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| Presentation | 2010-02-15 13:25 On Curvature of Color Spaces and its Implications Kohei Toko, Jinhui Chao (Chuo Univ.)  ITS2009-42 IE2009-136 |
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| Abstract | (in Japanese) | (See Japanese page) |
| (in English) | It is known that a color space is a Riemann space rather than a Euclidena space. For such a color space, one can still construct a generalized polar coordinates in the color space using Riemann geometry. This so-called Riemann normal coordinate system is consisted of geodesics and equa-geodesic-distance lines and provide us a generalization of the Munsell coordinates. In this paper we show that the curvature of a color space is an essentially invariant of color spaces which play an important role in construction of the Riemann normal coordinates. In particular, only for color spaces with negative curvature everywhere it is possible to build a global Riemann normal coordinates with geodesics. We calculate the curvatures in CIELUV and CIELAB and show possitive curvature is the reason for intersection of geodesics. A multipatch algorithm is proposed also to build a Riemann normal coordinates in a color space with possitive curvature. | |
| Keyword | (in Japanese) | (See Japanese page) |
| (in English) | Riemann geometry / Riemann curvature tensor / Geodesics / / / / / | |
| Reference Info. | IEICE Tech. Rep., vol. 109, pp. 29-34, Feb. 2010. | |
| Paper # | ||
| Date of Issue | 2010-02-08 (ITS, IE) | |
| ISSN | Print edition: ISSN 0913-5685 Online edition: ISSN 2432-6380 | |
| Copyright and reproduction |
All rights are reserved and no part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopy, recording, or any information storage and retrieval system, without permission in writing from the publisher. Notwithstanding, instructors are permitted to photocopy isolated articles for noncommercial classroom use without fee. (License No.: 10GA0019/12GB0052/13GB0056/17GB0034/18GB0034) | |
| Download PDF | ITS2009-42 IE2009-136 |
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| Conference Information | |
| Committee | ITE-AIT IE ITE-HI ITE-ME ITS |
| Conference Date | 2010-02-15 - 2010-02-16 |
| Place (in Japanese) | (See Japanese page) |
| Place (in English) | Graduate School of Information and Technology, Hokkaido Univ. |
| Topics (in Japanese) | (See Japanese page) |
| Topics (in English) | |
| Paper Information | |
| Registration To | ITE-HI |
| Conference Code | 2010-02-AIT-IE-HI-ME-ITS |
| Language | Japanese |
| Title (in Japanese) | (See Japanese page) |
| Sub Title (in Japanese) | (See Japanese page) |
| Title (in English) | On Curvature of Color Spaces and its Implications |
| Sub Title (in English) | |
| Keyword(1) | Riemann geometry |
| Keyword(2) | Riemann curvature tensor |
| Keyword(3) | Geodesics |
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| 1st Author's Name | Kohei Toko |
| 1st Author's Affiliation | Chuo University (Chuo Univ.) |
| 2nd Author's Name | Jinhui Chao |
| 2nd Author's Affiliation | Chuo University (Chuo Univ.) |
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| Speaker | Author-1 |
| Date Time | 2010-02-15 13:25:00 |
| Presentation Time | 25 minutes |
| Registration for | ITE-HI |
| Paper # | ITS2009-42, IE2009-136 |
| Volume (vol) | vol.109 |
| Number (no) | no.414(ITS), no.415(IE) |
| Page | pp.29-34 |
| #Pages | 6 |
| Date of Issue | 2010-02-08 (ITS, IE) |
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