Author ORCID Identifier
0009-0001-5287-0820
Document Type
Dissertation
Date of Award
5-31-2026
Degree Name
Doctor of Philosophy in Computing Sciences - (Ph.D.)
Department
Computer Science
First Advisor
Przemyslaw Musialski
Second Advisor
Vincent Oria
Third Advisor
Ioannis Koutis
Fourth Advisor
Tomer Weiss
Fifth Advisor
Paul Guerrero
Abstract
Neural signed distance fields have emerged as a powerful framework for representing three-dimensional geometry through continuous and differentiable neural functions. Their flexibility, resolution independence, and compatibility with gradient-based optimization make them especially attractive for surface reconstruction and geometric learning. However, despite these advantages, two fundamental challenges remain for engineering-grade applications. First, higher-order geometric properties such as curvature are difficult to model reliably during training and often require computationally expensive second-order differentiation. Second, while neural signed distance fields provide implicit surface representations, they do not directly yield a globally consistent forward map or parameterization for downstream geometric processing.
This dissertation addresses these limitations through a differential-geometric framework for neural signed distance fields, with contributions spanning curvature-aware reconstruction, efficient second-order regularization, adaptive training strategies, feature-aware sampling, and parameterized surface extraction. On the reconstruction side, this work first develops a finite-difference framework for second-order geometric regularization that replaces explicit Hessian computation with local function evaluations and first-order gradients. This formulation preserves the geometric objectives of existing curvature-based priors while substantially reducing memory usage and computational cost. Building on this foundation, the dissertation introduces the Off-Diagonal Weingarten loss, a curvature-aware regularizer designed for CAD-type neural signed distance field reconstruction. By directly constraining directional second-order structure in the tangent plane, this formulation provides a simpler and more stable alternative to determinant-based regularization and better reflects the anisotropic geometric structure of planar, cylindrical, and piecewise developable surfaces. The dissertation further investigates time-dependent weighting strategies for curvature regularization and demonstrates that strong-start decay schedules improve optimization stability in early training while preserving fine geometric detail in later stages. In addition, feature-aware sampling is introduced to increase the representation of geometrically informative regions during training, thereby improving the reconstruction of sharp features and detailed CAD structures that are often underemphasized under uniform sampling.
On the parameterization side, this dissertation introduces a shrinking-based framework for constructing a continuous forward map from a canonical domain to the reconstructed implicit surface. Rather than extracting only a discrete mesh, the proposed method progressively deforms an initial parameterized surface toward the zero level set of the learned signed distance field, producing an explicit, differentiable, and globally coherent parameterization. This formulation establishes a direct bridge between implicit neural representations and downstream geometric processing by integrating reconstruction and surface mapping within a unified framework.
Taken together, these contributions establish a unified dissertation framework for geometry-aware neural signed distance field learning. The resulting methods improve reconstruction fidelity, reduce the computational burden of curvature-aware optimization, enhance the recovery of feature-rich CAD geometry, and extend implicit neural surfaces beyond reconstruction toward explicit parameterized geometric representations. This work advances neural signed distance fields as a practical and principled foundation for high-fidelity surface modeling, engineering geometry reconstruction, and differentiable geometric processing.
Recommended Citation
Yin, Haotian, "Differential-geometric methods for neural signed distance fields: Parameterized surface extraction and curvature regularization for CAD models" (2026). Dissertations. 1891.
https://digitalcommons.njit.edu/dissertations/1891
