Estimating curvatures and the Darboux frame from unorganised noisy point cloud

Curvatures and the Darboux frame are useful tools for surface classification and 3D object recognition. However, it is still challenging for estimating these features on unorganised noisy points. A method is proposed to calculate these features from a general quadric surface fitted at each point. The TLS3L (total least squares on the three level sets) algorithm is introduced to permit fast, repeatable, and reliable fitting to the noisy input. The efficiency of the estimation is analysed theoretically and examined on several synthetic as well as real data sets. Comparative tests indicate that the proposed method excels the competitive ones.