ECM versus ICP for point registration

Iterative Closest Point (ICP) is a widely exploited method for point registration that is based on binary point-to-point assignments, whereas the Expectation Conditional Maximization (ECM) algorithm tries to solve the problem of point registration within the framework of maximum likelihood with point-to-cluster matching. In this paper, by fulfilling the implementation of both algorithms as well as conducting experiments in a scenario where dozens of model points must be registered with thousands of observation points on a pelvis model, we investigated and compared the performance (e.g. accuracy and robustness) of both ICP and ECM for point registration in cases without noise and with Gaussian white noise. The experiment results reveal that the ECM method is much less sensitive to initialization and is able to achieve more consistent estimations of the transformation parameters than the ICP algorithm, since the latter easily sinks into local minima and leads to quite different registration results with respect to different initializations. Both algorithms can reach the high registration accuracy at the same level, however, the ICP method usually requires an appropriate initialization to converge globally. In the presence of Gaussian white noise, it is observed in experiments that ECM is less efficient but more robust than ICP.

Automatic extraction of the mid-facial plane for cranio-maxillofacial surgery planning

Recently developed computer applications provide tools for planning cranio-maxillofacial interventions based on 3-dimensional (3D) virtual models of the patient's skull obtained from computed-tomography (CT) scans. Precise knowledge of the location of the mid-facial plane is important for the assessment of deformities and for planning reconstructive procedures. In this work, a new method is presented to automatically compute the mid-facial plane on the basis of a surface model of the facial skeleton obtained from CT. The method matches homologous surface areas selected by the user on the left and right facial side using an iterative closest point optimization. The symmetry plane which best approximates this matching transformation is then computed. This new automatic method was evaluated in an experimental study. The study included experienced and inexperienced clinicians defining the symmetry plane by a selection of landmarks. This manual definition was systematically compared with the definition resulting from the new automatic method: Quality of the symmetry planes was evaluated by their ability to match homologous areas of the face. Results show that the new automatic method is reliable and leads to significantly higher accuracy than the manual method when performed by inexperienced clinicians. In addition, the method performs equally well in difficult trauma situations, where key landmarks are unreliable or absent.

The von Mises-Fisher distribution of the first exit point from the hypersphere of the drifted Brownian motion and the density of the first exit time

A characterization is provided for the von Mises–Fisher random variable, in terms of first exit point from the unit hypersphere of the drifted Wiener process. Laplace transform formulae for the first exit time from the unit hypersphere of the drifted Wiener process are provided. Post representations in terms of Bell polynomials are provided for the densities of the first exit times from the circle and from the sphere.