Camera-Space Risk Fields for Selective Geometric Decisions

Downstream systems consume 3D reconstructions through binary spatial queries: along a given ray, does the first surface lie within distance $t$? We reframe sparse reconstruction as selective geometric decision making under true/false/abstain semantics with certified risk. Our method, CSRF (Camera-Space Risk Fields), fuses depth bounds from cross-representation 2D and 3D Gaussian seeds with a learned residual quantile band. To resolve viewpoint-dependent fidelity without forfeiting finite-sample validity, CSRF calibrates a single conformal radius and redistributes protection across camera space via an explicit McShane distance-cone field. The formulation is similarity-equivariant, operates without ground truth at deployment, and provides an exact discrete failure distribution. Under a pre-registered protocol with twelve training RGB images, CSRF is the only method to pass all gates across eight development scenes, answering $41.9\%$ of $9,227,904$ queries at $0.21\%$ conditional error, substantially outperforming conformalized-quantile and localized baselines that fail to satisfy the pre-registered gates. On two frozen held-out scenes, it achieves $80.4\%$ and $37.4\%$ yield at gates. Under camera shifts, preserves $97.8\%$ camera coverage where the global-radius baseline drops to $78.9\%$, with all retained failure modes transparently reported.