Combinatorics of the Gauss digitization under translation in 2D

International audienceThe action of a translation on a continuous object before its digitization generates several digital objects. This paper focuses on the combinatorics of the generated digital objects up to integer translations. In the general case, a worst-case upper bound is exhibited and proved to be reached on an example. Another upper bound is also proposed by making a link between the number of the digital objects and the boundary curve, through its self-intersections on the torus. An upper bound, quadratic in digital perimeter, is then derived in the convex case and eventually an asymptotic upper bound, quadratic in the grid resolution, is exhibited in the polygonal case. A few signicant examples finish the paper

Mass-spring modelling of vault springboard contact

Vaulting is a discipline in Men's and Women's Artistic Gymnastics. While the springboard contact is not judged, the success of the rest of the vault is underpinned by it. The purpose of this study was to develop an understanding of the mechanics of the springboard contact phase of gymnastic vaulting. An analysis of hopping in place, forward hopping and running jumps on a force platform showed that the force-mass centre displacement relationship during ground contact approximated that of a mass rebounding on a linear spring. Subsequently, two mass-spring models were developed using a symbolic mathematics package. Both models represented the gymnast as a rigid cylinder, with personalized linear and angular inertia characteristics, connected at its mass centre to a linear spring. A one spring model combined the springiness of the gymnast and the springboard in a single linear spring, while a two spring model treated them as separate linear springs. Handspring vaults performed by an elite male gymnast at a range of approach speeds and springboard settings were analysed to provide model inputs. Springboard properties were empirically determined and revealed that the springboard stiffness varied appreciably depending upon feet contact position. Given the touchdown kinematics and takeoff angle of the gymnast, the models estimated spring stiffness and linear and angular takeoff velocities, the spring stiffness and takeoff vertical velocity estimates showing some sensitivity to spring angle at touchdown. Simulations in which the touchdown kinematics and spring stiffnesses were systematically adjusted, identified their influence on takeoff kinematics and provided an insight into the mechanics of springboard. contact. Estimated (leg) spring stiffnesses were consistent with those reported in the literature for other activities and'simulation results showed that simple rebounds accounted for the majority of the takeoff velocities. Spring angle at touchdown was found to be most effective at modifying each of the takeoff variables, however to produce a selective effect on takeoff required a combination of adjustments to the touchdown. In proposing strategies for gymnasts, their ability to control each of the touchdown variables has to be considered

Volumetric relief map for the cortical subarachnoid space analysis

Purpose: Medical image visualization is an important step in the medical diagnosis of hydrocephalus. In this paper, we present planar representations called volumetric relief maps that are generated from three-dimensional images of the cerebrospinal fluid within the cortical subarachnoid space. Such maps are visually interpreted at once and allow to automatically characterize fluid distributions. Consequently, they help specialists to provide a diagnosis and to monitor patients instantly. Methods: Volumetric relief maps are generated by enclosing the cortical subarachnoid space with a hemisphere, and using a ray tracing method and a map projection technique from a hemisphere to a plane. Results: Visualization of maps indicates that healthy adults have more balanced fluid distributions with well-filled sulci, unlike hydrocephalus patients who have more or less large fluid depletions in the posterior regions of the brain. We showed that a moment-based approach allows to efficiently characterize such fluid distributions from maps. In particular, the center of mass of a distribution is an efficient discriminant factor to distinguish between healthy adults and hydrocephalus patients, with resulting sensitivity and specificity of 100%. In addition, we have noted that asymmetry of the fluid distribution increases with depletion for hydrocephalus patients; such asymmetry is generally oriented towards the frontal part of the fissura longitudinalis cerebri. Conclusions: This paper describes an innovative visualization tool used to analyze fluid distribution within the cortical subarachnoid space. It allows to efficiently discriminate between healthy adults and pathological cases, and to monitor patients before and after surgery

Estimating individual muscle forces in human movement

If individual muscle forces could be routinely calculated in vivo, non-invasively, considerable insight could be obtained into the etiology of injuries and the training of muscle for rehabilitation and sport. As there are generally more muscles crossing a joint than there are degrees of freedom at the joint, determining the individual forces in the muscles crossing a joint is a non-trivial problem. This study focused on the development of the procedures necessary to estimate the individual muscle forces during a dumbell curl, and the measurement procedures required for the determination of the necessary input parameters. The procedures developed could easily be applied to other body movements. [Continues.

Notes on shape orientation where the standard method does not work

Copyright © 2006 Elsevier. NOTICE: this is the author’s version of a work that was accepted for publication in Pattern Recognition . Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Pattern Recognition, Vol. 39 Issue 5 (2006), DOI: 10.1016/j.patcog.2005.11.010Notes: This paper introduces a new method for shape orientation. This method, which uses Nth-order centralised moments (N>2), can be applied to cases, such as many-fold symmetric shapes, for which the standard method does not work. The paper proves several desirable properties of shape orientation defined in this way, and also corrects the previous approach where the central moments were treated equally independently of N. It shows that the situation is essentially different depending on whether N is an even or odd number. This corrects the previous work of Tsai and Chou (Pattern Recognition, vol. 24, pp.95-104, 1991), which up to then represented the state of the art in the field.In this paper we consider some questions related to the orientation of shapes with particular attention to the situation where the standard method does not work. There are irregular and non-symmetric shapes whose orientation cannot be computed in a standard way, but in the literature the most studied situations are those where the shape under consideration has more than two axes of symmetry or where it is an n-fold rotationally symmetric shape with n>2.n>2. The basic reference for our work is [W.H. Tsai, S.L. Chou, Detection of generalized principal in rotationally symmetric shapes, Pattern Recognition 24 (1991) 95–104]. We give a very simple proof of the main result from [W.H. Tsai, S.L. Chou, Detection of generalized principal in rotationally symmetric shapes, Pattern Recognition 24 (1991) 95–104] and suggest a modification of the proposal on how the principal axes of rotationally symmetric shapes should be computed. We show some desirable property in defining the orientation of such shapes if the modified approach is applied. Also, we give some comments on the problems that arise when computing shape elongation

Development of an In-Vitro Passive and Active Motion Simulator for the Investigation of Shoulder Function and Kinematics

Injuries and degenerative diseases of the shoulder are common and may relate to the joint’s complex biomechanics, which rely primarily on soft tissues to achieve stability. Despite the prevalence of these disorders, there is little information about their effects on the biomechanics of the shoulder, and a lack of evidence with which to guide clinical practice. Insight into these disorders and their treatments can be gained through in-vitro biomechanical experiments where the achieved physiologic accuracy and repeatability directly influence their efficacy and impact. This work’s rationale was that developing a simulator with greater physiologic accuracy and testing capabilities would improve the quantification of biomechanical parameters. This dissertation describes the development and validation of a simulator capable of performing passive assessments, which use experimenter manipulation, and active assessments – produced through muscle loading. Respectively, these allow the assessment of functional parameters such as stability, and kinematic/kinetic parameters including joint loading. The passive functionality enables specimen motion to be precisely controlled through independent manipulation of each rotational degree of freedom (DOF). Compared to unassisted manipulation, the system improved accuracy and repeatability of positioning the specimen (by 205% & 163%, respectively), decreased variation in DOF that are to remain constant (by 6.8°), and improved achievement of predefined endpoints (by 21%). Additionally, implementing a scapular rotation mechanism improved the physiologic accuracy of simulation. This enabled the clarification of the effect of secondary musculature on shoulder function, and the comparison of two competing clinical reconstructive procedures for shoulder instability. This was the first shoulder system to use real time kinematic feedback and PID control to produce active motion, which achieved unmatched accuracy ( These developments can be a powerful tool for increasing our understanding of the shoulder and also to provide information which can assist surgeons and improve patient outcomes

Nonintrusive fast response oxygen monitoring system for high temperature flows

A new technique has been developed for nonintrusive in situ measurement of oxygen concentration, gas temperature, and flow velocity of the test media in hypersonic wind tunnels. It is based on absorption of near-infrared radiation from inexpensive GaAlAs laser diodes used in optoelectronics industry. It is designed for simultaneous measurements along multiple lines of sight accessed by fiber optics. Molecular oxygen concentration is measured from the magnitude of absorption signals; rotational gas temperature is measured from the intensity ratio of two oxygen absorption lines; and the flow velocity is measured from the Doppler shift of the absorption line positions. This report describes the results of an extensive series of tests of the prototype instrument in laboratory flames emphasizing assessment of the instruments capabilities for quantitative measurement of O2 concentration (mole fraction) and gas temperature