Sensor-Informed Per-Point Covariance for Structured-Light 3D Imaging

In fringe projection profilometry (FPP), depth is commonly recovered by fitting a phase-to-depth relation independently at each camera pixel. Although such pixel-wise calibration achieves high local accuracy, neighboring pixels can acquire markedly different calibration functions even when they observe the same smooth surface, producing spatially inconsistent geometry and structured surface artifacts. We propose a spatially coupled phase-depth transformation in which all pixels share a single low-dimensional mapping-global phase scalars combined with affine spatial terms on the undistorted reference-camera grid-rather than independent per-pixel fits, optionally augmented by a bounded, spatially smooth correction field. We further introduce a native-grid pairing scheme that constructs phase-depth calibration pairs directly on the reference-camera grid: when depth supervision comes from a rectified active-stereo pipeline, planes are fitted in stereo 3D and sampled back onto the camera grid along native rays, so the phase maps are never rectified. On a dental target with high-resolution scanner ground truth, the proposed model attains point-to-surface RMSE comparable to an active-stereo reference (about 12μm aggregate) while substantially improving spatial coherence over pixel-wise polynomial and rational calibration, and reduces the runtime mapping to a few element-wise operations per pixel with negligible parameter storage.

Image registration is an ill-posed dense vision task, where multiple solutions achieve similar loss values, motivating probabilistic inference. Variational inference has previously been employed to capture these distributions, however restrictive assumptions about the posterior form can lead to poor characterisation, overconfidence and low-quality samples. More flexible posteriors are typically bottlenecked by the complexity of high-dimensional covariance matrices required for dense 3D image registration. In this work, we present a memory and computationally efficient inference method, Structured SIR, that enables expressive, multi-modal, characterisation of uncertainty with high quality samples. We propose the use of a Sampled Importance Resampling (SIR) algorithm with a novel memory-efficient high-dimensional covariance parameterisation as the sum of a low-rank covariance and a sparse, spatially structured Cholesky precision factor. This structure enables capturing complex spatial correlations while remaining computationally tractable. We evaluate the efficacy of this approach in 3D dense image registration of brain MRI data, which is a very high-dimensional problem. We demonstrate that our proposed method produces uncertainty estimates that are significantly better calibrated than those produced by variational methods, achieving equivalent or better accuracy. Crucially, we show that the model yields highly structured multi-modal posterior distributions, enable effective and efficient uncertainty quantification.

Geometric foundation models hold promise for unconstrained dense geometry prediction from uncalibrated images. However, in current feed-forward designs, their predicted confidence scores are heuristic, lack probabilistic interpretation, and often fail to indicate where and how much the predicted geometry can be trusted. To address this gap, we present Trust3R, a lightweight evidential uncertainty framework for feed-forward 3D reconstruction. Trust3R combines gated residual mean refinement with a Normal-Inverse-Wishart evidential head, yielding a closed-form multivariate Student-t distribution for per-point geometric uncertainty. This design provides probabilistically grounded pointmap uncertainty estimates while adding moderate inference overhead. We evaluate on diverse indoor and outdoor benchmarks and compare against MASt3R's built-in confidence map as well as common uncertainty-aware baselines spanning single-pass heteroscedastic regression and sampling-based methods such as MC dropout and deep ensembles. Experimental results show that Trust3R consistently improves risk-coverage and sparsification, and generally improves geometric accuracy. These gains are reflected in stronger uncertainty ranking across benchmarks, with 25% lower AURC and 41% lower AUSE on ScanNet++, providing a practical reliability signal for uncertainty-aware weighting in downstream geometry pipelines. The project page and code are available at https://trust3r-z.github.io/.