| Presentation | 1998/12/18 Discrete Objects and Discrete Quasi-Objects Atsushi Imiya, Eckhardt Ulrich, |
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| PDF Download Page | PDF download Page Link |
| Abstract(in Japanese) | (See Japanese page) |
| Abstract(in English) | Assuming the planar 4-connectivity and the spatial 6-connectivity, we first introduce the curvature indexes of the boundary of a discrete object, and using these indices of points, we define the vertex angles of discrete surfaces as an extension of the chain codes of digital curves. Second, we prove the relation between the number of points indices and the numbers of holes, genus, and cavities of an object. Third, we define quasi-objects as the connected simplexes. Geometric relations between discrete quasi-objects and discrete objects prermit us to define the Euler characteristic for the planar 8-connected, and the spatial 18- and 26- connected objects using these for the planar 4-connected and the spatial 6-connected objects. Our results show that the planar 4-connectivity and the spatial 6-connectivity define the Euler characteristics of point sets in the discrete space. |
| Keyword(in Japanese) | (See Japanese page) |
| Keyword(in English) | Discrete object / Combinatorial topology / The Euler characteristic / Connectivity / Graph rewriting |
| Paper # | PRMU98-170 |
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| Conference Information | |
| Committee | PRMU |
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| Conference Date | 1998/12/18(1days) |
| Place (in Japanese) | (See Japanese page) |
| Place (in English) | |
| Topics (in Japanese) | (See Japanese page) |
| Topics (in English) | |
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| Paper Information | |
| Registration To | Pattern Recognition and Media Understanding (PRMU) |
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| Language | JPN |
| Title (in Japanese) | (See Japanese page) |
| Sub Title (in Japanese) | (See Japanese page) |
| Title (in English) | Discrete Objects and Discrete Quasi-Objects |
| Sub Title (in English) | |
| Keyword(1) | Discrete object |
| Keyword(2) | Combinatorial topology |
| Keyword(3) | The Euler characteristic |
| Keyword(4) | Connectivity |
| Keyword(5) | Graph rewriting |
| 1st Author's Name | Atsushi Imiya |
| 1st Author's Affiliation | Dept.of Information and Image Sciences() |
| 2nd Author's Name | Eckhardt Ulrich |
| 2nd Author's Affiliation | Dept.of Applied Mathematics, University of Hamburg |
| Date | 1998/12/18 |
| Paper # | PRMU98-170 |
| Volume (vol) | vol.98 |
| Number (no) | 490 |
| Page | pp.pp.- |
| #Pages | 8 |
| Date of Issue | |