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Isosurface Extraction for Signed Distance Functions using Power Diagrams.

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Title: Isosurface Extraction for Signed Distance Functions using Power Diagrams.
Authors: Kohlbrenner, M.1 (AUTHOR), Alexa, M.1 (AUTHOR)
Source: Computer Graphics Forum. May2025, Vol. 44 Issue 2, p1-10. 10p.
Subjects: Surface reconstruction, Implicit functions, Level set methods, Geometric analysis
Abstract: Contouring an implicit function typically considers function values in the vicinity of the desired level set, only. In a recent string of works, Sellán at al. have demonstrated that signed distance values contain useful information also if they are further away from the surface. This can be exploited to increase the resolution and amount of detail in surface reconstruction from signed distance values. We argue that the right tool for this analysis is a regular triangulation of the distance samples, with the weights chosen based on the distance values. The resulting triangulation is better suited for reconstructing the surface than a standard Delaunay triangulation of the samples. Moreover, the dual power diagram encodes the envelope enclosing the surface, consisting of spherical caps. We discuss how this information can be exploited for reconstructing the surface. In particular, the approach based on regular triangulations lends itself well to refining the sample set. Refining the sample set based on the power diagram outperforms other reconstruction methods relative to the sample count. [ABSTRACT FROM AUTHOR]
Copyright of Computer Graphics Forum is the property of Wiley-Blackwell and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: Isosurface Extraction for Signed Distance Functions using Power Diagrams.
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  Data: <searchLink fieldCode="AR" term="%22Kohlbrenner%2C+M%2E%22">Kohlbrenner, M.</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Alexa%2C+M%2E%22">Alexa, M.</searchLink><relatesTo>1</relatesTo> (AUTHOR)
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  Data: <searchLink fieldCode="JN" term="%22Computer+Graphics+Forum%22">Computer Graphics Forum</searchLink>. May2025, Vol. 44 Issue 2, p1-10. 10p.
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  Data: <searchLink fieldCode="DE" term="%22Surface+reconstruction%22">Surface reconstruction</searchLink><br /><searchLink fieldCode="DE" term="%22Implicit+functions%22">Implicit functions</searchLink><br /><searchLink fieldCode="DE" term="%22Level+set+methods%22">Level set methods</searchLink><br /><searchLink fieldCode="DE" term="%22Geometric+analysis%22">Geometric analysis</searchLink>
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  Data: Contouring an implicit function typically considers function values in the vicinity of the desired level set, only. In a recent string of works, Sellán at al. have demonstrated that signed distance values contain useful information also if they are further away from the surface. This can be exploited to increase the resolution and amount of detail in surface reconstruction from signed distance values. We argue that the right tool for this analysis is a regular triangulation of the distance samples, with the weights chosen based on the distance values. The resulting triangulation is better suited for reconstructing the surface than a standard Delaunay triangulation of the samples. Moreover, the dual power diagram encodes the envelope enclosing the surface, consisting of spherical caps. We discuss how this information can be exploited for reconstructing the surface. In particular, the approach based on regular triangulations lends itself well to refining the sample set. Refining the sample set based on the power diagram outperforms other reconstruction methods relative to the sample count. [ABSTRACT FROM AUTHOR]
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  Data: <i>Copyright of Computer Graphics Forum is the property of Wiley-Blackwell and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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      – Type: doi
        Value: 10.1111/cgf.70037
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      – Code: eng
        Text: English
    PhysicalDescription:
      Pagination:
        PageCount: 10
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    Subjects:
      – SubjectFull: Surface reconstruction
        Type: general
      – SubjectFull: Implicit functions
        Type: general
      – SubjectFull: Level set methods
        Type: general
      – SubjectFull: Geometric analysis
        Type: general
    Titles:
      – TitleFull: Isosurface Extraction for Signed Distance Functions using Power Diagrams.
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            NameFull: Kohlbrenner, M.
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            – D: 01
              M: 05
              Text: May2025
              Type: published
              Y: 2025
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            – TitleFull: Computer Graphics Forum
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