Intraoral scan (IoS) provides high-resolution data on the tooth crown, but does not contain information on the tooth root and thus has limitations in applications requiring 3D models of the whole tooth, e.g., virtual dental simulators. In this paper, we consider a diffusion-based model for root completion from IoS crowns. A key challenge is the lack of ground truth, i.e., the scan data of roots are typically unavailable. To train our model, we instead use the Cone-Beam CT (CBCT) data matched to IoS images, and use its crown as input and root as the pseudo-ground truth. Due to the difference in input data between training (CBCT crown) and inference (IoS crown), there is an issue of domain shift. To address the issue, we take a coarse-to-fine approach: we make a coarse prediction of roots using Coarse Estimator; introduce Perturbed Patch Generator (PPG) which generates patches from coarse points and perturbs them with noise for a robust prediction against the domain shift; and use Transformer denoiser for refined reconstruction. We also propose loss functions designed to facilitate the training of the denoiser with perturbed patches. Experiments show that our method outperforms prior techniques in various benchmark evaluations, demonstrating its robust performance in generating high-quality root data. Our code is available at https://github.com/yhJang94/RootCompletion.git.

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.