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

2026-05-24

AI Summary

This work addresses the challenges of slow reconstruction speed, geometric distortion, and boundary blurriness in three-dimensional dental arch reconstruction from a single panoramic X-ray image. The authors propose a K-U-KAN three-stage framework: first, Kolmogorov–Arnold networks extract depth-aware features; second, Koopman operators model phase-aware linear dynamical evolution; and third, a lightweight 3D attention U-KAN refines volumetric reconstruction along focal trough rays. By integrating the Beer–Lambert physical imaging model, dental arch geometric priors, and learnable linear dynamics, the method significantly enhances perceptual quality while preserving structural fidelity. It reduces training time by approximately 50% and enables efficient single-sample batch deployment in clinical settings.

Abstract

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.

Problem

• 3D dental reconstruction
• panoramic X-ray
• depth recovery
• implicit neural representations
• CNN limitations

Innovation

• Koopman operator
• Kolmogorov-Arnold Networks
• 3D dental reconstruction
• single-view X-ray
• implicit neural representation