An algorithm to map asymmetries of bilateral objects in point clouds

Abstract

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.

A Survey of Methods for Symmetry Detection on 3D High Point Density Models in Biomedicine

“…Combès et al recently presented a method able to directly estimate the symmetry plane without the need of intermediate pre-processing methods involving roto-translation and registration [31][32][33][34]. Even if theinitial estimation of the symmetry plane is carried out by employing the PCA method, its final evaluation (i.e., plane Π f ) was assessed by using an iterative procedure aiming at determining the minimum of a properly build objective function (given by the sum of the weighted distances between the points reflected with respect to Π f and the corresponding nearest points of the cloud).…”

“…It has to be noticed that ICP algorithms are computationally expensive. Therefore, a number of attempts to speed them up are in literature [31][32][33][34]. Other methods, such as the mirroring and registration method proposed by Spreeuwers [36], are not based on ICP (see Figure 15).…”

“…For this reason, symmetry plane can be better estimated using mirroring and registration methods which analyse the overlap of the point cloud describing the 3D object with its mirroring. The main drawback of this class of methods is the computation time since many of them use the ICP algorithm [31]. Moreover, they are sensitive to data asymmetries that result from the acquisition process.…”

Automatic symmetry plane estimation of bilateral objects in point clouds

“…However, as the classical ICP algorithm, which is essentially a least squares minimisation, our ICP-like algorithm is not robust to outliers. Classical techniques can be adapted to deal with this issue [4,12] and we have recently proposed a solution based on M-estimators [5]. However, another critical problem is that, as the criterion E T in the classical ICP algorithm, E P (and our modified criterion based on M-estimators) is based on discrete, one-to-one matches between the two sides of the object under study, relying on the closest point principle.…”

“…In the following this algorithm will be called tICP. This tICP algorithm is preferred to the modification based on M-estimators we proposed before [5] (termed mICP here) because of its lower run time.…”