Calibrated Closed-Form Uncertainty for Radiative Gaussian Splatting in Sparse-View CT

• URL: http://arxiv.org/abs/2607.13682v1
• Date: Wed, 15 Jul 2026 10:25:05 GMT
• Title: Calibrated Closed-Form Uncertainty for Radiative Gaussian Splatting in Sparse-View CT
• Abstract summary: We present the first systematic calibration study for Gaussian-splatting CT.<n>We show that the resulting per-voxel uncertainty ranks true reconstruction error on 14 of 15 scenes of the official benchmark.<n>We then dissect why uncalibrated acquisition scores can nevertheless select acceptable views.
• Score: 13.147279382369293
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Radiative Gaussian splatting has made sparse-view CT reconstruction fast, but existing methods output point estimates with no notion of where the reconstruction can be trusted. We exploit a property of transmissive X-ray imaging that RGB splatting cannot claim -- projection and voxelization are strictly linear in the per-Gaussian densities -- to equip radiative Gaussians with a variational density posterior whose predictive variance propagates in closed form, exactly, in a single forward pass, in both volume space ($σ^2(x)=\sum_i g_i(x)^2 s_i^2$) and projection space ($\mathrm{Var}[I_p]=\sum_i w_{i,p}^2 s_i^2$). We present the first systematic calibration study for Gaussian-splatting CT (Spearman / AUSE / ECE with temperature scaling), showing that the resulting per-voxel uncertainty ranks true reconstruction error on 14 of 15 scenes of the official benchmark across three view budgets -- 9 of 15 additionally meeting our magnitude-calibration target after a single temperature -- while the perturbation-ensemble heuristic of concurrent work, transplanted to voxel space under the same protocol on our development scenes, does not (rank correlation as low as $-0.08$). We then dissect why uncalibrated acquisition scores can nevertheless select acceptable views, identifying three regimes -- flat (isotropic, balanced), pathological (degenerate coverage), and anisotropic -- and showing, in controlled single-scene testbeds, that principled uncertainty earns a measurable premium only in the last, motivating a coverage-gated, maturity-scheduled acquisition policy; the same calibrated posterior further points toward a dose-adaptive stopping rule, whose experimental validation we leave to future work.

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