用3D高斯射线追踪提升断层成像精度,更物理、更灵活。
Radioactive 3D Gaussian Ray Tracing for Tomographic Reconstruction
- 基于射线追踪而非近似投影,实现更精确的正向建模
- 解析计算3D高斯体素的线积分,避免局部仿射退化
- 支持非线性几何校正,适合实际医学成像系统
3D高斯点阵(3DGS)是计算机视觉中一种新兴的渲染技术,通过将椭圆加权平均(EWA)点阵原理融入可微分流程,实现了实时高质量的新视角合成。在此基础上,R2-Gaussian将3DGS范式扩展至断层成像重建,通过修正积分偏差,在计算机断层扫描(CT)中达到领先性能。为保证可微性,R2-Gaussian采用局部仿射近似:将每个3D高斯在探测器上局部映射为2D高斯,并通过α混合生成投影。然而,该近似会降低重建的定量精度,并使非线性几何校正难以融入。为此,本文提出基于3D高斯射线追踪的断层成像框架。相比点阵模型,该方法具有两大优势:(i) 解析计算3D高斯原语的线积分,避免局部仿射坍缩,实现更物理一致的正向投影;(ii) 射线追踪形式明确控制射线起点与方向,便于精准应用非线性几何校正,如正电子发射断层扫描(PET)中的弧校正。这些特性使高斯基重建方法可适用于更广泛的现实断层成像系统,同时提升投影精度。
原文摘要 · Abstract (English)
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.
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