Novel applications of signed distance fields in 3D reconstruction of thin structures

Abstract

Three-dimensional reconstruction from sparse or incomplete observations presents a fundamental challenge in computer vision and graphics. Traditional approaches using voxels, point clouds, or meshes often struggle with floating geometric artifacts, thin geometric structures, and preserving topological continuity. This thesis introduces novel methodologies using neural signed distance fields (SDFs) to address these long-standing limitations in reconstructing complex geometry featuring thin structures, intricate branching patterns, and high-frequency details. Our research follows a deliberate progression addressing increasingly challenging scenarios from general object geometry to thin, complex structures in specialized medical domains. Our research begins with GeoGen, a novel SDF-based 3D generative model trained end-to-end from single-view collections of 2D images. GeoGen reinterprets volumetric density as an SDF, introducing geometric priors for valid mesh generation through an SDF depth-map consistency loss. This approach enables more coherent surface representations than traditional neural rendering methods by enforcing geometric constraints throughout the learning process. By leveraging the mathematical properties of SDFs, GeoGen generates surfaces with improved structural integrity and avoids the floating artifacts common in neural radiance-field methods. We evaluated GeoGen on ShapeNet Cars and a 19 800-identity Synthetic Human Heads benchmark, achieving 20% lower Chamfer distance than EG3D on both datasets while matching its 2D FID scores. CrossSDF cut Chamfer distance by an order of magnitude on thin-structure meshes and VesselSDF improved Dice from 0.69 to 0.72 and reduced Chamfer from 0.82 to 0.68 on the Medical Decathlon Hepatic-Vessel CT set. However, GeoGen exhibits limitations when predicting fine details and thin structures like hair or eyelashes. These limitations motivated our investigation into specialized SDF representations for thin-structure reconstruction, with medical imaging providing an ideal application domain due to its critical need for accurate depiction of complex anatomical structures. Building on these insights, we introduce CrossSDF, a novel approach for extracting a 3D SDF from 2D signed distances generated from planar contours. Our framework employs a hash-based neural reconstruction approach with three key innovations: a novel symmetric-difference loss that minimizes visual artifacts resulting from sparse cross-sectional data, an adaptive contour-sampling strategy that ensures thin structures are adequately represented during surface reconstruction, and a hybrid encoding architecture that combines a detail-preserving hash encoding with Fourier features to reduce grid-interpolation artifacts. This enables CrossSDF to produce high-fidelity 3D reconstructions of thin structures while maintaining topological consistency between slices. However, we observed that when applied to medical data with inherent sparsity between imaging planes, the quality of the reconstruction remained fundamentally limited by the accuracy of the initial 2D contour segmentation. This observation led us to develop VesselSDF, a comprehensive two-stage framework specifically optimized for vascular-network reconstruction from sparse medical imagery. Unlike CrossSDF, which operates on pre-segmented contours, VesselSDF addresses both the segmentation and reconstruction challenges within a unified pipeline. VesselSDF addresses the reconstruction of complex structures from cross-sections by treating vessel segmentation as a continuous SDF regression problem rather than a discrete voxel classification one. The first stage employs a 3D U-Net for binary vessel-occupancy prediction. The second stage transforms this binary occupancy into an appropriately scaled SDF through a specialized refiner network with geometric constraints. VesselSDF introduces a distance-weighted Gaussian regularizer that adaptively enforces smoothness based on proximity to vessel surfaces, ensuring global smoothness while preserving critical vessel boundaries. This is complemented by a surface-regularization term that suppresses artifacts and an anisotropic Eikonal regularization term that accounts for different spatial resolutions along the axial dimension. By systematically separating segmentation from geometric refinement and incorporating these specialized constraints, VesselSDF achieves superior reconstruction of complex vascular networks compared to state-of-the-art binary voxel classification methods (nnU-Net, 3D SA-UNet), even from highly anisotropic CT and MRI data with significant interslice gaps. Through extensive experimental evaluation across diverse datasets, we demonstrate that our neural SDF approaches produce high-fidelity reconstructions that preserve thin structures, maintain topological correctness, and accurately capture geometric details, even from limited observations. The methodologies developed in this thesis have significant implications for medical imaging, enabling more accurate surgical planning through improved vessel visualization, enhanced blood flow simulation for cardiovascular analysis, early detection of vascular pathologies through preserved fine vessel details, and reduced radiation exposure in CT scanning by maintaining diagnostic quality from sparser slice data. The methodologies developed in this thesis establish a framework for addressing reconstruction problems across different domains, illustrating the versatility and effectiveness of neural SDF representations for complex-geometry reconstruction.