GRAM: Graph-Guided Robust Registration with multi-scale compatibility for point clouds

Point cloud registration remains difficult in spatial metrology and large-scale 3D sensing because cross-source data fusion suffers from extreme outlier ratios ( > 99 % ), heavy sensor noise, and unknown scale drift. Algorithms using a single, fixed distance threshold generally fail to separate true inliers from structured noise. To solve this, we propose GRAM: a Graph-Guided Robust Registration framework with Multi-Scale Compatibility. In its front-end, GRAM builds a multi-scale Second-Order Spatial Compatibility ( SC 2 ) pyramid to isolate true inliers from pseudo-structured outliers, using graph-derived confidence scores to form higher-order spatial hypotheses. To manage cross-source scale drift, the back-end uses a lightweight scale-consistency discriminator that automatically switches between two states: a hard truncation mode for rigid SE ( 3 ) precision, and a progressive annealing mode for Sim ( 3 ) scale compensation. We tested GRAM across standard datasets, including long-term mobile mapping (KITTI) and large-scale topographic measurement (WHU-TLS). The results show it provides a reliable, fast, and practical registration solution for field environments with extreme outliers.