| 1. | Czech Technical University in Prague, Trojanova 13,120 00 Prague, Czech Republic |
| 2. | Meiji University, 1-1-1 Higashi-Mita, Tama-ku, Kawasaki-shi, Kanagawa 214-8571, Japan |
Automatic detection of objects in photos and images is beneficial in various scientific and industrial fields. This contribution suggests an algorithm for segmentation of color images by the means of the parametric mean curvature flow equation and CIE94 color distance function. The parametric approach is enriched by the enhanced algorithm for topological changes where the intersection of curves is computed instead of unreliable curve distance. The result is a set of parametric curves enclosing the object. The algorithm is presented on a test image and also on real photos.
| [1] |
M. Beneš, M. Kimura, P. Pauš, D. Ševčovič, T. Tsujikawa and S. Yazaki,
Application of a curvature adjusted method in image segmentation, Bulletin of the Institute of Mathematics, Academia Sinica (New Series), 2008 (2008), 509-523.
|
| [2] |
I. C. Consortium and et al., Specification icc. 1: 2004-10, (profile version 4.2. 0.0): Image technology colour management, 2004. Google Scholar |
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K. Deckelnick and G. Dziuk,
Discrete anisotropic curvature flow of graphs, ESAIM: Mathematical Modelling and Numerical Analysis, 33 (1999), 1203-1222.
doi: 10.1051/m2an:1999141. |
| [4] |
K. Deckelnick and G. Dziuk, Mean curvature flow and related topics, Frontiers in Numerical Analysis, Universitext, Springer, Berlin, (2002), 63–108. |
| [5] |
R. McDonald and K. J. Smith,
Cie94-a new colour-difference formula, Journal of the Society of Dyers and Colourists, 111 (1995), 376-379.
doi: 10.1111/j.1478-4408.1995.tb01688.x. |
| [6] |
S. Osher and R. Fedkiw, Level Set Methods and Dynamic Implicit Surfaces, Applied Mathematical Sciences, 153. Springer-Verlag, New York, 2003.
doi: 10.1007/b98879. |
| [7] |
P. Pauš and M. Beneš,
Direct approach to mean-curvature flow with topological changes, Kybernetika (Prague), 45 (2009), 591-604.
|
| [8] |
P. Pauš and M. Beneš, Algorithm for topological changes of parametrically described curves, Proceedings of ALGORITMY, (2009), 176–184. Google Scholar |
| [9] |
P. Pauš and S. Yazaki,
Exact solution for dislocation bowing and a posteriori numerical technique for dislocation touching-splitting, JSIAM Letters, 7 (2015), 57-60.
doi: 10.14495/jsiaml.7.57. |
| [10] |
D. Ševčovič, Qualitative and quantitative aspects of curvature driven flows of planar curves, Topics on Partial Differential Equations, Jindřich Nečas Cent. Math. Model. Lect. Notes, MatFyzPress, Prague, 2 (2007), 55–119. |
| [11] |
D. Ševčovič and S. Yazaki,
Evolution of plane curves with a curvature adjusted tangential velocity, Japan Journal of Industrial and Applied Mathematics, 28 (2011), 413-442.
doi: 10.1007/s13160-011-0046-9. |
show all references
| [1] |
M. Beneš, M. Kimura, P. Pauš, D. Ševčovič, T. Tsujikawa and S. Yazaki,
Application of a curvature adjusted method in image segmentation, Bulletin of the Institute of Mathematics, Academia Sinica (New Series), 2008 (2008), 509-523.
|
| [2] |
I. C. Consortium and et al., Specification icc. 1: 2004-10, (profile version 4.2. 0.0): Image technology colour management, 2004. Google Scholar |
| [3] |
K. Deckelnick and G. Dziuk,
Discrete anisotropic curvature flow of graphs, ESAIM: Mathematical Modelling and Numerical Analysis, 33 (1999), 1203-1222.
doi: 10.1051/m2an:1999141. |
| [4] |
K. Deckelnick and G. Dziuk, Mean curvature flow and related topics, Frontiers in Numerical Analysis, Universitext, Springer, Berlin, (2002), 63–108. |
| [5] |
R. McDonald and K. J. Smith,
Cie94-a new colour-difference formula, Journal of the Society of Dyers and Colourists, 111 (1995), 376-379.
doi: 10.1111/j.1478-4408.1995.tb01688.x. |
| [6] |
S. Osher and R. Fedkiw, Level Set Methods and Dynamic Implicit Surfaces, Applied Mathematical Sciences, 153. Springer-Verlag, New York, 2003.
doi: 10.1007/b98879. |
| [7] |
P. Pauš and M. Beneš,
Direct approach to mean-curvature flow with topological changes, Kybernetika (Prague), 45 (2009), 591-604.
|
| [8] |
P. Pauš and M. Beneš, Algorithm for topological changes of parametrically described curves, Proceedings of ALGORITMY, (2009), 176–184. Google Scholar |
| [9] |
P. Pauš and S. Yazaki,
Exact solution for dislocation bowing and a posteriori numerical technique for dislocation touching-splitting, JSIAM Letters, 7 (2015), 57-60.
doi: 10.14495/jsiaml.7.57. |
| [10] |
D. Ševčovič, Qualitative and quantitative aspects of curvature driven flows of planar curves, Topics on Partial Differential Equations, Jindřich Nečas Cent. Math. Model. Lect. Notes, MatFyzPress, Prague, 2 (2007), 55–119. |
| [11] |
D. Ševčovič and S. Yazaki,
Evolution of plane curves with a curvature adjusted tangential velocity, Japan Journal of Industrial and Applied Mathematics, 28 (2011), 413-442.
doi: 10.1007/s13160-011-0046-9. |
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