R3-RECON: Radiance-Field-Free Active Reconstruction via Renderability

In active reconstruction, an embodied agent must decide where to look next to efficiently acquire views that support high-quality novel-view rendering. Recent work on active view planning for neural rendering largely derives next-best-view (NBV) criteria by backpropagating through radiance fields or estimating information entropy over 3D Gaussian primitives. While effective, these strategies tightly couple view selection to heavy, representation-specific mechanisms and fail to account for the computational and resource constraints required for lightweight online deployment. In this paper, we revisit active reconstruction from a renderability-centric perspective. We propose $\mathbb{R}^{3}$-RECON, a radiance-fields-free active reconstruction framework that induces an implicit, pose-conditioned renderability field over SE(3) from a lightweight voxel map. Our formulation aggregates per-voxel online observation statistics into a unified scalar renderability score that is cheap to update and can be queried in closed form at arbitrary candidate viewpoints in milliseconds, without requiring gradients or radiance-field training. This renderability field is strongly correlated with image-space reconstruction error, naturally guiding NBV selection. We further introduce a panoramic extension that estimates omnidirectional (360$^\circ$) view utility to accelerate candidate evaluation. In the standard indoor Replica dataset, $\mathbb{R}^{3}$-RECON achieves more uniform novel-view quality and higher 3D Gaussian splatting (3DGS) reconstruction accuracy than recent active GS baselines with matched view and time budgets.