An algorithm to map asymmetries of bilateral objects in point clouds

We present a method to automatically quantify the local asymmetries of bilateral structures in point clouds. The method relies on the robust computation of the approximate symmetry plane of the object under study. This plane is defined as the minimiser of a criterion, based on a M-estimator and devised to reduce the influence of asymmetrical features of the object. An algorithm is then proposed to minimise this criterion. Once the algorithm has converged, the residual distances between the points and their symmetrical counterparts quantify the local asymmetries, yielding a 3D asymmetry map. We show the algorithm to be accurate, with a high capture range, on an ideal, perfectly symmetrical dataset. We investigate its robustness and accuracy properties on highly corrupted datasets. We also evaluate the accuracy of the obtained 3D maps using ground truth datasets where the asymmetries are known. Finally, we propose several original applications of this method on real data.