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First, we present several basic concepts concerning geometrical properties of 3D images, which include connectivity, the connected component, the Euler number, and deletability. Then we explain outlines of basic algorithms derived by using the forementioned concepts based on research results by the authors' group. Procedures referred to here are as follows: calculation of the Euler number, deletability test of 1\u2010voxels, shrinking, thinning, and border following. Finally, we add 51 references which may aid more detailed research; these references also will supplement the brief explanations and small number of procedures we are limited to in this article.<\/jats:p>","DOI":"10.1002\/scj.4690170109","type":"journal-article","created":{"date-parts":[[2007,7,7]],"date-time":"2007-07-07T10:22:26Z","timestamp":1183803746000},"page":"73-82","source":"Crossref","is-referenced-by-count":16,"title":["Basics of algorithms for processing three\u2010dimensional digitized pictures"],"prefix":"10.1002","volume":"17","author":[{"given":"Jun\u2010ichiro","family":"Toriwaki","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shigeki","family":"Yokoi","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2007,3,21]]},"reference":[{"key":"e_1_2_1_2_2","volume-title":"Medical Image Processing","author":"Onoe M.","year":"1982"},{"key":"e_1_2_1_3_2","unstructured":"M.Onoe J. 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Industrial applications of computed tomography Proc. of 15th Joint Conf. on Image Technology pp.407(Dec. 1982)."},{"key":"e_1_2_1_4_2","first-page":"3","article-title":"Color computer graphics in magnetic field analysis by means of the finite element method","volume":"17","author":"Nakamae E.","year":"1983","journal-title":"Computers and Graphics"},{"key":"e_1_2_1_5_2","first-page":"10","article-title":"Degree of nodular separation PQ and its application to the morphological analysis of chronic liver diseases","volume":"18","author":"Matsumoto J.","year":"1977","journal-title":"Liver (Kanzo)"},{"key":"e_1_2_1_6_2","unstructured":"S.YokoiandJ.ToriwakiAlgorithm for 3\u2010dimensional digital image processing Paper of the Professional Group on Computer Vision CV30\u20135 Information Processing Society of Japan(May 1984)."},{"key":"e_1_2_1_7_2","first-page":"7","article-title":"Topological properties of three\u2010dimensional digital images sampled on the face\u2010centered cubic lattice","volume":"65","author":"Yonekura T.","year":"1982","journal-title":"Trans. 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The application of 3D logical neighbor operations to sequences of 2D ultrasonic images Proc. 6th CCARC pp.362\u2013365(1979) (CCARC = Conf. on Computer Application in Radiology and Computer\/Aided Analysis of Radiological Images)."},{"key":"e_1_2_1_33_2","unstructured":"S. N.Srihari J. K.UdupaandM.Yau. Understanding the bin of parts Proc. I.E.E.E. International Conf. on Cybernetics and Society pp.44\u201348(1979)."},{"key":"e_1_2_1_34_2","first-page":"315","article-title":"A parallel thinning algorithm, for 3D pictures","volume":"17","author":"Tsao Y. F.","year":"1981","journal-title":"CGIP"},{"key":"e_1_2_1_35_2","first-page":"10","article-title":"A border\u2010following algorithm of three\u2010dimensional digitized binary pictures","volume":"67","author":"Matsumoto T.","year":"1984","journal-title":"Trans. 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