Harmonic image inpainting using the charge simulation method
Abstract It was recently reported that harmonic inpainting or Laplace interpolation when used in the context of image compression can yield impressive reconstruction results if the encoded pixels were carefully selected. Mathematically, the problem translates into a mixed Dirichlet–Neumann boundary...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Kalmoun, El Mostafa [verfasserIn] |
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| Format: |
E-Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2022 |
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| Schlagwörter: |
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| Anmerkung: |
© The Author(s), under exclusive licence to Springer-Verlag London Ltd., part of Springer Nature 2022 |
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| Übergeordnetes Werk: |
Enthalten in: Pattern Analysis & Applications - Springer-Verlag, 1999, 25(2022), 4 vom: 17. Apr., Seite 795-806 |
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| Übergeordnetes Werk: |
volume:25 ; year:2022 ; number:4 ; day:17 ; month:04 ; pages:795-806 |
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| DOI / URN: |
10.1007/s10044-022-01074-3 |
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| 520 | |a Abstract It was recently reported that harmonic inpainting or Laplace interpolation when used in the context of image compression can yield impressive reconstruction results if the encoded pixels were carefully selected. Mathematically, the problem translates into a mixed Dirichlet–Neumann boundary value problem with Dirichlet data coming from the known observations and reflecting conditions being imposed on the image physical boundary. Classical numerical solutions depend on finite difference schemes, which often induce instabilities and rely heavily on the choice of a convenient regularization parameter. In this paper, we propose an alternative numerical method, which is able to provide a robust harmonic reconstruction without requiring neither numerical integration nor discretization of the inpainting domain or its boundary. In fact, our approach is connected with the charge simulation method powered with the fast multipole method. Thereby, we approximate the harmonic reconstruction by a linear combination of the fundamental solutions of the Laplace equation. The experimental results on standard test images using uniformly, randomly and optimally distributed masks of different densities demonstrate the superior performance of our numerical approach over the finite difference method in terms of both reconstruction quality and speed. | ||
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10.1007/s10044-022-01074-3 doi (DE-627)SPR048407259 (SPR)s10044-022-01074-3-e DE-627 ger DE-627 rakwb eng Kalmoun, El Mostafa verfasserin (orcid)0000-0002-1434-2541 aut Harmonic image inpainting using the charge simulation method 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s), under exclusive licence to Springer-Verlag London Ltd., part of Springer Nature 2022 Abstract It was recently reported that harmonic inpainting or Laplace interpolation when used in the context of image compression can yield impressive reconstruction results if the encoded pixels were carefully selected. Mathematically, the problem translates into a mixed Dirichlet–Neumann boundary value problem with Dirichlet data coming from the known observations and reflecting conditions being imposed on the image physical boundary. Classical numerical solutions depend on finite difference schemes, which often induce instabilities and rely heavily on the choice of a convenient regularization parameter. In this paper, we propose an alternative numerical method, which is able to provide a robust harmonic reconstruction without requiring neither numerical integration nor discretization of the inpainting domain or its boundary. In fact, our approach is connected with the charge simulation method powered with the fast multipole method. Thereby, we approximate the harmonic reconstruction by a linear combination of the fundamental solutions of the Laplace equation. The experimental results on standard test images using uniformly, randomly and optimally distributed masks of different densities demonstrate the superior performance of our numerical approach over the finite difference method in terms of both reconstruction quality and speed. Harmonic image inpainting (dpeaa)DE-He213 Charge simulation method (dpeaa)DE-He213 Fast multipole method (dpeaa)DE-He213 Nasser, Mohamed M. S. aut Enthalten in Pattern Analysis & Applications Springer-Verlag, 1999 25(2022), 4 vom: 17. Apr., Seite 795-806 (DE-627)SPR008209189 nnns volume:25 year:2022 number:4 day:17 month:04 pages:795-806 https://dx.doi.org/10.1007/s10044-022-01074-3 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER AR 25 2022 4 17 04 795-806 |
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10.1007/s10044-022-01074-3 doi (DE-627)SPR048407259 (SPR)s10044-022-01074-3-e DE-627 ger DE-627 rakwb eng Kalmoun, El Mostafa verfasserin (orcid)0000-0002-1434-2541 aut Harmonic image inpainting using the charge simulation method 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s), under exclusive licence to Springer-Verlag London Ltd., part of Springer Nature 2022 Abstract It was recently reported that harmonic inpainting or Laplace interpolation when used in the context of image compression can yield impressive reconstruction results if the encoded pixels were carefully selected. Mathematically, the problem translates into a mixed Dirichlet–Neumann boundary value problem with Dirichlet data coming from the known observations and reflecting conditions being imposed on the image physical boundary. Classical numerical solutions depend on finite difference schemes, which often induce instabilities and rely heavily on the choice of a convenient regularization parameter. In this paper, we propose an alternative numerical method, which is able to provide a robust harmonic reconstruction without requiring neither numerical integration nor discretization of the inpainting domain or its boundary. In fact, our approach is connected with the charge simulation method powered with the fast multipole method. Thereby, we approximate the harmonic reconstruction by a linear combination of the fundamental solutions of the Laplace equation. The experimental results on standard test images using uniformly, randomly and optimally distributed masks of different densities demonstrate the superior performance of our numerical approach over the finite difference method in terms of both reconstruction quality and speed. Harmonic image inpainting (dpeaa)DE-He213 Charge simulation method (dpeaa)DE-He213 Fast multipole method (dpeaa)DE-He213 Nasser, Mohamed M. S. aut Enthalten in Pattern Analysis & Applications Springer-Verlag, 1999 25(2022), 4 vom: 17. Apr., Seite 795-806 (DE-627)SPR008209189 nnns volume:25 year:2022 number:4 day:17 month:04 pages:795-806 https://dx.doi.org/10.1007/s10044-022-01074-3 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER AR 25 2022 4 17 04 795-806 |
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10.1007/s10044-022-01074-3 doi (DE-627)SPR048407259 (SPR)s10044-022-01074-3-e DE-627 ger DE-627 rakwb eng Kalmoun, El Mostafa verfasserin (orcid)0000-0002-1434-2541 aut Harmonic image inpainting using the charge simulation method 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s), under exclusive licence to Springer-Verlag London Ltd., part of Springer Nature 2022 Abstract It was recently reported that harmonic inpainting or Laplace interpolation when used in the context of image compression can yield impressive reconstruction results if the encoded pixels were carefully selected. Mathematically, the problem translates into a mixed Dirichlet–Neumann boundary value problem with Dirichlet data coming from the known observations and reflecting conditions being imposed on the image physical boundary. Classical numerical solutions depend on finite difference schemes, which often induce instabilities and rely heavily on the choice of a convenient regularization parameter. In this paper, we propose an alternative numerical method, which is able to provide a robust harmonic reconstruction without requiring neither numerical integration nor discretization of the inpainting domain or its boundary. In fact, our approach is connected with the charge simulation method powered with the fast multipole method. Thereby, we approximate the harmonic reconstruction by a linear combination of the fundamental solutions of the Laplace equation. The experimental results on standard test images using uniformly, randomly and optimally distributed masks of different densities demonstrate the superior performance of our numerical approach over the finite difference method in terms of both reconstruction quality and speed. Harmonic image inpainting (dpeaa)DE-He213 Charge simulation method (dpeaa)DE-He213 Fast multipole method (dpeaa)DE-He213 Nasser, Mohamed M. S. aut Enthalten in Pattern Analysis & Applications Springer-Verlag, 1999 25(2022), 4 vom: 17. Apr., Seite 795-806 (DE-627)SPR008209189 nnns volume:25 year:2022 number:4 day:17 month:04 pages:795-806 https://dx.doi.org/10.1007/s10044-022-01074-3 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER AR 25 2022 4 17 04 795-806 |
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10.1007/s10044-022-01074-3 doi (DE-627)SPR048407259 (SPR)s10044-022-01074-3-e DE-627 ger DE-627 rakwb eng Kalmoun, El Mostafa verfasserin (orcid)0000-0002-1434-2541 aut Harmonic image inpainting using the charge simulation method 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s), under exclusive licence to Springer-Verlag London Ltd., part of Springer Nature 2022 Abstract It was recently reported that harmonic inpainting or Laplace interpolation when used in the context of image compression can yield impressive reconstruction results if the encoded pixels were carefully selected. Mathematically, the problem translates into a mixed Dirichlet–Neumann boundary value problem with Dirichlet data coming from the known observations and reflecting conditions being imposed on the image physical boundary. Classical numerical solutions depend on finite difference schemes, which often induce instabilities and rely heavily on the choice of a convenient regularization parameter. In this paper, we propose an alternative numerical method, which is able to provide a robust harmonic reconstruction without requiring neither numerical integration nor discretization of the inpainting domain or its boundary. In fact, our approach is connected with the charge simulation method powered with the fast multipole method. Thereby, we approximate the harmonic reconstruction by a linear combination of the fundamental solutions of the Laplace equation. The experimental results on standard test images using uniformly, randomly and optimally distributed masks of different densities demonstrate the superior performance of our numerical approach over the finite difference method in terms of both reconstruction quality and speed. Harmonic image inpainting (dpeaa)DE-He213 Charge simulation method (dpeaa)DE-He213 Fast multipole method (dpeaa)DE-He213 Nasser, Mohamed M. S. aut Enthalten in Pattern Analysis & Applications Springer-Verlag, 1999 25(2022), 4 vom: 17. Apr., Seite 795-806 (DE-627)SPR008209189 nnns volume:25 year:2022 number:4 day:17 month:04 pages:795-806 https://dx.doi.org/10.1007/s10044-022-01074-3 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER AR 25 2022 4 17 04 795-806 |
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10.1007/s10044-022-01074-3 doi (DE-627)SPR048407259 (SPR)s10044-022-01074-3-e DE-627 ger DE-627 rakwb eng Kalmoun, El Mostafa verfasserin (orcid)0000-0002-1434-2541 aut Harmonic image inpainting using the charge simulation method 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s), under exclusive licence to Springer-Verlag London Ltd., part of Springer Nature 2022 Abstract It was recently reported that harmonic inpainting or Laplace interpolation when used in the context of image compression can yield impressive reconstruction results if the encoded pixels were carefully selected. Mathematically, the problem translates into a mixed Dirichlet–Neumann boundary value problem with Dirichlet data coming from the known observations and reflecting conditions being imposed on the image physical boundary. Classical numerical solutions depend on finite difference schemes, which often induce instabilities and rely heavily on the choice of a convenient regularization parameter. In this paper, we propose an alternative numerical method, which is able to provide a robust harmonic reconstruction without requiring neither numerical integration nor discretization of the inpainting domain or its boundary. In fact, our approach is connected with the charge simulation method powered with the fast multipole method. Thereby, we approximate the harmonic reconstruction by a linear combination of the fundamental solutions of the Laplace equation. The experimental results on standard test images using uniformly, randomly and optimally distributed masks of different densities demonstrate the superior performance of our numerical approach over the finite difference method in terms of both reconstruction quality and speed. Harmonic image inpainting (dpeaa)DE-He213 Charge simulation method (dpeaa)DE-He213 Fast multipole method (dpeaa)DE-He213 Nasser, Mohamed M. S. aut Enthalten in Pattern Analysis & Applications Springer-Verlag, 1999 25(2022), 4 vom: 17. Apr., Seite 795-806 (DE-627)SPR008209189 nnns volume:25 year:2022 number:4 day:17 month:04 pages:795-806 https://dx.doi.org/10.1007/s10044-022-01074-3 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER AR 25 2022 4 17 04 795-806 |
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Abstract It was recently reported that harmonic inpainting or Laplace interpolation when used in the context of image compression can yield impressive reconstruction results if the encoded pixels were carefully selected. Mathematically, the problem translates into a mixed Dirichlet–Neumann boundary value problem with Dirichlet data coming from the known observations and reflecting conditions being imposed on the image physical boundary. Classical numerical solutions depend on finite difference schemes, which often induce instabilities and rely heavily on the choice of a convenient regularization parameter. In this paper, we propose an alternative numerical method, which is able to provide a robust harmonic reconstruction without requiring neither numerical integration nor discretization of the inpainting domain or its boundary. In fact, our approach is connected with the charge simulation method powered with the fast multipole method. Thereby, we approximate the harmonic reconstruction by a linear combination of the fundamental solutions of the Laplace equation. The experimental results on standard test images using uniformly, randomly and optimally distributed masks of different densities demonstrate the superior performance of our numerical approach over the finite difference method in terms of both reconstruction quality and speed. © The Author(s), under exclusive licence to Springer-Verlag London Ltd., part of Springer Nature 2022 |
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Abstract It was recently reported that harmonic inpainting or Laplace interpolation when used in the context of image compression can yield impressive reconstruction results if the encoded pixels were carefully selected. Mathematically, the problem translates into a mixed Dirichlet–Neumann boundary value problem with Dirichlet data coming from the known observations and reflecting conditions being imposed on the image physical boundary. Classical numerical solutions depend on finite difference schemes, which often induce instabilities and rely heavily on the choice of a convenient regularization parameter. In this paper, we propose an alternative numerical method, which is able to provide a robust harmonic reconstruction without requiring neither numerical integration nor discretization of the inpainting domain or its boundary. In fact, our approach is connected with the charge simulation method powered with the fast multipole method. Thereby, we approximate the harmonic reconstruction by a linear combination of the fundamental solutions of the Laplace equation. The experimental results on standard test images using uniformly, randomly and optimally distributed masks of different densities demonstrate the superior performance of our numerical approach over the finite difference method in terms of both reconstruction quality and speed. © The Author(s), under exclusive licence to Springer-Verlag London Ltd., part of Springer Nature 2022 |
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Abstract It was recently reported that harmonic inpainting or Laplace interpolation when used in the context of image compression can yield impressive reconstruction results if the encoded pixels were carefully selected. Mathematically, the problem translates into a mixed Dirichlet–Neumann boundary value problem with Dirichlet data coming from the known observations and reflecting conditions being imposed on the image physical boundary. Classical numerical solutions depend on finite difference schemes, which often induce instabilities and rely heavily on the choice of a convenient regularization parameter. In this paper, we propose an alternative numerical method, which is able to provide a robust harmonic reconstruction without requiring neither numerical integration nor discretization of the inpainting domain or its boundary. In fact, our approach is connected with the charge simulation method powered with the fast multipole method. Thereby, we approximate the harmonic reconstruction by a linear combination of the fundamental solutions of the Laplace equation. The experimental results on standard test images using uniformly, randomly and optimally distributed masks of different densities demonstrate the superior performance of our numerical approach over the finite difference method in terms of both reconstruction quality and speed. © The Author(s), under exclusive licence to Springer-Verlag London Ltd., part of Springer Nature 2022 |
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<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000caa a22002652 4500</leader><controlfield tag="001">SPR048407259</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20230509114146.0</controlfield><controlfield tag="007">cr uuu---uuuuu</controlfield><controlfield tag="008">221026s2022 xx |||||o 00| ||eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/s10044-022-01074-3</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)SPR048407259</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(SPR)s10044-022-01074-3-e</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-627</subfield><subfield code="b">ger</subfield><subfield code="c">DE-627</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1=" " ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Kalmoun, El Mostafa</subfield><subfield code="e">verfasserin</subfield><subfield code="0">(orcid)0000-0002-1434-2541</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Harmonic image inpainting using the charge simulation method</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2022</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">Text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">Computermedien</subfield><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">Online-Ressource</subfield><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">© The Author(s), under exclusive licence to Springer-Verlag London Ltd., part of Springer Nature 2022</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Abstract It was recently reported that harmonic inpainting or Laplace interpolation when used in the context of image compression can yield impressive reconstruction results if the encoded pixels were carefully selected. Mathematically, the problem translates into a mixed Dirichlet–Neumann boundary value problem with Dirichlet data coming from the known observations and reflecting conditions being imposed on the image physical boundary. Classical numerical solutions depend on finite difference schemes, which often induce instabilities and rely heavily on the choice of a convenient regularization parameter. In this paper, we propose an alternative numerical method, which is able to provide a robust harmonic reconstruction without requiring neither numerical integration nor discretization of the inpainting domain or its boundary. In fact, our approach is connected with the charge simulation method powered with the fast multipole method. Thereby, we approximate the harmonic reconstruction by a linear combination of the fundamental solutions of the Laplace equation. The experimental results on standard test images using uniformly, randomly and optimally distributed masks of different densities demonstrate the superior performance of our numerical approach over the finite difference method in terms of both reconstruction quality and speed.</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Harmonic image inpainting</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Charge simulation method</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Fast multipole method</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Nasser, Mohamed M. S.</subfield><subfield code="4">aut</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Enthalten in</subfield><subfield code="t">Pattern Analysis & Applications</subfield><subfield code="d">Springer-Verlag, 1999</subfield><subfield code="g">25(2022), 4 vom: 17. 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