The core of most registration algorithms aligns scan data by pairs, minimizing their relative distance. This local optimization must generally pass through a validation procedure to ensure the global coherence of the resulting alignments. This work introduces an iterative framework to guarantee the global coherence of the registration process. The iteration alternates registration and reconstruction steps, including alignments with the proper reconstructed surface, until the alignment of all the scans converges. The framework adapts to different contexts by choosing which scans are aligned and which are used for the reconstruction. This choice is based on the alignment and reconstruction errors. Derivations of this framework are presented with a rough automatic registration, increasing its robustness.