A segmentation and model-reconstruction algorithm is proposed based on polynomial approximation and on a new version of the “region growing” methodology. First, an initial partition is calculated on the basis of differential-geometric properties of the range image. Then, the first merging procedure is applied (“merge with constraints”) aiming at correctly identifying principal surfaces of the model. It examines all possible mergers of regions and selects those satisfying strict compatibility constraints. The second merging procedure relaxes these constraints to produce the “extended” regions and surfaces of the final segmentation. Theoretical work is presented proving the consistency of these merging procedures. Finally, application of the algorithm on industrial data is presented demonstrating the efficiency of the proposed methodology.