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Reconstructing sphere motion is an essential part of indoor screen-based ball sports. Current sphere recognition techniques require expensive high-precision equipment and complex field deployment, which limits the application of these techniques. This paper proposes a novel method for recognizing and recovering sphere motion based on a low-frame-rate monocular camera. The method captures ball motion streaks in input images, reconstructs trajectories in space, and then estimates ball speed. We evaluated the effectiveness of the streak detection method and obtained an F1-score of 0.97. We also compared the performance of the proposed trajectory reconstruction method with existing methods, and the proposed method outperformed the compared techniques.

A greater variety of technologies are being applied in sports and health with the advancement of technology, but most optoelectronic systems have strict environmental restrictions and are usually costly. To visualize and perform quantitative analysis on the football kick, we introduce a 3D motion analysis system based on a six-axis inertial measurement unit (IMU) to reconstruct the motion trajectory, in the meantime analyzing the velocity and the highest point of the foot during the backswing. We build a signal processing system in MATLAB and standardize the experimental process, allowing users to reconstruct the foot trajectory and obtain information about the motion within a short time. This paper presents a system that directly analyzes the instep kicking motion rather than recognizing different motions or obtaining biomechanical parameters. For the instep kicking motion of path length around 3.63 m, the root mean square error (RMSE) is about 0.07 m. The RMSE of the foot velocity is 0.034 m/s, which is around 0.45% of the maximum velocity. For the maximum velocity of the foot and the highest point of the backswing, the error is approximately 4% and 2.8%, respectively. With less complex hardware, our experimental results achieve excellent velocity accuracy.

Efficient handwriting trajectory reconstruction (TR) requires specific writing surfaces for detecting movements of digital pens. Although several motion-based solutions have been developed to remove the necessity of writing surfaces, most of them are based on classical sensor fusion methods limited, by sensor error accumulation over time, to tracing only single strokes. In this work, we present an approach to map the movements of an IMU-enhanced digital pen to relative displacement data. Training data is collected by means of a tablet. We propose several pre-processing and data-preparation methods to synchronize data between the pen and the tablet, which are of different sampling rates, and train a convolutional neural network (CNN) to reconstruct multiple strokes without the need of writing segmentation or post-processing correction of the predicted trajectory. The proposed system learns the relative displacement of the pen tip over time from the recorded raw sensor data, achieving a normalized error rate of 0.176 relative to unit-scaled tablet ground truth (GT) trajectory. To test the effectiveness of the approach, we train a neural network for character recognition from the reconstructed trajectories, which achieved a character error rate of 19.51%. Finally, a joint model is implemented that makes use of both the IMU data and the generated trajectories, which outperforms the sensor-only-based recognition approach by 0.75%.

The next generation of Intelligent Transportation Systems (ITS) will strongly rely on a high level of detail and coverage in traffic data acquisition. Beyond aggregated traffic parameters like the flux, mean speed, and density used in macroscopic traffic analysis, a continuous location estimation of individual vehicles on a microscopic scale will be required. On the infrastructure side, several sensor techniques exist today that are able to record the data of individual vehicles at a cross-section, such as static radar detectors, laser scanners, or computer vision systems. In order to record the position data of individual vehicles over longer sections, the use of multiple sensors along the road with suitable synchronization and data fusion methods could be adopted. This paper presents appropriate methods considering realistic scale and accuracy conditions of the original data acquisition. Datasets consisting of a timestamp and a speed for each individual vehicle are used as input data. As a first step, a closed formulation for a sensor offset estimation algorithm with simultaneous vehicle registration is presented. Based on this initial step, the datasets are fused to reconstruct microscopic traffic data using quintic Bezi&eacute, r curves. With the derived trajectories, the dependency of the results on the accuracy of the individual sensors is thoroughly investigated. This method enhances the usability of common cross-section-based sensors by enabling the deriving of non-linear vehicle trajectories without the necessity of precise prior synchronization.

The command of a microprocessor-controlled lower limb prosthesis classically relies on the gait mode recognition. Real time computation of the pose of the prosthesis (i.e., attitude and trajectory) is useful for the correct identification of these modes. In this paper, we present and evaluate an algorithm for the computation of the pose of a lower limb prosthesis, under the constraints of real time applications and limited computing resources. This algorithm uses a nonlinear complementary filter with a variable gain to estimate the attitude of the shank. The trajectory is then computed from the double integration of the accelerometer data corrected from the kinematics of a model of inverted pendulum rolling on a curved arc foot. The results of the proposed algorithm are evaluated against the optoelectronic measurements of walking trials of three people with transfemoral amputation. The root mean square error (RMSE) of the estimated attitude is around 3&deg, close to the Kalman-based algorithm results reported in similar conditions. The real time correction of the integration of the inertial measurement unit (IMU) acceleration decreases the trajectory error by a factor of 2.5 compared to its direct integration which will result in an improvement of the gait mode recognition.

Motorcycle drivers are considered among the most vulnerable road users, as attested by the number of crashes increasing every year. The significant part of the fatalities relates to &ldquo, single vehicle&rdquo, loss of control in bends. During this investigation, a system based on an instrumented multi-sensor platform and an algorithmic study was developed to accurately reconstruct motorcycle trajectories achieved when negotiating bends. This system is used by the French Gendarmerie in order to objectively evaluate and to examine the way riders take their bends in order to better train riders to adopt a safe trajectory and to improve road safety. Data required for the reconstruction are acquired using a motorcycle that has been fully instrumented (in VIROLO++ Project) with several redundant sensors (reference sensors and low-cost sensors) which measure the rider actions (roll, steering) and the motorcycle behavior (position, velocity, acceleration, odometry, heading, and attitude). The proposed solution allowed the reconstruction of motorcycle trajectories in bends with a high accuracy (equal to that of fixed point positioning). The developed algorithm will be used by the French Gendarmerie in order to objectively evaluate and examine the way riders negotiate bends. It will also be used for initial training and retraining in order to better train riders to learn and estimate a safe trajectory and to increase the safety, efficiency and comfort of motorcycle riders.

The 16O+27Al elastic and inelastic angular distributions have been measured in a broad angular range (13°

A general technique to study the transmission efficiency of charged particles through a large acceptance magnetic device is presented. This basically involves the measurement of the impact positions and angles of the particles in any plane normal to the optical axis and the use of a powerful algorithm for the reconstruction of the trajectories. This latter is designed to perform the calculations of highly non-linear transport functions and is essential when high-order aberrations are not negligible. The technique is applied to study the transport efficiency of the heavy ions produced in different nuclear reactions and analyzed by the MAGNEX large acceptance spectrometer. Both the angular integral and differential efficiency have been deduced with overall accuracy of about ±1.5% and ±5%, respectively.

Détecteur VAMOS; VAMOS (VAriable MOde Spectrometer) is a large solid angle ray-tracing spectrometer employing numerical methods for reconstructing the particle trajectory. Complete identification of reaction products has been achieved by trajectory reconstruction. Equipped with a versatile detection system, VAMOS is capable of identifying reaction products from diverse reactions using beams at GANIL. The technique for trajectory reconstruction and its application for identifying reaction products are presented. The angular acceptance of the spectrometer has been studied using Monte Carlo simulation by an ion optics code. The spectrometer was coupled to the high efficiency EXOGAM γ-array to obtain γ-recoil coincidences for studying nuclei far from stability. The main features of the spectrometer as well as some results applied to experiments in deep inelastic collisions are described.

The problem of the description of magnetic field for large bending magnets is addressed in relation to the requirements of modern techniques of trajectory reconstruction. The crucial question of the interpolation and extrapolation of fields known at a discrete number of points is analysed. For this purpose a realistic field model of the large dipole of the MAGNEX spectrometer, obtained with finite elements three dimensional simulations, is used. The influence of the uncertainties in the measured field to the quality of the trajectory reconstruction is treated in detail. General constraints for field measurements in terms of required resolutions, step sizes and precisions are thus extracted.

A technique to measure the momentum vector of the ions produced in a nuclear reaction and analyzed by a magnetic spectrometer is presented. It consists of a powerful procedure for the reconstruction of the ions trajectory based on the use of a focal plane detector, accurate three-dimensional models of the magnetic fields and efficient algorithms to solve the highly non-linear transport equations. The technique is quite general and reliable even with large acceptance optical devices. Experimental results obtained with the MAGNEX spectrometer show a remarkable resolution of about 0.2° in the horizontal direction, 0.7° in the vertical one and 1/1800 in the momentum modulus. A high degree of accuracy is also found in the reconstruction of both the direction and the modulus of the momentum vector, with the latter strongly depending on the order of reconstruction.

A technique to interpolate complex three-dimensional field distributions such as those produced by large magnets is presented. It is based on a modified charge density method where the elementary sources of the magnetic field are image charges with Gaussian shape placed on a three-dimensional surface. The strengths of the charges are found as the solution of a best-fit problem, whose special features are discussed in detail. The method is tested against the measured field of the MAGNEX large acceptance quadrupole, showing a high level of accuracy together with an effective compensation of the effect of the experimental errors present in the data. In addition the model field is in general analytical and Maxwellian. As a consequence, the reliability of the presented technique to the challenging problem of trajectory reconstruction in modern large acceptance spectrometers is demonstrated.

International audience; The VAMOS spectrometer operational at GANIL is a large acceptance variable mode spectrometer designed for nuclear reaction studies using radioactive and stable ion beams. The spectrometer coupled with ancillary detectors like EXOGAM has been successfully used in recent experiments on (in)elastic, few nucleon transfer reactions in inverse kinematics and search for nuclei far from stability using deep inelastic transfer reactions In large acceptance spectrometers, the experimental resolution is worsened by aberrations of third and higher orders. Hardware corrections are limited and cannot completely correct the non-linear effects. Thus software reconstruction of trajectories (ray tracing) is essential to obtain the required resolution and identification of the products. A numerical method has been developed for reconstruction of ion trajectories and correction of aberrations in VAMOS. We have devised a procedure to select an optimum subset of closest trajectories for each focal plane event (x, θ, y, ϕ) from the database (generated by an ion-optics calculation). A polynomial fit to the momentum vector of the reaction product in terms of (x, θ, y, ϕ) is made only to this subset. Such an approach is found to give improved resolutions compared to fitting a single polynomial over the entire phase space. Extraction of charge state and angular distributions are rather difficult due to the variation of acceptance over the large phase space. Mass identification of the reaction products and characteristics of the spectrometer acceptance with its variation for different rigidities have been obtained. Applications to 238U+48Ca and 238U+58Ni systems at 5.5 MeV/u will be presented.