SplineSplat: 3D Ray Tracing for Higher-Quality Tomography
Youssef Haouchat, Sepand Kashani, Aleix Boquet-Pujadas, Philippe Thévenaz, Michael Unser
TL;DR
The paper addresses high-quality 3D tomography by representing volumes with overlapping, tensor-product B-spline bases and extending the classic DDA ray-tracing to handle such bases in 3D. A learned projector, implemented as a shallow MLP $f_\theta$, estimates the basis contributions to line integrals, enabling a geometry-agnostic forward model $\mathcal{P}$ without closed-form expressions. In experiments on the 3D Simulated Brain Database, the SplineSplat approach with quadratic B-splines achieves substantially higher PSNR ($=28.02$ dB) than voxel-based methods ($=22.29$ dB) under well-posed conditions. The method is projection-geometry agnostic and improves tomographic reconstructions by leveraging smoother, higher-order basis functions coupled with learned basis-contribution modeling, with potential applicability across tomographic modalities.
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.