An anisotropic PDE model for image inpainting
A PDE model based on an image specific auto generated multi-well potential function and a 4th order anisotropic diffusion with good performance with respect to loss due to smoothing effects has been proposed for grayscale image inpainting. An unconditionally stable numerical scheme using the notion...
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| Published in | Computers & mathematics with applications (1987) Vol. 79; no. 9; pp. 2701 - 2721 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
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01.05.2020
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| Abstract | A PDE model based on an image specific auto generated multi-well potential function and a 4th order anisotropic diffusion with good performance with respect to loss due to smoothing effects has been proposed for grayscale image inpainting. An unconditionally stable numerical scheme using the notion of convexity splitting in time and Fourier spectral method in space has been derived. The stable scheme is both consistent and convergent. Numerical computations are done for some standard test images and results are compared with the results of other existing models in the literature using image analysis specs such as PSNR, SNR, and SSIM. |
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| AbstractList | A PDE model based on an image specific auto generated multi-well potential function and a 4th order anisotropic diffusion with good performance with respect to loss due to smoothing effects has been proposed for grayscale image inpainting. An unconditionally stable numerical scheme using the notion of convexity splitting in time and Fourier spectral method in space has been derived. The stable scheme is both consistent and convergent. Numerical computations are done for some standard test images and results are compared with the results of other existing models in the literature using image analysis specs such as PSNR, SNR, and SSIM. |
| Author | Kumar, B.V. Rathish Halim, Abdul |
| Author_xml | – sequence: 1 givenname: Abdul surname: Halim fullname: Halim, Abdul email: abdul.math91@gmail.com organization: Department of Mathematics and Statistics, IIT Kanpur, 208016, India – sequence: 2 givenname: B.V. Rathish surname: Kumar fullname: Kumar, B.V. Rathish email: drbvrk.abdul@gmail.com, drbvrk11@gmail.com organization: Department of Mathematics and Statistics, IIT Kanpur, 208016, India |
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| Cites_doi | 10.1006/jvci.2001.0487 10.1109/ICCV.1999.790383 10.1109/TIP.2006.887728 10.1007/s10851-006-5257-3 10.1137/060660631 10.4310/CMS.2011.v9.n2.a4 10.1109/JSTSP.2011.2138676 10.1137/080728548 10.1109/34.56205 10.1109/TIP.2008.919367 10.1017/S0956792502004904 10.1109/TIP.2003.819861 10.1016/0167-2789(92)90242-F |
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| Keywords | Cahn-Hilliard equation Convexity splitting Inpainting 4th-order PDE Fidelity term |
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| SubjectTerms | 4th-order PDE Cahn-Hilliard equation Convexity Convexity splitting Fidelity term Image analysis Inpainting Mathematical models Spectral methods |
| Title | An anisotropic PDE model for image inpainting |
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