NeBLa: Neural Beer-Lambert for 3D Reconstruction of Oral Structures from Panoramic Radiographs

TL;DR

NeBLa tackles 3D oral-structure reconstruction from a single panoramic X-ray by introducing SimPX, a CBCT-derived PX-like representation built on the Beer-Lambert law. It jointly learns unpaired PX↔SimPX translation with semantic teeth regularization and a NeRF-inspired density estimator conditioned on SimPX, enabling 3D output without prior dental-arch shapes or paired PX–CBCT data. The method demonstrates superior quantitative and qualitative reconstruction performance over state-of-the-art baselines and shows robustness to real-world PX artifacts. This approach has practical implications for educational AR/VR visualization and enhanced dental diagnostics while highlighting avenues to better model PX geometry and scanner-specific trajectories.

Abstract

Panoramic radiography (Panoramic X-ray, PX) is a widely used imaging modality for dental examination. However, PX only provides a flattened 2D image, lacking in a 3D view of the oral structure. In this paper, we propose NeBLa (Neural Beer-Lambert) to estimate 3D oral structures from real-world PX. NeBLa tackles full 3D reconstruction for varying subjects (patients) where each reconstruction is based only on a single panoramic image. We create an intermediate representation called simulated PX (SimPX) from 3D Cone-beam computed tomography (CBCT) data based on the Beer-Lambert law of X-ray rendering and rotational principles of PX imaging. SimPX aims at not only truthfully simulating PX, but also facilitates the reverting process back to 3D data. We propose a novel neural model based on ray tracing which exploits both global and local input features to convert SimPX to 3D output. At inference, a real PX image is translated to a SimPX-style image with semantic regularization, and the translated image is processed by generation module to produce high-quality outputs. Experiments show that NeBLa outperforms prior state-of-the-art in reconstruction tasks both quantitatively and qualitatively. Unlike prior methods, NeBLa does not require any prior information such as the shape of dental arches, nor the matched PX-CBCT dataset for training, which is difficult to obtain in clinical practice. Our code is available at https://github.com/sihwa-park/nebla.

Figures (16)

• Figure 1: (a) Illustration of the process for panoramic radiography. The receptor and X-ray source rotate around the patient. The center of rotation, marked in red, moves along a curve to form a focal trough on the teeth region. (b) Process of generating SimPX. SimPX images are rendered by hypothetical rays traversing through CBCT data, whose trajectories are similar to those in (a).
• Figure 2: Overview of NeBLa. Function $\gamma(\mathbf{x})$ denotes the positional encoding applied to position $\mathbf{x}$ sampled from a ray, as in mildenhall2020nerf. FC stands for the fully connected layer.
• Figure 3: Qualitative comparison of 3D reconstruction results from real PX image using volume rendering and maximum intensity projection.
• Figure 4: Qualitative comparison of 3D reconstruction results from SimPX images of two different patients using volume rendering.
• Figure 5: Qualitative comparison of translated PX images with real PX.