[论文解读] Radioactive 3D Gaussian Ray Tracing for Tomographic Reconstruction

Ling Chen, Bao Yang|arXiv (Cornell University)|Feb 1, 2026

Medical Imaging Techniques and Applications被引用 0

一句话总结

论文为基于3D高斯光线追踪的断层成像重建框架，能够通过3D高斯基元的解析线积分来计算前向投影，提高PET和CT在基于投影投射的前向投影精度与几何灵活性，优于基于splatting的方法。

ABSTRACT

3D Gaussian Splatting (3DGS) has recently emerged in computer vision as a promising rendering technique. By adapting the principles of Elliptical Weighted Average (EWA) splatting to a modern differentiable pipeline, 3DGS enables real-time, high-quality novel view synthesis. Building upon this, R2-Gaussian extended the 3DGS paradigm to tomographic reconstruction by rectifying integration bias, achieving state-of-the-art performance in computed tomography (CT). To enable differentiability, R2-Gaussian adopts a local affine approximation: each 3D Gaussian is locally mapped to a 2D Gaussian on the detector and composed via alpha blending to form projections. However, the affine approximation can degrade reconstruction quantitative accuracy and complicate the incorporation of nonlinear geometric corrections. To address these limitations, we propose a tomographic reconstruction framework based on 3D Gaussian ray tracing. Our approach provides two key advantages over splatting-based models: (i) it computes the line integral through 3D Gaussian primitives analytically, avoiding the local affine collapse and thus yielding a more physically consistent forward projection model; and (ii) the ray-tracing formulation gives explicit control over ray origins and directions, which facilitates the precise application of nonlinear geometric corrections, e.g., arc-correction used in positron emission tomography (PET). These properties extend the applicability of Gaussian-based reconstruction to a wider range of realistic tomography systems while improving projection accuracy.

研究动机与目标

• Motivate tomographic reconstruction accuracy and geometric fidelity beyond local affine splatting.
• Develop a differentiable forward model using analytic line integrals through 3D Gaussian primitives.
• Ensure compatibility with diverse scanner geometries and nonlinear geometric corrections (e.g., arc correction in PET).
• Provide a tractable optimization framework to recover Gaussian parameters from projection data.

提出的方法

• Represent the scene with 3D Gaussian primitives parameterized by position, covariance, density, and orientation.
• Derive and implement the analytic line integral of a single anisotropic 3D Gaussian along a ray to obtain the forward projection (I(r) = sum_i ρ_i * sqrt(2π/A_i) * exp(-0.5*(C_i - B_i^2/A_i))).
• Use ray tracing with a BVH and GPU acceleration (OptiX) to cast rays per pixel and accumulate analytic integrals.
• Allow flexible ray origins/directions to accommodate different scanner geometries (e.g., PET arcs, oblique LORs) without resorting to 2D affine projections.
• Adopt a densify-and-prune strategy and PyTorch/OptiX implementation on RTX 3080 Ti for efficient optimization.
• Compare with R2-Gaussian and OSEM on PET and CT datasets, evaluating quantitative metrics and qualitative image quality.

实验结果

研究问题

• RQ1 Can analytic line integrals through 3D Gaussian primitives provide a more physically accurate forward projection than local affine splatting in tomographic reconstruction?
• RQ2 How does a ray-tracing based Gaussian framework handle diverse scanner geometries, including arc-corrected PET configurations?
• RQ3 What are the quantitative and qualitative improvements in PET and CT reconstructions when using 3D Gaussian ray tracing compared to R2-Gaussian and traditional methods?
• RQ4 What are the computational trade-offs (speed vs. accuracy) of analytic ray-tracing vs. splatting-based approaches in this setting?
• RQ5 Can the framework readily incorporate nonlinear geometric corrections and be extended toward fully quantitative PET reconstruction?

主要发现

• Analytic line integrals for 3D Gaussians yield a differentiable forward projection that avoids local affine approximations.
• The framework supports arbitrary ray origins and directions, enabling accurate modeling of PET arc corrections and oblique lines of response.
• In PET experiments, the method achieved best quantitative accuracy across most NEMA spheres, with five of six spheres within 5% diameter error and improved SBR relative to baselines.
• Arc correction improved spatial resolution in a three-point-source Monte Carlo test, reducing variability across sources.
• CT reconstructions showed higher PSNR with the proposed method compared to R2-Gaussian, with statistically significant PSNR gains (p = 0.0048); SSIM was comparable.
• Visual reconstructions on realistic brain PET data demonstrated finer anatomical detail and reduced artifacts versus OSEM and R2-Gaussian.
• Method remains slower than splatting-based methods due to explicit ray tracing, but offers superior geometric fidelity and potential for further acceleration