Radioactive 3D Gaussian Ray Tracing for Tomographic Reconstruction

2026-02-01

AI Summary

This work proposes a novel tomographic reconstruction framework based on analytical ray tracing through 3D Gaussian primitives, addressing the limitations of existing 3D Gaussian splatting methods that rely on local affine approximations. By explicitly computing the integral of rays traversing each 3D Gaussian, the method establishes a physically consistent forward projection model that naturally accommodates complex nonlinear geometric corrections—such as PET arc-length correction—without resorting to affine approximations. This approach enables high-precision, differentiable projection and reconstruction, significantly improving quantitative accuracy. Consequently, it expands the applicability of Gaussian-based representations to real-world tomographic imaging systems, including clinical PET/CT scanners.

Technology Category

• Computer Vision: 3D Computer Vision
• Machine Learning: Calibration & Uncertainty Quantification
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Security and Privacy: Data transparency and provenance
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

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.

Problem

• tomographic reconstruction
• 3D Gaussian Splatting
• ray tracing
• geometric correction
• projection accuracy

Innovation

• 3D Gaussian ray tracing
• tomographic reconstruction
• analytical line integral
• nonlinear geometric correction
• differentiable rendering