Prototype-Guided Differentiable Range Optimization for Rotation-Robust Geometric Reconstruction

Geometric reconstruction seeks to recover complete foundational topologies from partial 3D observations, a task significantly complicated by unknown object orientations. Conventional approaches often rely on canonically aligned training data and process Cartesian coordinates in a pose-dependent manner. Furthermore, severe occlusion restricts the structural evidence required to infer unobserved regions, while errors in rotation-invariant representations frequently do not translate proportionally into Cartesian space. To address these limitations, we propose PA-RangeLM (Prototype-Assisted Range Levenberg–Marquardt), a two-stage framework tailored for rotation-robust geometric reconstruction. To explicitly compensate for missing structures, our Prototype Auxiliary Branch introduces sparse, complete-shape priors during training without modifying the inference architecture. To address coordinate mapping discrepancies, RangeLM integrates Bounded Range Correction and Uncertainty-drived Weighting into a differentiable coordinate recovery process. By encoding partial inputs as distances to local anchors and optimizing coordinate recovery end to end, the framework operates in the observed frame without canonicalization or explicit pose estimation. Empirical evaluations under random-rotation protocols demonstrate that PA-RangeLM consistently outperforms established rotation-robust baselines in standard coordinate metrics. Code and supplementary details are provided for review. The anonymous project page is available at https://pa-rangelm.github.io/.