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MULTIGRID METHOD FOR A MODIFIED CURVATURE DRIVEN DIFFUSION MODEL FOR IMAGE INPAINTING

Journal of Computational Mathematics 2008年第6期26卷 856-875页

作者： Carlos Brito-Loeza Department of Mathematical Sciences University of Liverpool

Digital inpainting is a fundamental problem in image processing and many variational models for this problem have appeared recently in the literature. Among them are the very successfully Total Variation （TV） model [11] designed for local inpainting and its improved version for large scale inpainting： the Curvature-Driven Diffusion （CDD） model [10]. For the above two models, their associated Euler Lagrange equations are highly nonlinear partial differential equations. For the TV model there exists a relatively fast and easy to implement fixed point method, so adapting the multigrid method of [24] to here is immediate. For the CDD model however, so far only the well known but usually very slow explicit time marching method has been reported and we explain why the implementation of a fixed point method for the CDD model is not straightforward. Consequently the multigrid method as in [Savage and Chen, Int. J. Comput. Math., 82 （2005）, pp. 1001-1015] will not work here. This fact represents a strong limitation to the range of applications of this model since usually fast solutions are expected. In this paper, we introduce a modification designed to enable a fixed point method to work and to preserve the features of the original CDD model. As a result, a fast and efficient multigrid method is developed for the modified model. Numerical experiments are presented to show the very good performance of the fast algorithm.

关键词： Image inpainting variational models Regularization Multilevel methods.

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Efficient Dual Algorithms for Image Segmentation Using TV-Allen-Cahn Type models

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Communications in Computational Physics 2011年第4期9卷 859-877页

作者： Li-Lian Wang Ying Gu Division of Mathematical Sciences School of Physical and Mathematical SciencesNanyang Technological University637371Singapore

variational image segmentation based on the Mumford and Shah model[31],together with implementation by the piecewise constant level-set method(PCLSM)[26],leads to fully nonlinear Total Variation(TV)-Allen-Cahn *** commonlyused numerical approaches usually suffer from the difficulties not only with the nondifferentiability of the TV-term,but also with directly evolving the discontinuous piecewise constant-structured *** this paper,we propose efficient dual algorithms to overcome these *** use of a splitting-penalty method results in TVAllen-Cahn type models associated with different"double-well"potentials,which allow for the implementation of the dual algorithm of Chambolle[8].Moreover,we present a new dual algorithm based on an edge-featured penalty of the dual variable,which only requires to solve a vectorial Allen-Cahn type equation with linear∇(div)-diffusion rather than fully nonlinear diffusion in the Chambolle’s ***,more efficient numerical algorithms such as time-splitting method and Fast Fourier Transform(FFT)can be *** numerical tests show that two dual algorithms are much faster and more stable than the primal gradient descent approach,and the new dual algorithm is at least as efficient as the Chambolle’s algorithm but is more *** demonstrate that the new method also provides a viable alternative for image restoration.

关键词： variational models image segmentation TV-Allen-Cahn type equations dual algorithms splitting-penalty methods FFT.

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A Mean Curvature Regularized Based Model for Demodulating Phase Maps from Fringe Patterns

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Communications in Computational Physics 2018年第6期24卷 27-43页

作者： Carlos Brito-Loeza Ricardo Legarda-Saenz Arturo Espinosa-Romero Anabel Martin-Gonzalez CLIR at Facultad de Matematicas Universidad Autonoma de YucatanMexico

We introduce a variationalmethod for demodulating phasemaps fromfringe *** newmethod is based on themean curvature of the level sets of the phase surface that is used for *** performance of the method is illustrated w... 详细信息

关键词： Fringe analysis interferometry high-order regularization variational models

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