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Volume Preserving Neural Shape Morphing.

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Title: Volume Preserving Neural Shape Morphing.
Authors: Buonomo, Camille1 (AUTHOR), 1, Julie Digne1 (AUTHOR), Chaine, Raphaëlle1 (AUTHOR)
Source: Computer Graphics Forum. Aug2025, Vol. 44 Issue 5, p1-12. 12p.
Subjects: Morphing (Computer animation), Conservation of mass, Artificial neural networks, Level set methods, Flow velocity
Abstract: Shape interpolation is a long standing challenge of geometry processing. As it is ill‐posed, shape interpolation methods always work under some hypothesis such as semantic part matching or least displacement. Among such constraints, volume preservation is one of the traditional animation principles. In this paper we propose a method to interpolate between shapes in arbitrary poses favoring volume and topology preservation. To do so, we rely on a level set representation of the shape and its advection by a velocity field through the level set equation, both shape representation and velocity fields being parameterized as neural networks. While divergence free velocity fields ensure volume and topology preservation, they are incompatible with the Eikonal constraint of signed distance functions. This leads us to introduce the notion of adaptive divergence velocity field, a construction compatible with the Eikonal equation with theoretical guarantee on the shape volume preservation. In the non constant volume setting, our method is still helpful to provide a natural morphing, by combining it with a parameterization of the volume change over time. We show experimentally that our method exhibits better volume preservation than other recent approaches, limits topological changes and preserves the structures of shapes better without landmark correspondences. [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.)
Database: Engineering Source
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DbLabel: Engineering Source
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PubType: Academic Journal
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  Data: Volume Preserving Neural Shape Morphing.
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  Data: <searchLink fieldCode="JN" term="%22Computer+Graphics+Forum%22">Computer Graphics Forum</searchLink>. Aug2025, Vol. 44 Issue 5, p1-12. 12p.
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  Data: <searchLink fieldCode="DE" term="%22Morphing+%28Computer+animation%29%22">Morphing (Computer animation)</searchLink><br /><searchLink fieldCode="DE" term="%22Conservation+of+mass%22">Conservation of mass</searchLink><br /><searchLink fieldCode="DE" term="%22Artificial+neural+networks%22">Artificial neural networks</searchLink><br /><searchLink fieldCode="DE" term="%22Level+set+methods%22">Level set methods</searchLink><br /><searchLink fieldCode="DE" term="%22Flow+velocity%22">Flow velocity</searchLink>
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  Data: Shape interpolation is a long standing challenge of geometry processing. As it is ill‐posed, shape interpolation methods always work under some hypothesis such as semantic part matching or least displacement. Among such constraints, volume preservation is one of the traditional animation principles. In this paper we propose a method to interpolate between shapes in arbitrary poses favoring volume and topology preservation. To do so, we rely on a level set representation of the shape and its advection by a velocity field through the level set equation, both shape representation and velocity fields being parameterized as neural networks. While divergence free velocity fields ensure volume and topology preservation, they are incompatible with the Eikonal constraint of signed distance functions. This leads us to introduce the notion of adaptive divergence velocity field, a construction compatible with the Eikonal equation with theoretical guarantee on the shape volume preservation. In the non constant volume setting, our method is still helpful to provide a natural morphing, by combining it with a parameterization of the volume change over time. We show experimentally that our method exhibits better volume preservation than other recent approaches, limits topological changes and preserves the structures of shapes better without landmark correspondences. [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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RecordInfo BibRecord:
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        Value: 10.1111/cgf.70196
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      – Code: eng
        Text: English
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        PageCount: 12
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      – SubjectFull: Morphing (Computer animation)
        Type: general
      – SubjectFull: Conservation of mass
        Type: general
      – SubjectFull: Artificial neural networks
        Type: general
      – SubjectFull: Level set methods
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      – SubjectFull: Flow velocity
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      – TitleFull: Volume Preserving Neural Shape Morphing.
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            – D: 01
              M: 08
              Text: Aug2025
              Type: published
              Y: 2025
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