K-U-KAN: Koopman-Enhanced U-KAN for 3D Dental Reconstruction from a Single Panoramic X-ray 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.

Generating a 3D dental volume from a single panoramic radiograph (PXR) could provide a low-radiation alternative to Cone-Beam Computed Tomography (CBCT), but the problem is highly underdetermined: panoramic acquisition integrates 3D attenuation along curved X-ray paths into a 2D image, leaving depth-resolved anatomy unobserved. Existing implicit and generative approaches often produce oversmoothed geometry or anatomically inconsistent hallucinations, lacking geometry-driven supervision and relying on smooth representations unable to precisely localize sharp anatomical boundaries. We propose X-Splat, the first Gaussian Splatting framework for generating CBCT-like 3D dental volumes from a single PXR. X-Splat uses the known panoramic acquisition geometry as a generation scaffold: learnable anisotropic Gaussian primitives are initialized along the X-ray paths that formed the input image and adjusted in a single feed-forward pass, constrained by Beer-Lambert reprojection and multi-view radiographic training supervision. A lightweight residual refiner adds dataset-level anatomical priors without overriding the geometry already resolved by the Gaussians. We train on synthetic PXR-CBCT pairs, enabling direct volumetric supervision without paired real scans. We further introduce segmentation-based geometry-aware metrics, providing the first evaluation of PXR-based generation over maxillofacial anatomy. X-Splat outperforms NeRF- and GAN-based baselines, recovering individual teeth, cortical boundaries, and alveolar structure, including the mandibular canal which prior methods fail to reconstruct. Code will be available at https://github.com/tomek1911/X-Splat

Recent advances in 3D feedforward reconstruction neural networks have achieved remarkable success in dense reconstruction from images without any camera parameters. Yet, equipping these models with robust semantic understanding remains an open problem. Here we introduce an approach that performs 3D reconstruction and 3D panoptic segmentation in a unified framework. We build on existing 3D reconstruction models and augment them with a set-based mask decoder. The approach is jointly trained with a geometric and semantic loss, which are shown to be mutually beneficial. More precisely, the features are initialized from the geometric information and then finetuned to capture jointly geometry and semantics. We demonstrate the generality of our approach by successfully applying our framework both to online and all-to-all attention reconstruction backbones. Our method achieves state-of-the-art performance in 3D panoptic segmentation across ScanNet, ScanNet200, and ScanNet++ datasets. Ablation studies show that such joint training of a unified model equips 3D feedforward reconstruction neural networks with panoptic segmentation and yields mutually beneficial improvements.