Mumford-Shah-Euler Flow with Sphere Constraint and Applications to Color Image Inpainting
作者： Jonas Haehnle , Andreas Prohl
DOI: 10.1137/100795620
关键词:
摘要: Two fully discrete finite element-based algorithms to approximate the $L^2$ gradient flow of Mumford-Shah-Euler functional for unit vector fields are proposed, analyzed, and compared. The first scheme uses a penalization strategy, second Lagrange multiplier, enforce sphere constraint, respectively. Both schemes applied color image inpainting in chromaticity brightness model also compared with standard Mumford-Shah functional, as well channelwise red-green-blue inpainting.
aip.org
sci-hub.se 参考文章(51)
Jonas Haehnle, Numerical Analysis of the Mumford-Shah and Mumford-Shah-Euler Functionals for Sphere-Valued Functions, and applications to Numerical Image Processing Universität Tübingen. ,(2010)
Ennio De Giorgi, Some remarks on Γ-convergence and least squares method Birkhäuser Boston. pp. 135- 142 ,(1991) , 10.1007/978-1-4684-6787-1_8
L. Ridgway Scott, Susanne C Brenner, The Mathematical Theory of Finite Element Methods ,(2007)
Bei Tang, Guillermo Sapiro, Vicent Caselles, Diffusion of General Data on Non-Flat Manifolds viaHarmonic Maps Theory: The Direction Diffusion Case International Journal of Computer Vision. ,vol. 36, pp. 149- 161 ,(2000) , 10.1023/A:1008152115986
David Mumford, Elastica and Computer Vision Springer, New York, NY. pp. 491- 506 ,(1994) , 10.1007/978-1-4612-2628-4_31
M. Nitzberg, D. Mumford, T. Shiota, Filtering, segmentation, and depth ,(1993)
Vivette Girault, Pierre-Arnaud Raviart, Finite Element Methods for Navier-Stokes Equations: Theory and Algorithms ,(1986)
M. Droske, Martin Rumpf, A level set formulation for Willmore flow Interfaces and Free Boundaries. ,vol. 6, pp. 361- 378 ,(2004) , 10.4171/IFB/105
Sören Bartels, Andreas Prohl, Constraint preserving implicit finite element discretization of harmonic map flow into spheres Mathematics of Computation. ,vol. 76, pp. 1847- 1859 ,(2007) , 10.1090/S0025-5718-07-02026-1