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

TL;DR

CrossSDF tackles reconstructing a 3D signed-distance field from planar cross-sections by learning $f(\mathbf{x}; \boldsymbol{\theta})$ guided by 2D SDFs and contours. It introduces a symmetric-difference loss to avoid laddering, an adaptive contour sampling strategy to preserve thin structures, and a hybrid hash-Fourier encoding to reduce grid artifacts while maintaining detail. The approach achieves state-of-the-art results on synthetic and real data, including medical CT scans, for both thin and thick geometries and under aligned or non-aligned cross-sections. These contributions yield robust, high-fidelity 3D reconstructions without the interpolation artifacts common to prior methods, with potential impact on medical visualization and diagnostic workflows.

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.

Figures (16)

• Figure 1: We propose CrossSDF, a novel approach for reconstructing a 3D signed-distance field from 2D cross-sections. The input is a set of 2D cross-sections that sample an unobserved ground-truth geometric object by planar intersection (denoted as black lines overlayed on the ground truth Alveolis structure on the left). CrossSDF (middle) accurately reconstructs thin structures without breakages, over-smoothing, or cross-sectional artifacts observed in competing methods (right).
• Figure 2: CrossSDF takes a set of planar cross-sections as input. These cross-sections result in contours which denote the surface boundaries of the target geometry of interest (left, black lines) and each induces a 2D signed distance field (SDF) in its respective plane. From this, we generate a set of planar sample points $\Omega_{\text{pl}}$ and their 2D SDF labels. During training, points are encoded using our hybrid encoder before being passed to the SDF network $M_{\text{SDF}}$ for prediction. At each iteration we create a set of 3D samples $\Omega_{\text{reg}}$ to apply volumetric regularization. The combination of our novel sampling, loss function, and hybrid encoding results in a high quality 3D SDF.
• Figure 3: Close-up of the "figure eight" object from \ref{['fig:overview']} when fitting a 3D SDF directly to the 2D SDF labels. Displayed are the input contours (black) along with 2D SDF gradient vectors (green arrows). Here the neural 3D SDF attempts to remain orthogonal to the cross-sections, resulting in a "laddering" effect.
• Figure 4: Reconstruction results on thin structures featuring the Heart (top row) and Pulmonary (bottom row) for various methods. Results are presented using both input-aligned and non-aligned planes, displayed on the ground truth meshes.
• Figure 5: Reconstruction results on thick structures featuring the Armadillo (top row) and Balloon Dog (bottom row) for various methods. Results are presented using both non-aligned and input-aligned planes, displayed on the ground truth meshes.