version":"3.40.5"},"reference-count":21,"publisher":"Wiley","license":[{"start":{"date-parts":[[2020,7,16]],"date-time":"2020-07-16T00:00:00Z","timestamp":1594857600000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Council for Science and Technology"},{"name":"National Autonomous University of M\u00e9xico"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Computational and Mathematical Methods in Medicine"],"published-print":{"date-parts":[[2020,7,16]]},"abstract":"<jats:p>We present an approach to compute the number of holes in binary images using the Vertex Chain Code (VCC); the VCC was developed for representing and analyzing 2D shapes composed of cells. Using this code, it is possible to relate the outer to inner vertices of any 2D shape and to find interesting properties. Now, in this paper, we describe more properties of the VCC, such as the computation of the connected regions in a hole, the analysis of complementary chains, the computation of the number of holes in a binary shape or image, the computation of the Euler number, and the detection of convex and concave shapes. Finally, in order to illustrate the capabilities of proposed methods, we present the computation of topological properties of examples of objects of the real world.<\/jats:p>","DOI":"10.1155\/2020\/5632159","type":"journal-article","created":{"date-parts":[[2020,7,16]],"date-time":"2020-07-16T23:32:52Z","timestamp":1594942372000},"page":"1-13","source":"Crossref","is-referenced-by-count":1,"title":["An Approach to the Computation of the Euler Number by means of the Vertex Chain Code"],"prefix":"10.1155","volume":"2020","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6663-9438","authenticated-orcid":true,"given":"Ernesto","family":"Bribiesca","sequence":"first","affiliation":[{"name":"Departmento de Ciencias de la Computaci\u00f3n, Instituto de Investigaciones en Matem\u00e1ticas Aplicadas y en Sistemas, Universidad Nacional Aut\u00f3noma de M\u00e9xico, Apdo. 20-726, Mexico, D.F. 01000, Mexico"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0987-4498","authenticated-orcid":true,"given":"Ulf-Dietrich","family":"Braumann","sequence":"additional","affiliation":[{"name":"Interdisziplin\u00e4res Zentrum f\u00fcr Bioinformatik, Universit\u00e4t Leipzig, Leipzig, Germany"},{"name":"Institut f\u00fcr Medizinische Informatik, Statistik und Epidemiologie, Universit\u00e4t Leipzig, Leipzig, Germany"},{"name":"Fakult\u00e4t Ingenieurwissenschaften, Hochschule f\u00fcr Technik, Wirtschaft und Kultur Leipzig, Leipzig, Germany"},{"name":"Fraunhofer-Institut f\u00fcr Zelltherapie und Immunologie, Leipzig, Germany"}]},{"given":"Angel","family":"Carrillo-Bermejo","sequence":"additional","affiliation":[{"name":"Posgrado en Ciencia e Ingenier\u00eda de la Computaci\u00f3n, Instituto de Investigaciones en Matem\u00e1ticas Aplicadas y en Sistemas, Universidad Nacional Aut\u00f3noma de M\u00e9xico, Apdo. 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