CrossSDF: 3D Reconstruction of Thin Structures From Cross-Sections

2024-12-05

arXiv.org

AI Summary

Reconstructing 3D geometry from sparse planar cross-sections suffers from thin-structure distortion, topological discontinuities, and interpolation artifacts. To address these challenges—particularly for slender structures such as blood vessels—this paper proposes a neural implicit reconstruction method. Its core innovation is the first explicit incorporation of 2D contour signed distance fields (SDFs) into neural SDF training, achieved via a cross-section-aware loss function that jointly enforces cross-sectional alignment constraints and topology-preserving regularization. This dual objective ensures both local geometric fidelity and global topological continuity. Experiments on medical imaging datasets with sparse slices demonstrate that our method significantly outperforms state-of-the-art point-cloud- and voxel-based approaches: it eliminates oversmoothing and interpolation artifacts, achieves higher surface accuracy, preserves fine structural integrity, and improves connectivity robustness.

Technology Category

• Computer Vision: 3D Computer Vision
• Machine Learning: Learning with Manifolds
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Semantics and Knowledge: Scalable techniques for the creation, curation, publication, maintenance, and consumption of large, Web-based, structured, reusable, knowledge graphs and ontologies

Abstract

Reconstructing complex structures from planar cross-sections is a challenging problem, with wide-reaching applications in medical imaging, manufacturing, and topography. Out-of-the-box point cloud reconstruction methods can often fail due to the data sparsity between slicing planes, while current bespoke methods struggle to reconstruct thin geometric structures and preserve topological continuity. This is important for medical applications where thin vessel structures are present in CT and MRI scans. This paper introduces CrossSDF, a novel approach for extracting a 3D signed distance field from 2D signed distances generated from planar contours. Our approach makes the training of neural SDFs contour-aware by using losses designed for the case where geometry is known within 2D slices. Our results demonstrate a significant improvement over existing methods, effectively reconstructing thin structures and producing accurate 3D models without the interpolation artifacts or over-smoothing of prior approaches.

Problem

• Reconstructing thin structures from sparse cross-sections
• Preserving topology in 3D medical imaging models
• Avoiding interpolation artifacts in neural SDF training

Innovation

• Uses 2D signed distances for 3D reconstruction
• Trains neural SDFs with contour-aware losses
• Improves thin structure reconstruction accuracy