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Neural implicit representation is a promising approach for reconstructingsurfaces from point clouds. Existing methods combine various regularizationterms, such as the Eikonal and Laplacian energy terms, to enforce the learnedneural function to possess the properties of a Signed Distance Function (SDF).However, inferring the actual topology and geometry of the underlying surfacefrom poor-quality unoriented point clouds remains challenging. In accordancewith Differential Geometry, the Hessian of the SDF is singular for pointswithin the differential thin-shell space surrounding the surface. Our approachenforces the Hessian of the neural implicit function to have a zero determinantfor points near the surface. This technique aligns the gradients for anear-surface point and its on-surface projection point, producing a rough butfaithful shape within just a few iterations. By annealing the weight of thesingular-Hessian term, our approach ultimately produces a high-fidelityreconstruction result. Extensive experimental results demonstrate that ourapproach effectively suppresses ghost geometry and recovers details fromunoriented point clouds with better expressiveness than existing fitting-basedmethods.

Neural-Singular-Hessian: Implicit Neural Representation of Unoriented Point Clouds by Enforcing Singular Hessian