arXiv:2607.13682cs.CVcs.LG2026-07

提出可精确计算的不确定性公式,显著降低计算成本且更可靠。

Posterior Variance Is a Constraint Map, Not an Error Map: Closed-Form Uncertainty for Radiative Gaussian Splatting in Sparse-View CT

论文配图:Posterior Variance Is a Constraint Map, Not an Error Map: Closed-Form Uncertainty for Radiative Gaussian Splatting in Sparse-View CT
图 1 · 摘自论文原文
  • 基于线性投影推导出闭式解,单次前向传播完成
  • 在15个场景中14个正确排序真实误差,但内部组织不准确
  • 揭示模型分歧无法捕捉系统偏差,适合临床影像分析

辐射高斯点阵能快速准确重建稀疏视角CT,近期工作为每个高斯点附带后验分布以生成体素级不确定性图。本文探究该图实际意义:后验方差是数据约束图,而非误差图——其预警可信,无警报则不可信。利用X射线渲染在高斯密度上的严格线性特性,我们推导出一种夹紧感知的闭式表达,可在不变光栅化器中单次前向传播内精确计算,覆盖体积与投影空间:即同期采样估计器的无限样本极限,成本降低约8倍。在官方15场景基准上,该不确定性在14/15场景中正确排序真实误差。但若限制于物体内部(临床读片区域),相关性急剧下降(中位斯皮尔曼相关0.11,0/15通过)——深度集成与正对数正态后验表现一致。机制分析显示:约90%内部误差为可重复偏置,模型分歧无法察觉;73-81%全体积相关性由物体/周围对比度驱动;一个精确可解控制实验表明,观测到的内部相关性比理想校准后验低4-5倍。误差尺度本质是工程问题,本文通过重参数化后验将跨场景温度跨度从19.3倍压缩至2.6倍,单一温度可泛化至未见场景(10/15留一场景测试通过),修复后的尺度遵循泊松预测的-1/2幂律。本文提炼出可提前发现此类幻觉的评估方法:掩码校准、种子级偏差分解、精确后验参照,并公开所有协议、种子与每轮证据。

原文摘要 · Abstract (English)

Radiative Gaussian splatting reconstructs sparse-view CT fast and accurately, and recent work attaches per-Gaussian posteriors to yield per-voxel uncertainty maps. We ask what such a map actually measures: posterior variance is a data-constraint map, not an error map -- its alarms are trustworthy, its all-clears are not. Exploiting the strict linearity of X-ray rendering in the per-Gaussian densities, we derive a clamp-aware closed form that the unchanged rasterizer evaluates exactly in one forward pass, in volume and projection space: the infinite-sample limit of the sampling estimator of concurrent work, at ~8x lower cost. On the official 15-scene benchmark this uncertainty ranks true error on 14 of 15 scenes. Restricted to the object interior -- the tissue a clinician reads -- the ranking collapses (median Spearman 0.11, 0/15 pass), identically for a deep ensemble and for a strictly positive log-normal posterior: three constructions, two estimator families, no survivors. The mechanism is structural: about 90% of in-object error is bias that reproduces across retrainings, invisible to model disagreement; 73-81% of the full-volume correlation is carried by object/surround contrast; and an exactly solvable control puts the observed in-object ranking 4-5x below what a perfectly calibrated posterior with the same sigma-spread would score. The error scale, by contrast, is an engineering problem, and we solve it: reparameterizing the posterior contracts the cross-scene temperature spread from 19.3x to 2.6x, one scene-agnostic temperature transfers to unseen scenes (10/15 leave-one-scene-out), and the repaired scale tracks photon count at the Poisson-predicted -1/2 power. We distill evaluation practice that would have caught the illusion -- masked calibration, seed-wise bias decomposition, an exact-posterior reference -- and release all protocols, seeds and per-run evidence.

CT重建不确定性建模高斯点阵医学影像

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