  Neural implicit representation is a promising approach for reconstructing
surfaces from point clouds. Existing methods combine various regularization
terms, such as the Eikonal and Laplacian energy terms, to enforce the learned
neural function to possess the properties of a Signed Distance Function (SDF).
However, inferring the actual topology and geometry of the underlying surface
from poor-quality unoriented point clouds remains challenging. In accordance
with Differential Geometry, the Hessian of the SDF is singular for points
within the differential thin-shell space surrounding the surface. Our approach
enforces the Hessian of the neural implicit function to have a zero determinant
for points near the surface. This technique aligns the gradients for a
near-surface point and its on-surface projection point, producing a rough but
faithful shape within just a few iterations. By annealing the weight of the
singular-Hessian term, our approach ultimately produces a high-fidelity
reconstruction result. Extensive experimental results demonstrate that our
approach effectively suppresses ghost geometry and recovers details from
unoriented point clouds with better expressiveness than existing fitting-based
methods.
