Edges Compete for Trust: Group Relative Edge Optimization for Building Reconstruction from Point Clouds

Building reconstruction aims to extract compact wireframes from point clouds. Recent edge-based methods achieve impressive results but suffer from sparse supervision from one-to-one matching, which leaves most edge proposals under-optimized. In this paper, we present Group Relative Edge Optimization (GREO), the first attempt to incentivize dense supervision across edges proposals through reinforcement learning-style optimization in wireframe reconstruction. Specifically, GREO computes edge-level rewards based on geometric alignment quality and transforms them into target confidence distributions via group-wise normalization. In addition, we incorporate entropy regularization to maintain distributional stability and prevent confidence collapse. This joint optimization enables dense and discriminative supervision across all edge proposals through cross-entropy minimization. Experiments on the large-scale Building3D dataset demonstrate that our powerful and versatile GREO integrates seamlessly into existing edge-based methods as a plug-and-play training strategy, achieving state-of-the-art performance on both the Entry-level and Tallinn benchmarks while adding no inference overhead.