mlsanityData to 7 Oct 2026

Electrostatics-Inspired Surface Reconstruction (EISR): Recovering 3D Shapes as a Superposition of Poisson's PDE Solutions

arXiv 2602.11642 ↗First posted 12 Feb 2026cs.CVcited by 0

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Abstract (arXiv)

Implicit shape representation, such as SDFs, is a popular approach to recover the surface of a 3D shape as the level sets of a scalar field. Several methods approximate SDFs using machine learning strategies that exploit the knowledge that SDFs are solutions of the Eikonal partial differential equation (PDEs). In this work, we present a novel approach to surface reconstruction by encoding it as a solution to a proxy PDE, namely Poisson's equation. Then, we explore the connection between Poisson's equation and physics, e.g., the electrostatic potential due to a positive charge density. We employ Green's functions to obtain a closed-form parametric expression for the PDE's solution, and leverage the linearity of our proxy PDE to find the target shape's implicit field as a superposition of solutions. Our method shows improved results in approximating high-frequency details, even with a small number of shape priors.

Key facts. No citing papers in the map yet (data through 7 Oct 2026). Builds on 46 of its 70 references that are in the map. First posted on arXiv 12 Feb 2026.

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References · 46

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34 more
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