Image segmentation of flame front of a smoldering experiment by gradient flow of curves
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Published
Sep 21, 2024
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Abstract
In this paper, we review our computational strategy for image segmentation of experimental data of smoldering phenomena by the gradient flow of closed planar curves. The experimental images are preprocessed using an edge-preserving, inhomogeneous Perona-Malik equation. The gradient flow method is modified by a locally acting artificial pushing term penetrating concavities and by tangential redistribution stabilizing the appropriate positioning of discretization points.
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Kolář, M., Yazaki, S., & Sakakibara, K.
(2024).
Image segmentation of flame front of a smoldering experiment by gradient flow of curves.
Proceedings Of The Conference Algoritmy, , 119 - 128.
Retrieved from http://www.iam.fmph.uniba.sk/amuc/ojs/index.php/algoritmy/article/view/2161/1033
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References
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[3] S. Kobayashi and S. Yazaki, Convergence of a Finite Difference Scheme for a Flame/Smoldering-Front Evolution Equation and Its Application to Wavenumber Selection, Computational Methods in Applied Mathematics 23 (2022) 545–563.
[4] S. Kobayashi, Y. Uegata and S. Yazaki, The existence of intrinsic rotating wave solutions of a flame/smoldering-front evolution equation, JSIAM Lett. 12 (2020) 53–56.
[5] M. Goto, K. Kuwana, Y. Uegata and S. Yazaki, A method how to determine parameters arising in a smoldering evolution equation by image segmentation for experiment’s movies, Discrete Contin. Dyn. Syst. Ser. S 14 (2019) 881–891.
[6] D. Cremers, M. Rousson, R. Deriche, A Review of Statistical Approaches to Level Set Segmentation: Integrating Color, Texture, Motion and Shape, International Journal of Computer Vision, 72 (2007), 195–215.
[7] Y. Boykov, G. Funka-Lea, Graph cuts and efficient n-d image segmentation, International Journal of Computer Vision, 70 (2006), 109–131.
[8] A. Handlovičová, K. Mikula and F. Sgallari, Semi-implicit complementary volume scheme for solving level set like equations in image processing and curve evolution, Numerische Mathematik, 93 (2003), 675–695.
[9] M. Beneš, V. Chalupecký and K. Mikula, Geometrical Image Segmentation by the Allen-Cahn Equation, Applied Numerical Mathematics 51(2) (2013) 187–205.
[10] R. Chabiniok, R. Máca, M. Beneš and J. Tiňtěra, Segmentation of MRI data by means of nonlinear diffusion, Kybernetika 49(2) (2013) 301–318.
[11] K. Mikula, D. Ševčovič, Computational and qualitative aspects of evolution of curves driven by curvature and external force, Comput. Visual. Sci., 6 (2004), 211–225.
[12] K. Mikula, D. Ševčovič, Evolution of curves on a surface driven by the geodesic curvature and external force, Appl. Anal., 85 (2006), 345–362.
[13] M. Kolář, M. Beneš and D. Ševčovič, Computational analysis of the conserved curvature driven flow for open curves in the plane, Mathematics and Computers in Simulation, 126 (2016), 1–13.
[14] M. Kolář and S. Yazaki, Comparison study of image segmentation techniques by curvature-driven flow of graphs, JSIAM Letters, 13 (2021), 48–51.
[15] M. Beneš, M. Kolář M, and D. Ševčovič , Curvature driven flow of a family of interacting curves with applications, Math. Method. Appl. Sci., 43 (2020), pp. 4177-4190.
[16] P. Pauš, M. Beneš, M. Kolář and J. Kratochvı́l, Dynamics of dislocations described as evolving curves interacting with obstacles, Modelling and Simulation in Materials Science and Engineering, 24 (2016), 035003.
[17] D. Ševčovič and S. Yazaki, Evolution of plane curves with a curvature adjusted tangential velocity, Japan J. Indust. Appl. Math., 28 (2011), 413.
[18] Ch. Wai-Pak, L. Kin-Man and S. Wan-Chi, An adaptive active contour model for highly irregular boundaries, Pattern Recognition, 34 (2001), 323–331.
[19] V. Srikrishnan, S. Chaudhuri, S. D. Roy and D. Ševčovič, On Stabilisation of Parametric Active Contours, in Computer Vision and Pattern Recognition, IEEE Conference on Computer Vision and Pattern Recognition, Minneapolis, USA (2007), 1–6.
[20] R. McDonald and K. J. Smith, Cie94-a new colour difference formula, Journal of the Society of Dyers and Colourists 111 (1995), 376–379.
[21] I. C. Consortium et al., Specification icc. 1: 2004-10, (profile version 4.2.0.0): Image technology colour management (2004).
[22] P. Perona and J. Malik, Scale-space and edge detection using anisotropic diffusion, IEEE Transactions on Pattern Analysis and Machine Intelligence, 12 (1990), pp. 629–639.
[23] F. Catté, P. L. Lions, J. M. Morel and T. Coll, Image selective smoothing and edge detection by nonlinear diffusion, SIAM Journal on Numerical Analysis, 29 (1992), pp. 192–193.
[24] G. Aubert and P. Kornprobst, Mathematical Problems in Image Processing, Partial Differential Equations and the Calculus of Variations, Springer, New York, 2002.
[25] C. L. Epstein and M. Gage, The curve shortening flow. In: A.J. Chorin, A.J. Majda (eds), Wave Motion: Theory, Modelling, and Computation. Mathematical Sciences Research Institute Publications, vol. 7, Springer, New York, 1987.