Stochastic modication of Newtonian dynamics and Induced potential -application to spiral galaxies and the dark potential

Using the formalism of stochastic embedding developed by [J. Cresson, D. Darses, J. Math. Phys. 48, 072703 (2007)], we study how the dynamics of the classical Newton equation for a force deriving from a potential is deformed under the assumption that this equation can admit stochastic processes as solutions. We focus on two denitions of a stochastic Newton's equation called dierential and variational. We rst prove a stochastic virial theorem which is a natural generalization of the classical case. The stochasticity modies the virial relation by adding a potential term called the induced potential which corresponds in quantum mechanics to the Bohm potential. Moreover, the dierential stochastic Newton equation naturally provides an action functional which sat-ises a stochastic Hamilton-Jacobi equation. The real part of this equation corresponds to the classical Hamilton-Jacobi equation with an extra potential term corresponding to the induced potential already observed in the stochastic virial theorem. The induced potential has an explicit form depending on the density of the stochastic processes solutions of the stochastic Newton equation. It is proved that this density satises a nonlinear Schr{\"o}dinger equation. Applying this formalism for the Kepler potential, one proves that the induced potential coincides with the ad-hoc ''dark potential'' used to recover a at rotation curve of spiral galaxies. We then discuss the application of the previous formalism in the context of spiral galaxies following the proposal and computations given by [D. Da Rocha and L. Nottale, Chaos, Solitons and Fractals, 16(4):565-595, 2003] where the emergence of the ''dark potential'' is seen as a consequence of the fractality of space in the context of the Scale relativity theory

Investigation of 3D glenohumeral displacements from 3D reconstruction using biplane X-ray images: Accuracy and reproducibility of the technique and preliminary analysis in rotator cuff tear patients

Rotator cuff (RC) tears may be associated with increased glenohumeral instability; however, this instability is difficult to quantify using currently available diagnostic tools. Recently, the three-dimensional (3D) reconstruction and registration method of the scapula and humeral head, based on sequences of low-dose biplane X-ray images, has been proposed for glenohumeral displacement assessment. This research aimed to evaluate the accuracy and reproducibility of this technique and to investigate its potential with a preliminary application comparing RC tear patients and asymptomatic volunteers. Accuracy was assessed using CT scan model registration on biplane X-ray images for five cadaveric shoulder specimens and showed differences ranging from 0.6 to 1.4 mm depending on the direction of interest. Intra- and interobserver reproducibility was assessed through two operators who repeated the reconstruction of five subjects three times, allowing defining 95% confidence interval ranging from ±1.8 to ±3.6 mm. Intraclass correlation coefficient varied between 0.84 and 0.98. Comparison between RC tear patients and asymptomatic volunteers showed differences of glenohumeral displacements, especially in the superoinferior direction when shoulder was abducted at 20 and 45 . This study thus assessed the accuracy of the low-dose 3D biplane X-ray reconstruction technique for glenohumeral displacement assessment and showed potential in biomechanical and clinical research.Fondation Paris-Tech Programme BIOMECAM Chaire ParisTech Institut de Recherche Robert-Sauvé en Santé et Sécurité du Travail du Québec Natural Science and Engineering Research Council of Canada Fonds de Recherche sur la Nature et les Technologies du Québec Fonds de Recherche en Santé du Québec, EOS Imaging, and French pôle de compétitivité MEDICEN (STEREOS + program)

Recalage rigide simultané multi-objets (contribution à l'analyse morpho-fonctionnelle robuste des systèmes ostéo-articulaires)

Ce travail contribue à la compréhension de la dynamique interne des systèmes ostéo-articulaires complexes. La méthodologie proposée s'intéresse en priorité aux mouvements des segments osseux avec pour exigence supplémentaire de produire une description précise de leur morphologie. La nature numérique de l'information spatiale (séquence de volumes IRM ou scanner X) et l'imprécision de toute méthode de segmentation font que les instances temporelles du mouvement sont empreintes d'erreurs incontournables rendant ces dernières imparfaitement superposables. L'idée développée repose sur l'exploitation de la redondance d'information intrinsèque à tout protocole de mesure visant l'étude des mouvements. La démarche proposée opère par mise en correspondance robuste et simultanée des instances géométriques par consensus médian. A la fin du processus, il est possible de créer une surface représentant l'unique corps réel à partir des meilleures zones segmentées des différentes instances.RENNES1-BU Sciences Philo (352382102) / SudocSudocFranceF

Performing accurate joint kinematics from 3-d in vivo image sequences through consensus-driven simultaneous registration.

International audienceThis paper addresses the problem of the robust registration of multiple observations of the same object. Such a problem typically arises whenever it becomes necessary to recover the trajectory of an evolving object observed through standard 3-D medical imaging techniques. The instances of the tracked object are assumed to be variously truncated, locally subject to morphological evolutions throughout the sequence, and imprinted with significant segmentation errors as well as significant noise perturbations. The algorithm operates through the robust and simultaneous registration of all surface instances of a given object through median consensus. This operation consists of two interwoven processes set up to work in close collaboration. The first one progressively generates a median and implicit shape computed with respect to current estimations of the registration transformations, while the other refines these transformations with respect to the current estimation of their median shape. When compared with standard robust techniques, tests reveal significant improvements, both in robustness and precision. The algorithm is based on widely-used techniques, and proves highly effective while offering great flexibility of utilization

Fast 3D object mass properties computation method in 3D images

International audience

Performing accurate rigid kinematics measurements from 3D in vivo image sequences through median consensus simultaneous registration

International audienceWhile focusing at accurate 3D joint kinematics, this paper explores the problem of how to perform a robust rigid registration for a sequence of object surfaces observed using standard 3D medical imaging techniques. Each object instance is assumed to give access to a polyhedral encoding of its boundary. We consider the case where object instances are noised with significant truncations and segmentation errors. The proposed method aims to tackle this problem in a global way, fully exploiting the duality between redundancy and complementarity of the available instances set. The algorithm operates through robust and simultaneous registration of all geometrical instances on a virtual instance accounting for their median consensus. When compared with standard robust techniques, trials reveal significant gains, as much in robustness as in accuracy. The considered applications are mainly focused on generating highly accurate kinematics in relation to the bone structures of the most complex joints - the tarsus and the carpus - for which no alternative examination techniques exist, enabling fine morphological analysis as well as access to internal joint motions

Estimation du trièdre d'inertie d'une forme polyèdrique : comparaison de deux méthodes et application au recalage rigide

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Analyse cinématique optimale d'un corps solide à l'aide d'un recalage multiple par consensus médian

International audience

Extraction automatique de structures 3D complexes - Application à la segmentation de l’oreille interne à partir de volumes numériques

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Intérêt des "Graphes de Courbure de Forme Subdivisé" pour décrire la déformation des structures complexes

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