An adaptive image inpainting method based on the modified mumford-shah model and multiscale parameter estimation
Thanh D.N.H., V.B. Surya Prasath, Nguyen Van Son, Le Minh Hieu

Department of Information Technology, Hue College of Industry, Hue 530000 VN,
Division of Biomedical Informatics, Cincinnati Children’s Hospital Medical Center, Cincinnati, OH 45229 USA,
Department of Biomedical Informatics, College of Medicine, University of Cincinnati, OH 45267 USA
Department of Electrical Engineering and Computer Science, University of Cincinnati, OH 45221 USA,
Department of Robotics and Production Adaptation, Tula State University, Tula 300012, Russia,
Ballistic Research Laboratory, Military Weapon Institute, Hanoi 100000, Vietnam,
Department of Economics, University of Economics, The University of Danang, Danang 550000, Vietnam

Аннотация:
Image inpainting is a process of filling missing and damaged parts of image. By using the Mumford-Shah image model, the image inpainting can be formulated as a constrained optimization problem. The Mumford-Shah model is a famous and effective model to solve the image inpainting problem. In this paper, we propose an adaptive image inpainting method based on multiscale parameter estimation for the modified Mumford-Shah model. In the experiments, we will handle the comparison with other similar inpainting methods to prove that the combination of classic model such the modified Mumford-Shah model and the multiscale parameter estimation is an effective method to solve the inpainting problem.

Ключевые слова:
image inpainting, Mumford-Shah model, modified Mumford-Shah model, regularization, Euler-Lagrange equation, inverse gradient, multiscale.

Цитирование:
Thanh DNH, Prasath VBS, Son NV, Son NV, Hieu LM. An adaptive image inpainting method based on the modified Mumford-Shah model and multiscale parameter estimation. Computer Optics 2019; 43(2): 251-257. DOI: 10.18287/2412-6179-2019-43-2-251-257.

Литература:

  1. Chan, T. Image processing and analysis: variational, PDE, wavelet, and stochastic methods / T. Chan, J. Shen. – Philadelphia: Society for Industrial and Applied Mathematics Philadelphia, 2005.
  2. Grossauer, H. Digital image inpainting: Completion of images with missing data regions / H. Grossauer. – Innsbruck: Simon & Schuster, 2008.
  3. Esedoglu, S. Digital inpainting based on the Mumford-Shah-Euler image model / S. Esedoglu, J. Shen // European Journal of Applied Mathematics. – 2002. – Vol. 13, Issue 4. – P. 353-370.
  4. Tauber, Z. Review and preview: Disocclusion by inpainting for image-based rendering / Z. Tauber, Z.N. Li, M.S. Drew // IEEE Transactions on Systems, Man, and Cybernetics. – 2007. – Vol. 37, Issue 4. – P. 527-540.
  5. Zayed, A. Advances in Shannon's sampling theory / A. Zayed. – CRC Press, 2018.
  6. Prasath, V.B.S. Image restoration with total variation and iterative regularization parameter estimation / V.B.S. Prasath, D.N.H. Thanh, N.X. Cuong, N.H. Hai // ACM The Eighth International Symposium on Information and Communication Technology (SoICT 2017). – 2017. – P. 378-384.
  7. Thanh, D.N.H. A method of total variation to remove the mixed Poisson-Gaussian noise / D.N.H. Thanh, S. Dvoenko // Pattern Recognition and Image Analysis. – 2016. – Vol. 26, Issue 2. – P. 285-293.
  8. Thanh, D.N.H. Image noise removal based on total variation / D.N.H. Thanh, S. Dvoenko // Computer Optics. – 2015. – Vol. 39(4). – P. 564-571. – DOI: 10.18287/0134-2452-2015-39-4-564-571.
  9. Rogers, C.A. Hausdorff measures / C.A. Rogers. – Cambridge: Cambridge University Press, 1998.
  10. Torben, P. Ambrosio-Tortorelli segmentation of stochastic images: Model extensions, theoretical investigations and numerical methods / P. Torben, M.K. Robert, P. Tobias // International Journal of Computer Vision. – 2013. – Vol. 103, Issue 2. – P. 190-212.
  11. Ambrosio, L. Approximation of functional depending on jumps by elliptic functional via gamma convergence / L. Ambrosio, M. Tortorelli // Communications on Pure and Applied Mathematics. – 1990. – Vol. 43, Issue 8. – P. 999-1036.
  12. Prasath, V.B.S. Quantum noise removal in X-Ray images with adaptive total variation regularization / V.B.S. Prasath // Informatica. – 2017. – Vol. 28, Issue 3. – P. 505-515.
  13. Shen, J. Mathematical models for local nontexture inpaintings / J. Shen, T.F. Chan // SIAM Journal on Applied Mathematics. – 2002. – Vol. 62, Issue 3. – P. 1019-1043.
  14. Schönlieb, C.B. Partial differential equation methods for image inpainting / C.B. Schönlieb. – Cambridge: Cambridge University Press, 2015.
  15. Dahl, J. Algorithms and software for total variation image reconstruction via first-order methods / J. Dahl, P.C. Hansen, S.H. Jensen, T.L. Jensen // Numer Algo. – 2010. – Vol. 52. – P. 67-91.
  16. Rudin, L.I. Nonlinear total variation based noise removal algorithms / L.I. Rudin, S. Osher, E. Fatemi // Physica D, vol. 60, p. 259–268, 1990.
  17. Mumford, D. Optimal approximations by piecewise smooth functions and associated variational problems / D. Mumford, J. Shah // Communications on Pure and Applied Mathematics. – 1989. – Vol. 42, Issue 5. – P. 577-685.
  18. Matus, P.P. Difference schemes on nonuniform grids for the two-dimensional convection–diffusion equation / P.P. Matus, L.M. Hieu // Computational Mathematics and Mathematical Physics. – 2017. – Vol. 57, Issue 12. – P. 1994-2004.
  19. Prasath, V.B.S. Multiscale Tikhonov-total variation image restoration using spatially varying edge coherence exponent / V.B.S. Prasath, D. Vorotnikov, R. Pelapur, S. Jose, G. Seetharaman, K. Palaniappan // IEEE Transactions on Image Processing. – 2015. – Vol. 24, Issue 12. – P. 5220-5235.
  20. Thanh, D.N.H. A review on CT and X-ray images denoising methods / D.N.H. Thanh, V.B.S. Prasath, L.M. Hieu // Informatica. –2019. – Vol. 43. – (forthcoming).

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