One Sphere, Many Charts: Group-Consistent Panoramic Depth from Frozen Foundation Models

Depth foundation models transfer strong monocular priors across visual domains, but their predictions can still depend on the planar chart used to encode the same 360° scene. We study this sensitivity as a cross-parameterization consistency problem and introduce ChartSym-Depth, a training-free test-time method that reconciles predictions across multiple spherical charts. For each re-parameterized equirectangular projection (ERP), ChartSym-Depth predicts depth, maps the result back to the same physical rays, and fuses the aligned estimates in log-depth space using spatially varying reliability weights. Under the default evenly spaced yaw schedule, exact cyclic shifts, covariant prediction–weight pairs, and fusion invariant to branch order and equivariant to common spatial shifts yield a group-consistent inference operator without assuming intrinsic spherical equivariance of the backbone. Experiments on Matterport3D-360 and Stanford2D3D show lower mean depth and seam errors, improved rotational consistency, and greater robustness to the tested perturbations. Uniform log fusion accounts for most of the gain in depth accuracy, with seam weighting providing a further improvement. The gains extend across Depth Anything 3 Base, Depth Pro, and Metric3D v2 on fixed 100-panorama diagnostic subsets. In-group canonical-reference consistency error is below 5×10−5 m, while unseen-yaw and pitch consistency errors decrease by 42.0–44.6% and 37.0–38.1%, respectively, relative to Direct ERP. With Depth Anything 3 Large and reference-dependent per-panorama scale alignment after fusion, ChartSym-Depth reaches an absolute relative error (AbsRel) of 0.0693 on Matterport3D-360 and a root mean square error (RMSE) of 0.2509 m on Stanford2D3D. The default six-chart method requires six backbone evaluations, with no panoramic supervision, parameter updates, or architectural changes.