Properties of Gauss digitized sets and digital surface integration

International audienceThis paper presents new topological and geometrical properties of Gauss digitizations of Euclidean shapes, most of them holding in arbitrary dimension $d$. We focus on $r$-regular shapes sampled by Gauss digitization at gridstep $h$. The digitized boundary is shown to be close to the Euclidean boundary in the Hausdorff sense, the minimum distance $\frac{\sqrt{d}}{2}h$ being achieved by the projection map $\xi$ induced by the Euclidean distance. Although it is known that Gauss digitized boundaries may not be manifold when $d \ge 3$, we show that non-manifoldness may only occur in places where the normal vector is almost aligned with some digitization axis, and the limit angle decreases with $h$. We then have a closer look at the projection of the digitized boundary onto the continuous boundary by $\xi$. We show that the size of its non-injective part tends to zero with $h$. This leads us to study the classical digital surface integration scheme, which allocates a measure to each surface element that is proportional to the cosine of the angle between an estimated normal vector and the trivial surface element normal vector. We show that digital integration is convergent whenever the normal estimator is multigrid convergent, and we explicit the convergence speed. Since convergent estimators are now available in the litterature, digital integration provides a convergent measure for digitized objects

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

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.

A Novel Method for In Vivo Evaluation of Finger Kinematics for Analysis of Activities of Daily Living

This thesis examines the development of a six degrees of freedom finger coordinate system that employs electromagnetic tracking to measure finger kinematics. Secondarily, this thesis validated the in vivo finger coordinate system, and is then used to examine range of motion in the fingers in patients with hand osteoarthritis. Lastly, this thesis examines the range of motion of individuals with and without hand arthritis during various activities of daily living, performed with and with joint protection program principles. This study presents a foundation for finger kinematic evaluation and describes a methodology that will be used for larger studies to be conducted to examine finger kinematics in various clinical and functional applications

Investigating the effect of manual physical activity on the form of human hand entheses

Reconstructing physical activity based on human skeletal remains comprises a fundamental objective of anthropological sciences. Entheses, the areas of muscle attachment on the bone surfaces, have been widely utilized as occupational stress markers. However, most previous methods for analyzing entheseal morphology (size and/or shape) are characterized by substantially low precision, lack of three-dimensional (3D) multivariate statistical analysis, and absence of individuals documented for their long-term physical activities. Furthermore, no previous study used histological methods for assessing the effect of physical activity on the interindividual variability of entheseal surfaces. My past research put forth a precise methodology for measuring the 3D size of hand entheseal areas, identifying two main multivariate patterns among entheses. On this basis, this PhD thesis performed a multi-disciplinary approach to the analysis of hand entheseal form (a term encompassing both size and shape) and its potential relationship with habitual physical activities. In Paper I, the hand entheses of a thoroughly documented sample were analyzed using a highly precise 3D method of quantification, followed by multivariate statistical analysis. The utilized material is part of an anthropological collection which is gradually becoming a unique universal reference for the most detailed documentation of the specimens’ lifelong physical activities. The results revealed a close statistical association between multivariate patterns of hand entheses and the nature of individuals’ long-term occupational profiles. In the framework of an ongoing multidisciplinary research project, the developed method of entheseal analysis was applied for reconstructing the occupational profile of an unidentified individual from Basel (Paper II). The results indicated that this specimen was involved in precise manual activities relying on thumb-index finger interactions. This outcome came in agreement with other research on the physical activities of this individual. Paper III introduced a new and precise geometric morphometric approach for investigating hand entheseal 3D shape, identifying a statistically significant interaction between 3D size and shape variation in three hand entheses. In this way, it set a novel basis for future research on both aspects of entheseal form (3D size and shape), bridging the gap between quantitative and qualitative methods of entheseal analysis. Furthermore, the results showed that larger phalangeal entheses present a proportionally more projecting surface, which is linked to greater moment arm and biomechanical efficiency for the attaching muscle. Finally, paper IV presented a microscopic histological analysis of hand entheses, which reported an interaction between entheseal morphology and the levels of applied biomechanical forces. Particularly, the elevated bone areas of hand entheses were associated with greater concentrations of calcified fibrocartilage, which is widely considered as a direct indicator of biomechanical stress. As a consequence, individual entheses with elevated marginal areas comprised evidence of greater biomechanical stress. Overall, this PhD thesis identified a clear interaction between physical activity and human hand entheses based on three methodological approaches and four separate analyses. The multivariate 3D analysis showed that the patterns among different hand entheses reflect the nature of an individual’s lifelong occupational activities. At the same time, the shape of larger entheseal areas is proportionally projecting, providing greater biomechanical efficiency for the attaching muscle. Finally, higher entheseal bone elevation seems to be related with greater biomechanical stress (i.e., higher concentrations of calcified fibrocartilage)