X-Splat: Gaussian Splatting for 3D CBCT Generation from Single Panoramic Radiograph

Panoramic radiograph (PR) is fundamentally used in routine dental care, but it inherently provides only a two-dimensional (2D) projection of complex three-dimensional (3D) craniofacial anatomy. Most existing learning-based methods attempt to computationally recover this 3D information by directly regressing native cone-beam computed tomography (CBCT) volumes from PR. However, this direct mapping requires the model to simultaneously learn common anatomical structures and patient-specific morphological variations. This entangled formulation makes the ill-posed 2D-to-3D inverse problem highly ambiguous, often producing over-smoothed reconstructions with blurred anatomical boundaries. To address this, we propose HyDAR-Pano3D, a two-stage framework that reformulates PR-to-CBCT reconstruction as a disentangled anatomical recovery problem. In Stage 1, a dual-encoder network integrates radiographic features with SAM-derived semantic priors to reconstruct an arch-normalized canonical volume. In Stage 2, an Anatomical Restoration Network predicts a prior-constrained structured deformation field to map this canonical volume back to the native space, restoring individual morphological variations. Experiments on three large-scale datasets show that HyDAR-Pano3D significantly outperforms baseline methods ($p < 0.05$), achieving a 25.76 dB PSNR, 85.70% SSIM, and an 83.83% overall anatomical Dice score. The synthesized volumes successfully support downstream segmentation of whole teeth (82.4% Dice) and the inferior alveolar canal (72.2% Dice), demonstrating that our disentangled approach preserves clinically relevant structures to enable robust anatomy-aware assessment when CBCT data is unavailable.

A panoramic X-ray compresses a 3D jaw into a 2D strip; we aim to recover the missing depth cleanly and fast. Existing implicit neural representations render realistic volumes but are slow to train, sensitive to sampling and positional encodings, and costly in practice. Pure CNN baselines are efficient yet struggle with the dental arch's long-range geometry, blur fine enamel-dentin boundaries, and offer little interpretability. We present K-U-KAN, a three-stage pipeline that (i) lifts 2D features into depth-aware observables with Kolmogorov-Arnold Networks, (ii) advances these observables by a stable, phase-aware linear evolution via a Koopman token block, and (iii) places the predicted depth bins onto focal-trough rays before a lightweight 3D attention U-KAN refines the volume. This marriage of physics (Beer-Lambert image formation), geometry (horseshoe focal trough), and learned linear dynamics yields sharp anatomy, fewer artifacts, and robust behavior on native radiographic intensities with batch size one. On held-out data, K-U-KAN matches transformer/implicit baselines on signal and structure metrics, clearly improves perceptual quality, and trains in roughly half the time-making single-view PX $\to$ CBCT reconstruction more practical for clinical pipelines.

Sparse-view X-ray 3D reconstruction is essential for reducing radiation exposure, but recovering a density field from a handful of X-ray projections is severely ill-posed. Recently, 3D Gaussian Splatting has achieved state-of-the-art performance in sparse-view reconstruction by representing the volume using explicit, optimized primitives, but it requires dozens of projected views. With fewer views, reconstruction quality degrades severely since the explicit primitives are optimized freely without any anatomical information. Anatomical structures, in contrast, share similar geometry and density across a population. Their variations are bounded within a limited range that statistical shape models can capture. This paper proposes a shape-guided Gaussian splatting framework for sparse-view X-ray 3D reconstructions. Our contribution lies in driving Gaussian positions toward anatomically valid configurations, alongside atlas-based density regularization. Our method ensures anatomically consistent reconstruction and improves PSNR by 2.83 dB over a state-of-the-art Gaussian splatting baseline with as few as 5 views. Code Available: https://github.com/polyshape-lab/ShapeGuidedGaussian