Underwater multidimensional metrology in degraded environments with augmented reality devices

We propose an underwater multidimensional metrology approach in degraded environments utilizing augmented reality devices. The approach uses a risk-aware next-best-view (NBV) framework for metrology in degraded visual environments, introducing a conditional value-at-risk (CVaR) objective to guide viewpoint selection. Using anisotropy-aware geodesic metrics, local sensitivities, and a CVaR optimization, the approach prioritizes views that reduce worst-case geodesic-length uncertainty. We validated the performance of the proposed system experimentally on turbid scenes with augmented reality device imagery and five-dimensional WaterSplat reconstructions. The results across increasing turbidity demonstrate that CVaR achieves 2 - 3 × greater median error reduction compared to entropy-based NBV selection. We further conduct controlled synthetic experiments to analyze asymptotic error plateaus. To the best of our knowledge, this is the first report on an augmented reality-based NBV approach aimed at improving metrology in turbid environments.