Analysis of binning of normals for spherical harmonic cross-correlation

Spherical harmonic cross-correlation is a robust registration technique that uses the normals of two overlapping point clouds to bring them into coarse rotational alignment. This registration technique however has a high computational cost as spherical harmonics need to be calculated for every normal. By binning the normals, the computational efficiency is improved as the spherical harmonics can be pre-computed and cached at each bin location. In this paper we evaluate the efficiency and accuracy of the equiangle grid, icosahedron subdivision and the Fibonacci spiral, an approach we propose. It is found that the equiangle grid has the best efficiency as it can perform direct binning, followed by the Fibonacci spiral and then the icosahedron, all of which decrease the computational cost compared to no binning. The Fibonacci spiral produces the highest achieved accuracy of the three approaches while maintaining a low number of bins. The number of bins allowed by the equiangle grid and icosahedron are much more restrictive than the Fibonacci spiral. The performed analysis shows that the Fibonacci spiral can perform as well as the original cross-correlation algorithm without binning, while also providing a significant improvement in computational efficiency

Unique Compact Representation of Magnetic Fields using Truncated Solid Harmonic Expansions

Precise knowledge of magnetic fields is crucial in many medical imaging applications like magnetic resonance imaging or magnetic particle imaging (MPI) as they are the foundation of these imaging systems. For the investigation of the influence of field imperfections on imaging, a compact and unique representation of the magnetic fields using real solid spherical harmonics, which can be obtained by measuring a few points of the magnetic field only, is of great assistance. In this manuscript, we review real solid harmonic expansions as a general solution of Laplace's equation including an efficient calculation of their coefficients using spherical t-designs. We also provide a method to shift the reference point of an expansion by calculating the coefficients of the shifted expansion from the initial ones. These methods are used to obtain the magnetic fields of an MPI system. Here, the field-free-point of the spatial encoding field serves as unique expansion point. Lastly, we quantify the severity of the distortions of the static and dynamic fields in MPI by analyzing the expansion coefficients.Comment: 25 page

Force and Torque Analytical Models of a Reaction Sphere Actuator Based on Spherical Harmonic Rotation and Decomposition

This paper presents an analytical model for the force and torque developed by a reaction sphere actuator for satellite attitude control. The reaction sphere is an innovative momentum exchange device consisting of a magnetic bearings spherical rotor that can be electronically accelerated in any direction making all the three axes of stabilized spacecrafts controllable by a unique device. The spherical actuator is composed of an 8-pole permanent magnet spherical rotor and of a 20-coil stator. Force and torque analytical models are derived by solving the Laplace equation and applying the Lorentz force law. The novelty consists in exploiting powerful properties of spherical harmonic functions under rotation to derive closed-form linear expressions of forces and torques for all possible orientations of the rotor. Specifically, the orientation of the rotor is parametrized using seven decomposition coefficients that can be determined noniteratively and in a linear fashion by measuring the radial component of the magnetic flux density from at least seven different locations. Therefore, force and torque models for all possible orientations of the rotor are expressed in closed form as linear combination of mutually orthogonal force and torque characteristic matrices, which are computed offline. The proposed analytical models are experimentally validated using a developed laboratory prototype

Registration techniques for computer assisted orthopaedic surgery

The registration of 3D preoperative medical data to patients is a key task in developing computer assisted surgery systems. In computer assisted surgery, the patient in the operation theatre must be aligned with the coordinate system in which the preoperative data has been acquired, so that the planned surgery based on the preoperative data can be carried out under the guidance of the computer assisted surgery system.The aim of this research is to investigate registration algorithms for developing computer assisted bone surgery systems. We start with reference mark registration. New interpretations are given to the development of well knowm algorithms based on singular value decomposition, polar decomposition techniques and the unit quaternion representation of the rotation matrix. In addition, a new algorithm is developed based on the estimate of the rotation axis. For non-land mark registration, we first develop iterative closest line segment and iterative closest triangle patch registrations, similar to the well known iterative closest point registration, when the preoperative data are dense enough. We then move to the situation where the preoperative data are not dense enough. Implicit fitting is considered to interpolate the gaps between the data . A new ellipsoid fitting algorithm and a new constructive implicit fitting strategy are developed. Finally, a region to region matching procedure is proposed based on our novel constructive implicit fitting technique. Experiments demonstrate that the new algorithm is very stable and very efficient

Influence des défauts de forme sur le comportement des liaisons (étude expérimentale et théorique)

L objectif de l étude est d identifier le comportement des liaisons d un mécanisme du point de vue des déplacements en fonction des défauts de forme et des jeux. Le sujet est abordé selon une approche théorique et une approche expérimentale.La partie théorique montre la dualité entre les deux concepts utilisés : le domaine jeu et la surface convexe des différences. Elle montre également la typologie des domaines et l influence des incertitudes de forme sur ces domaines.En parallèle, un dispositif expérimental est développé. Il permet, non seulement, de réaliser la mesure des déplacements dans la liaison avec l exactitude nécessaire, mais aussi, de valider les résultats par une simulation de l assemblage à partir de la mesure 3D des surfaces en contact. L expérimentation porte sur plusieurs couples de surfaces comportant des défauts de forme de différents types. L'influence d'un chargement mécanique est étudiée afin de quantifier les déformations locales de surfaces de contact et l'évolution des écarts de position entre les pièces.The aim of the study is to identify, in terms of displacements, the joint behavior of a mechanism in function of form defects and gaps. Two approaches are proposed : a theoretical approach and an experimental one.The theoretical part presents the duality between the two concepts used in the experimental approach : gap hull and convex difference surface. It outlines also the typology of gap hulls and the influence of the form uncertainties on gap hulls.In parallel, an experimental device is developed. It allows, not only, to carry out the measure of displacements in the joint with the necessary accuracy, but also, to validate the results by an assembly simulation from the 3D measurement of the surfaces in contact. The experimentation involves several pairs of surfaces with different types of form defects. The influence of mechanical loads is studied in order to quantify the local deformation of the surfaces in contact and the evolution of location deviations between these surfaces.BORDEAUX1-Bib.electronique (335229901) / SudocSudocFranceF

Determination of the orientation of 3D objects using spherical harmonics

International audienceThe paper describes a method for estimation of the orientation of 3D objects without point correspondence information. It is based on decomposition of the object onto a basis of spherical harmonics. Tensors are obtained, and their normalization provides the orientation of the object. Theoretical and experimental results show that the approach is more accurate than the classical method based on the diagonalisation of the inertia matrix. Fast registration of 3D objects is a problem of practical interest in domains such as robotics and medical imaging, where it helps to compare multimodal data