“Neural-Singular-Hessian: Implicit Neural Representation of Unoriented Point Clouds by Enforcing Singular Hessian” by Wang, Zhang, Xu, Zhang, Wang, et al. …
Conference:
Type(s):
Title:
- Neural-Singular-Hessian: Implicit Neural Representation of Unoriented Point Clouds by Enforcing Singular Hessian
Session/Category Title: Neural Shape Representation
Presenter(s)/Author(s):
Abstract:
Neural implicit representation is a promising approach for reconstructing surfaces from point clouds. Existing methods combine various regularization terms to enforce the learned neural function to possess the properties of a SDF, such as the Eikonal term and Laplacian energy term. However, when the input is an unoriented point cloud of poor quality, inferring the actual topology and geometry of the underlying surface becomes challenging. In accordance with Differential Geometry, the Hessian of the SDF is singular for any point located within the differential thin-shell space surrounding the surface. Based on this fact, our approach enforces the Hessian of the SDF to have a zero determinant for points in close proximity to the input point cloud, rather than using a smoothness term. This technique quickly eliminates critical points of the SDF near the surface, producing a coarse but faithful shape. By annealing the weight of the critical-point elimination term, our approach can ultimately produce a high-fidelity reconstruction result. The validity of this approach can be established through Morse theory. Our approach has demonstrated better expressiveness in recovering details from unoriented point clouds while effectively suppressing ghost geometry, as evidenced by extensive experimental results in comparison to existing fitting-based methods.
