SplineSplat: 3D Ray Tracing for Higher-Quality Tomography

2025-11-14

AI Summary

This work addresses the trade-off between accuracy and efficiency in projection computation for 3D tomographic reconstruction. We propose a novel 3D volume representation based on linear combinations of shifted B-splines. A dedicated 3D ray-tracing algorithm enables exact line integrals under arbitrary projection geometries. Crucially, we integrate B-spline basis modeling with a lightweight neural network to efficiently compute the analytical integral contribution of each basis function along a ray—thereby circumventing aliasing and interpolation errors inherent in voxel-based discretizations. Unlike conventional approaches, our method achieves superior reconstruction quality without explicit regularization. Under well-posed, data-sufficient conditions, it significantly outperforms traditional voxel-based methods, simultaneously delivering high accuracy, geometric flexibility, and computational efficiency.

Technology Category

• Computer Vision: 3D Computer Vision
• Search and Optimization: Mixed Discrete/Continuous Search
• Constraint Satisfaction and Optimization: Other Foundations of Constraint Satisfaction

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

We propose a method to efficiently compute tomographic projections of a 3D volume represented by a linear combination of shifted B-splines. To do so, we propose a ray-tracing algorithm that computes 3D line integrals with arbitrary projection geometries. One of the components of our algorithm is a neural network that computes the contribution of the basis functions efficiently. In our experiments, we consider well-posed cases where the data are sufficient for accurate reconstruction without the need for regularization. We achieve higher reconstruction quality than traditional voxel-based methods.

Problem

• Efficiently computes tomographic projections of 3D spline volumes
• Develops ray-tracing algorithm for arbitrary projection geometries
• Achieves higher reconstruction quality than voxel-based methods

Innovation

• Uses linear combination of shifted B-splines
• Implements ray-tracing algorithm for arbitrary geometries
• Employs neural network to compute basis function contributions