Bharath Vedantha Desikan

The methodThe reconstruction is 3D Gaussian Splatting, and the renderer carries arbitrary per-Gaussian channels, so depth and depth squared pass through it together. One render then returns the mean depth and the second moment along every ray, and the difference between them is a per-pixel variance: the disagreement among the surfaces the model believes might be there. Accumulated opacity, the signal normally used, stops being informative once the model has placed something at every pixel. Candidate viewpoints come from a 95-point Fibonacci hemisphere, scored on variance and unseen area, then penalised for angular closeness to the viewpoints already chosen that round, so a batch of four spreads around the object.

The setupGazebo Harmonic with a PX4 X500 quadcopter and a 640 × 480 RGB-D gimbal camera, on an RTX 4070 Ti SUPER, with the model capped at 500K Gaussians and trained at 320 × 240. A mission is 4 seed views followed by 11 rounds of 4, for 48 views. Depth variance held about three times the dynamic range of opacity over a mission, while alpha coverage saturated near 0.66 by the third round.

The methodOne hundred thousand Gaussians are initialised on a Poisson mesh obtained from an RGB-D survey. Their positions are frozen and only appearance parameters are learned, which makes the model's information content tractable. Viewpoints are then ranked by D-optimal information gain computed from a diagonal Fisher Hessian accumulated over the current training set. Scoring uses only the candidate pose and the current model, so the image at that pose is not needed in advance.

The failure it exposedAnalysis of the Taylor linearisation underlying the Fisher criterion showed the ranking is reliable only once the model has converged between steps, and that a single seed view leaves an unobserved parameter subspace whose information gain is degenerate. Four azimuthally separated seed views remove that subspace.

The methodThe localisation error was characterised first, from a logged visual-odometry run of 973 keyframes. The drift is an accumulating, temporally correlated process, distinct from independent pose noise, and it grows about two and a half times faster where the camera loses features over open water. A one-parameter random walk calibrated to that run reproduced both the magnitude and the temporal structure. Five synthetic temperature fields were then reconstructed from a budget-limited survey, under exact positions and under injected drift, with two kernels and with both fixed coverage and variance-based adaptive sampling.

What governs itThe additional error concentrated where the field gradient is steep, and it approached a floor that further samples did not breach. At fixed magnitude the temporal correlation of the drift mattered little next to the magnitude itself. The governing quantity is the product of the squared field gradient with the covariance of the positional error.

The platformThe R/V Karin Valentine, a low size, weight and power surface vessel built in the DREAMS Lab, running a Pixhawk flight controller on PX4 with an ODROID companion computer for ROS 2. The payload is a 1-D sonar for depth and a multi-probe water-quality sonde on a motorised winch, which descends in one-metre steps and dwells at each depth.

The methodScalar fields were reconstructed from a lawnmower survey by Gaussian process regression, comparing squared-exponential and Matérn kernels against a non-stationary Matérn whose local length-scale matrix varies with position. Hyperparameters were fit by maximising the log marginal likelihood with a Cholesky factorisation of the covariance, and the maps were written into a DeepGIS and Folium stack so posterior mean and uncertainty could be inspected as planning products.