X-Field: A Physically Grounded Representation for 3D X-ray Reconstruction

TL;DR

This work introduces X-Field, a physically grounded 3D representation for X-ray imaging that models internal materials with ellipsoids carrying distinct attenuation coefficients and computes per-ray segment lengths for accurate attenuation integration, leveraging the Beer-Lambert framework in log-space. The method advances by (i) deriving an explicit segment-length formulation in normalized device coordinates, (ii) resolving ellipsoid overlaps with a precedence rule and an Oriented Bounding Box-based pixel-ellipsoid association, (iii) applying Hybrid Progressive Initialization to seed geometry, and (iv) performing Material-Based Optimization to refine material boundaries. Empirical results on real human organs and synthetic objects show X-Field surpasses state-of-the-art methods in X-ray Novel View Synthesis and sparse-view CT reconstruction, achieving PSNR gains up to about 2.44 dB for NVS and 3.98 dB for CT with as few as 5–10 input views. This work has practical implications for reducing radiation exposure while preserving diagnostic fidelity and can extend to reconstructing translucent internal structures beyond medical imaging.

Abstract

X-ray imaging is indispensable in medical diagnostics, yet its use is tightly regulated due to potential health risks. To mitigate radiation exposure, recent research focuses on generating novel views from sparse inputs and reconstructing Computed Tomography (CT) volumes, borrowing representations from the 3D reconstruction area. However, these representations originally target visible light imaging that emphasizes reflection and scattering effects, while neglecting penetration and attenuation properties of X-ray imaging. In this paper, we introduce X-Field, the first 3D representation specifically designed for X-ray imaging, rooted in the energy absorption rates across different materials. To accurately model diverse materials within internal structures, we employ 3D ellipsoids with distinct attenuation coefficients. To estimate each material's energy absorption of X-rays, we devise an efficient path partitioning algorithm accounting for complex ellipsoid intersections. We further propose hybrid progressive initialization to refine the geometric accuracy of X-Filed and incorporate material-based optimization to enhance model fitting along material boundaries. Experiments show that X-Field achieves superior visual fidelity on both real-world human organ and synthetic object datasets, outperforming state-of-the-art methods in X-ray Novel View Synthesis and CT Reconstruction.

Figures (8)

• Figure 1: Comparison of Imaging Processes and Corresponding 3D Representations. (a) Visible light interacts with surface mainly through scattering and reflection. NeRF nerf and 3DGS 3dgs model this process by accumulating directional light rays. (b) Rooted in X-rays' attenuation and penetration properties, our X-Field models the radiological density of different materials to reveal internal structure.
• Figure 2: Overview of X-Field.(a) Hybrid Progressive Initialization. We begin with X-ray images to construct a coarse initialization using combined iterative methods. (b) Physically Grounded Ellipsoid Representation. We transform initialized ellipsoids into NDC space and associate them with pixels. We then compute the attenuation integral along the ray, considering segment length and ellipsoid intersections. (c) Material-Based Optimization. Our optimization captures detailed materials' boundaries for high-quality rendering.
• Figure 3: Pixel-Ellipse Association. (a) The baseline, based on AABB toth1985aabb, results in incorrect associations. (b) The pixels selected by OBB gottschalk1996obb. (c) Our method only retains pixels truly aligned with the projected ellipse to ensure physical faithfulness.
• Figure 4: Comparison of Initialization Methods. Our Hybrid Progressive Initialization produces clear shapes, whereas Random x_gaussian and FDK r2_gaussian initialization sacrifice the geometry prior.
• Figure 5: Illustration of Adaptive Optimization Strategy.(a) Ground-truth Geometry and Material Distribution, with different colors indicating distinct materials. (b) Geometry-Based Optimization3dgs, which fits the ellipsoids closely to the object geometry. (c) Our Material-Based Optimization, which further refines the ellipsoids to capture the material distribution.