Symmetrized Poisson Reconstruction

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dc.contributor.authorKohlbrenner, Maximilianen_US
dc.contributor.authorLiu, Hongyien_US
dc.contributor.authorAlexa, Marcen_US
dc.contributor.authorKazhdan, Mishaen_US
dc.contributor.editorAttene, Marcoen_US
dc.contributor.editorSellán, Silviaen_US
dc.date.accessioned2025-06-20T07:41:07Z
dc.date.available2025-06-20T07:41:07Z
dc.date.issued2025
dc.description.abstractMany common approaches for reconstructing surfaces from point clouds leverage normal information to fit an implicit function to the points. Normals typically play two roles: the direction provides a planar approximation to the surface and the sign distinguishes inside from outside. When the sign is missing, reconstructing a surface with globally consistent sidedness is challenging. In this work, we investigate the idea of squaring the Poisson Surface Reconstruction, replacing the normals with their outer products, making the approach agnostic to the signs of the input/estimated normals. Squaring results in a quartic optimization problem, for which we develop an iterative and hierarchical solver, based on setting the cubic partial derivatives to zero. We show that this technique significantly outperforms standard L-BFGS solver and demonstrate reconstruction of surfaces from unoriented noisy input in linear time.en_US
dc.description.number5
dc.description.sectionheadersReconstruction
dc.description.seriesinformationComputer Graphics Forum
dc.description.volume44
dc.identifier.doi10.1111/cgf.70210
dc.identifier.issn1467-8659
dc.identifier.pages17 pages
dc.identifier.urihttps://doi.org/10.1111/cgf.70210
dc.identifier.urihttps://diglib.eg.org/handle/10.1111/cgf70210
dc.publisherThe Eurographics Association and John Wiley & Sons Ltd.en_US
dc.rightsAttribution 4.0 International License
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/
dc.subjectcurve and surface reconstruction, outer product, polynomial optimization CCS Concepts: Computing methodologies → Shape modeling; Mathematics of computing → Nonlinear equations; Numerical analysis
dc.subjectcurve and surface reconstruction
dc.subjectouter product
dc.subjectpolynomial optimization CCS Concepts
dc.subjectComputing methodologies → Shape modeling
dc.subjectMathematics of computing → Nonlinear equations
dc.subjectNumerical analysis
dc.titleSymmetrized Poisson Reconstructionen_US
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