Effect of voxel size on the accuracy of 3D reconstructions with cone beam CT.

OBJECTIVES: The various types of cone beam CT (CBCT) differ in several technical characteristics, notably their spatial resolution, which is defined by the acquisition voxel size. However, data are still lacking on the effects of voxel size on the metric accuracy of three-dimensional (3D) reconstructions. This study was designed to assess the effect of isotropic voxel size on the 3D reconstruction accuracy and reproducibility of CBCT data. METHODS: The study sample comprised 70 teeth (from the Institut d\u27Anatomie Normale, Strasbourg, France). The teeth were scanned with a KODAK 9500 3D® CBCT (Carestream Health, Inc., Marne-la-Vallée, France), which has two voxel sizes: 200 µm (CBCT 200 µm group) and 300 µm (CBCT 300 µm group). These teeth had also been scanned with the KODAK 9000 3D® CBCT (Carestream Health, Inc.) (CBCT 76 µm group) and the SCANCO Medical micro-CT XtremeCT (SCANCO Medical, Brüttisellen, Switzerland) (micro-CT 41 µm group) considered as references. After semi-automatic segmentation with AMIRA® software (Visualization Sciences Group, Burlington, MA), tooth volumetric measurements were obtained. RESULTS: The Bland-Altman method showed no difference in tooth volumes despite a slight underestimation for the CBCT 200 µm and 300 µm groups compared with the two reference groups. The underestimation was statistically significant for the volumetric measurements of the CBCT 300 µm group relative to the two reference groups (Passing-Bablok method). CONCLUSIONS: CBCT is not only a tool that helps in diagnosis and detection but it has the complementary advantage of being a measuring instrument, the accuracy of which appears connected to the size of the voxels. Future applications of such measurements with CBCT are discussed

Operator theory and function theory in Drury-Arveson space and its quotients

The Drury-Arveson space $H^2_d$, also known as symmetric Fock space or the $d$-shift space, is a Hilbert function space that has a natural $d$-tuple of operators acting on it, which gives it the structure of a Hilbert module. This survey aims to introduce the Drury-Arveson space, to give a panoramic view of the main operator theoretic and function theoretic aspects of this space, and to describe the universal role that it plays in multivariable operator theory and in Pick interpolation theory.Comment: Final version (to appear in Handbook of Operator Theory); 42 page

de Branges-Rovnyak spaces: basics and theory

For $S$ a contractive analytic operator-valued function on the unit disk ${\mathbb D}$, de Branges and Rovnyak associate a Hilbert space of analytic functions ${\mathcal H}(S)$ and related extension space ${\mathcal D(S)}$ consisting of pairs of analytic functions on the unit disk ${\mathbb D}$. This survey describes three equivalent formulations (the original geometric de Branges-Rovnyak definition, the Toeplitz operator characterization, and the characterization as a reproducing kernel Hilbert space) of the de Branges-Rovnyak space ${\mathcal H}(S)$, as well as its role as the underlying Hilbert space for the modeling of completely non-isometric Hilbert-space contraction operators. Also examined is the extension of these ideas to handle the modeling of the more general class of completely nonunitary contraction operators, where the more general two-component de Branges-Rovnyak model space ${\mathcal D}(S)$ and associated overlapping spaces play key roles. Connections with other function theory problems and applications are also discussed. More recent applications to a variety of subsequent applications are given in a companion survey article

An explicit state-space approach to the one-block super-optimal distance problem

An explicit state-space approach is presented for solving the super-optimal Nehari-extension problem. The approach is based on the all-pass dilation technique developed in (Jaimoukha and Limebeer in SIAM J Control Optim 31(5):1115–1134, 1993) which offers considerable advantages compared to traditional methods relying on a diagonalisation procedure via a Schmidt pair of the Hankel operator associated with the problem. As a result, all derivations presented in this work rely only on simple linear-algebraic arguments. Further, when the simple structure of the one-block problem is taken into account, this approach leads to a detailed and complete state-space analysis which clearly illustrates the structure of the optimal solution and allows for the removal of all technical assumptions (minimality, multiplicity of largest Hankel singular value, positive-definiteness of the solutions of certain Riccati equations) made in previous work (Halikias et al. in SIAM J Control Optim 31(4):960–982, 1993; Limebeer et al. in Int J Control 50(6):2431–2466, 1989). The advantages of the approach are illustrated with a numerical example. Finally, the paper presents a short survey of super-optimization, the various techniques developed for its solution and some of its applications in the area of modern robust control

Analyse céphalométrique tridimentionnelle : diagnostic des dysmorphies antéropostérieures et verticales

À partir d'une saisie scanner, l'analyse céphalométrique tridimensionnelle issue des logiciels C2000 et Cépha3 DT permet : - une lecture parfaite de l'architecture maxillo-faciale globale : le modèle de description squelettique est basé sur l'identification de huit repères liés à l'axe neuro-matriciel de la croissance faciale (têtes des marteaux, supra-orbitaires, infra-orbitaires, mentonniers). Il a été décrit largement et il est aujourd'hui utilisé par tous ceux qui sont concernés par l'étude de la face humaine ; - une identification parfaite des positions dentaires linéaires et angulaires (coordonnées du centre d'inertie, torque et tipping de chaque dent), par rapport aux arcades et un repérage des arcades par rapport à l'architecture maxillo-faciale. Les auteurs ont développé le niveau alvéolodentaire de l'analyse à l'intention des orthodontistes. Les auteurs ont étudié les paramètres antéropostérieurs et verticaux d'un échantillon de 134 patients. Il est ainsi possible : - de rapprocher les paramètres 3D des paramètres conventionnels 2D et de sélectionner les paramètres 3D les plus pertinents, - de critiquer certaines mesures usuelles en céphalométrie conventionnelle, - d'analyser la matrice de corrélation. Elle montre certaines relations intéressantes entre paramètres antéropostérieurs, verticaux et transversaux, squelettiques ou dentoalvéolaires, et en dénie d'autres : ainsi, les positions angulaires des incisives dépendent des dysmorphies antéropostérieures squelettiques ou alvéolaires, mais pas des dysmorphies verticales

Une nouvelle construction cephalometrique tridimensionnelle. Un nouveau parametre d'analyse tridimensionnelle: les axes d'inertie. Un nouveau concept: l'equilibre maxillo-facial. [A new 3-dimensional cephalometry model. A new 3-dimensional parameter analysis: the axis of inertia. A new idea: maxillofacial equilibrium]

The authors propose a biomensurativ 3 D method based on the plotting of 8 anatomical landmarks situated on the trigeminal axis and the selection of teeth. In the analysis of this construction, we have employed mathematical tools unusual in developmental biology, the axis of inertia. The 3 D analysis allows to evidence the architectural, structural and functional balance of the dentomaxillofacial complex. This balance must be substituted to the normality concept to directly linked to cultural criterias and to the selection of mean parameters among culturally and ethnically homogeneous populations. Therapy does not have to lead to the normality of mean parameters but to the return or to the discovery of a real balance