Non-visual Motion Tracking

Non-visual Motion Tracking Additionally, (Taylor et al. 2010) demonstrated that the OSSCA method, which employs a combined use of OCST, SCoRE, and SARA techniques to process marker data and allows the estimation of joint parameters from kinematic data alone, without the necessity to use generic anatomical relationship assumptions, returns more reliable, repeatable and reproducible results than a standard generic regression approach. Although the accuracy of the data acquired by means of optical motion capture systems is very high in the controlled environment of the lab, the ambulatory use of this type of equipment is cumbersome and presents significant limitations which can not only compromise the precision of the acquired data, e.g. dependency on line-of-sight, limited range and latency of data (Schepers et al. 2010), but also the practicability of the acquisition itself, e.g. necessity of power source, set-up time, outdoor calibration of the system. Non-visual motion tracking Non-visual motion tracking is a sensor based technique, which can be carried out, amongst others, with acoustic, magnetic, or inertial sensors, or with a combination of these methods. Ultrasound based acoustic systems, e.g. the Bat system (Ward et al. 1997), Vallidis (Hazas and Ward 2002), the Cricket location system (Priyantha et al. 2000) and WearTrack (Foxlin and Harrington 2000), are capable of tracking the locations of pulse emitting beckons by using the time-of-flight information of audio signals. This type of motion tracking system is wireless, however, as with visual motion tracking, occlusion of the signal emitter poses a significant limitation. In contrast, magnetic systems, e.g. MotionStar ® (Ascension Technology), are capable of estimating their position and orientation within the global coordinate system, by using information from the local magnetic environment, and are, therefore, not constricted by line-of-sight. However, these systems are very sensitive to ferromagnetic interferences. Inertial motion capture systems, e.g. Moven (Xsens Technologies) and Alert (Verhaert), employ the use of accelerometer and gyroscopes to measure inclination angles. These systems are highly accurate, however, sensitive to vibration and subject to integration drift over time. In fact, throughout the past decade, the use of inertial sensors has gained increased popularity within researchers (Foxlin 1996; Roetenberg et al. 2007a; Roetenberg et al. 2005; Roetenberg et al. 2009; Roetenberg et al. 2003; Roetenberg et al. 2007b; Roetenberg and Veltink 2005), as well as general population. Many people schedule their daily activity based on the data presented by certain applications on their smartphones (e.g. Health app, Argus, MyFitnessPal), their smartwatches (e.g. Sony, LG, AppleWatch, Fitbit Surge) or pedometers and wristbands (e.g. Fitbit Flex, Garmin vivofit, Polar Loop, Jawbone). However, in the field of research, there is a need for more complex systems, which can provide more comprehensive information, of a larger variety. For this purpose, hybrid systems, combine the use of different techniques to compensate for the shortcomings of individual systems. Such hybrid systems are represented by acoustic-inertial systems (Vlasic et al. 2007; Ward et al. 2005), e.g. Constellationà ¢Ã¢â‚¬Å¾Ã‚ ¢ (Foxlin et al. 1998), optical-inertial systems, e.g. Hy-Birdà ¢Ã¢â‚¬Å¾Ã‚ ¢ (Ascension Technology) and inertial-magnetic systems, e.g. MERG sensors (Bachmann 2000), MTw development kit (Xsens Technologies), MVN Biomech and MVN Awinda (Xsens Technologies). Combined inertial and magnetic sensing is currently one of the more popular choices in this area of study and will be discussed at length in the following paragraphs. The light weight, wireless and cheap, inertial sensors equipped with accelerometers, gyroscopes and magnetometers enable, when positioned on the human body, the computation of angular orientation of the anatomical segments to which they are attached to (Bellusci et al. 2013; Roetenberg et al. 2003). The on-board gyroscopes measure angular velocity, based on the principle of angular momentum, according to the following fundamental equation: (1) Where: à Ã¢â‚¬Å¾ torque on the gyroscope; L angular momentum; I moment of inertia; à Ã¢â‚¬ ° angular velocity; ÃŽÂ ± angular acceleration. The most commonly used gyroscopes for human motion studies are piezo-electric, capable of detecting vibration of mass. When an object vibrates while rotating, it is subject to the Coriolis Effect. This causes a second vibration to occur orthogonally to the initial vibration direction. The rate of turn can be calculated from this latter vibration. According to the following equations: (2) Where: m mass; à ¡Ã‚ ´Ã‚   momentary speed of the mass with reference to the moving object to which it is attached. The resulting gyroscope signals are then defined as being the sum of angular velocity à Ã¢â‚¬ °t, offset due to temperature of gyroscope bt, and white noise à ¡Ã‚ ´Ã‚  G,t (Eq. 3). (3) The gyroscope output is very accurate, however, it is subject to errors and drift caused by integration of the signal over time, and the gyroscope temperature which can produce small offset errors, leading to large integration errors when calculating orientation. The use of compensatory estimation algorithms, such as Kalman filters can reduce the inherent errors in the gyroscope output signal (Roetenberg et al. 2003). Kalman filters are mathematical algorithms used to efficiently minimize the mean of the squared error of a system output (Welch and Bishop 1995). Kalman filters are particularly useful for combining parameters of different measurement systems so that the advantages of one compensates for the weakness of the other, e.g. accelerometers are often used in conjunction with gyroscopes, in order to compensate for inclination drifts in the gyroscope signal. The accelerometers measure the gravitational acceleration g and the vector sum of acceleration a. The output accelerometer signals are defined as the sum of acceleration at, gravity gt and white noise à ¡Ã‚ ´Ã‚  A,t. (4) The inclination information provided by gt can be used to correct the orientation drifts of the gyroscope (Roetenberg et al. 2003). A further common example of Kalman filtering, is using magnetometer readings to correct for the gyroscopes vertical axis drifts (Roetenberg et al. 2003). Magnetometers have the ability to detect local magnetic north and adjust heading direction. The principles by which the magnetometers work are described by following equation: (5) Where: ym,t magnetic signals; mt earth magnetic field vector; dt disturbance vector; vm,t -white noise. In real life measuring conditions the distribution of the magnetic field is often more complex and other parameters, such as changes in magnetic flux and the magnetic inclination angle, which can affect the magnitude of the magnetic disturbance, should be taken in consideration. The major limitations of using inertial and magnetic sensing for motion tracking are represented by the following factors: Ferromagnetic interferences can distort the local magnetic field and affect the measurements for the orientation about the vertical axis (Roetenberg et al. 2003). The velocity and type of movement performed and the geometry of the body segment to which the sensor is applied can affect the accuracy of the measurements (Roetenberg et al. 2005); Distances between body segments cannot be assessed by means of numerical integration (Roetenberg and Veltink 2005); Previous studies in which this type of equipment was used report a high accuracy of the output data (Cutti et al. 2010; Ferrari et al. 2010a; Seel et al. 2014), however, the limitations in using this motion capture system are far from being overcome. The most important and challenging aspect of the study is to use the acquired information in a biomechanically meaningful manner, e.g. the parameters declared as joint angles, need to be as anatomically accurate as possible, for this purpose assuming the joint angles can be calculated as the angles of movement between two anatomical segments is not enough, a more complex mathematical model needs to be developed in order to address the biomechanical characteristics of the studied joint. There are a variety of protocols and algorithms available for post processing of sensor data stemming from human motion studies. A common approach for solving a human kinematics problem is to compare the human body to a robot manipulator. Similarly to a robot manipulator, which forms a kinematic chain from links interconnected by joints, the human body can be considered a kinematic chain formed of anatomical segments connected by articulations. In theory, this is a very efficient manner to solve a biomechanical problem. Cutti et al., for example, use the Danavit-Hartenberg convention of robotics in their Outwalk protocol, which states that a kinematic chain with n joints will have n+1 links (Fig 2.4). To solve the kinematics, a coordinate system is rigidly attached to each link. In this case, when joint is actuated, the adjacent and its attached coordinate frame perform a motion. Whichever motion is performed by the kinematic chain, the coordinates of each point on are constant when expressed in the coordinate frame (Zatsiorsky 1998). The Danavit-Hartenberg convention has two conditions which need to be satisfied in order for the kinematic solution to be effective. The variables of a joint (e.g. rotation angles) are defined by the two coordinate systems of the links adjacent to the joint. So, for example, the coordinates of the frame are expressed in the frame. Firstly, the orthonormality of the frames needs to be established, meaning needs to be perpendicular to . Secondly, the projection of in the frame ought to intersect . Comparing the human body to a robotics model is a good starting point. However, using the, frequently associated, strap-down integration method when measuring human kinematics with sensing units poses a very important limitation (Seel et al. 2014). The strap-down-integration method is based on using sensing units securely fixed to the even surfaces of robotic elements. However, there is a significant difference between a robotic setup and an anatomical system. Firstly, aligning the sensor to an anatomical location, such that one axes of the sensor coordinate system coincides exactly with an axis of the anatomical joint, is nearly impossible (Seel et al. 2014). This issue has been addressed in different manners by researchers so far. In the Outwalk protocol, Cutti and Ferrari et al. define as many coordinate frames for each link as the joints they form. Each anatomical segment has, therefore, a distal and a proximal coordinate frame. The joint variables are defined by the distal coordinate frame of one segment and the proximal coordinate frame of its adjacent segment. Another issue that needs to be addressed, when discussing a human biomechanical model, is an almost certain misalignment of the thigh axis with the segments coordinate system. Some studies completely ignore the misalignment between the anatomical and the sensor axes (Seel et al. 2014). In the Outwalk protocol this problem is solved by expressing the flexion-extension axis of the knee in the coordinate system of the distal femur and defining the other revolution axes of the coordinate frame as being orthogonal with respect to the new axis. This is another promising approach, however, in order for this method to be effective, the knee flexion-extension axis needs to be accurately identified. In the case of hinge joints, such as the simplified model of a knee joint, it is possible to calculate data from inertial sensors attached to both ends of the joint. However, this resulting data still needs to be translated into joint related coordinate systems and although, it is impossible to determine the initial position of the sensors on the anatomical segment, there is a possibility to determine the direction of the joint axes, by using different approaches to identify a functional movement axis from a set of dynamic motion data (Cutti et al. 2010; Ferrari et al. 2010a; Seel et al. 2014). In their protocol Cutti and Ferrari et al. use Woltrings mathematical solution for determining the finite helical axis (reviewed in (Zatsiorsky 1998)) to identify the knee flexion-extension axis. Woltrings solution appears to be fitting at least for most motion capture systems (Seel et al. 2014). However, the sensing units used in our study cannot measure translation. This would pose a big problem and could potentially result in substantial errors. In order for the outcome of the study to be successful, it needs to satisfy a set of conditions: (1) it is very important that the resulting post-processed sensor data is biomechanically meaningful to the musculoskeletal system; (2) data acquisition needs to be user friendly, rapid and easy to complete; (2) sensor mounting is not allowed to restrict the participants movement in any manner; (3) the resulting data needs to relate to true anatomical joint angles; and (4) the resulting information needs to be comparable to the reference system (Vicon). Seel et al. offer a solution based on rotational angle estimates alone, which is not only more simple from a data acquisition and processing point of view, but also functions on principles similar to SARA and SCoRE. In the protocol proposed by Seel et al. the knee is assumed to be a simple hinge, with one sensor attached to each segment forming the joint. In order to compensate for the lack of information concerning the initial position of the sensors on the anatomical segments, the unit length direction vectors and the orientations of the two segments attached to the hinge joint (Fig 2.6) are estimated as described below. The Seel et al. solution only employs the use of what is considered to be raw accelerometer and gyroscope output data from the two sensors, the thigh sensor and the shank sensor. In reality, any output data produced by the Xsens sensors, used in Seel et al.s study and the current study, is pre-processed in real-time by the on-board Kalman filter. For the purpose of the summary of the following protocol, all data indexed with 1 refers to thigh sensor data and data derived there from, and all data indexed with 2 refers to shank data and data derived there from. Firstly, the unit length direction vectors of the flexion-extension axis of the knee , are identified in the local coordinates of the sensors, by using an optimisation algorithm to compute the values of . Where the spherical coordinates for are: (6) (7) With the following sum of squared errors: ; (8) A search function is then used to find which satisfy the following condition: (9) Where: angular rates recorded by the thigh and shank sensor, respectively, with the sample period: constant; Euclidean norm. The acceleration measured by each sensor is the sum of the acceleration due to movement around the joint centre and the acceleration due to the rotation of the sensor around the joint centre. In order to estimate the knee joint position expressed in the local coordinate systems of the sensors, the amounts by which are shifted in order to obtain the acceleration of the joint centre, are estimated first. Two arbitrary points along the axes are estimated using a Gauss-Newton optimization algorithm. These points are shifted as close as possible to the sensor origin by applying: (10) (11) The radial and tangential acceleration due to the rotation of the sensor around the joint centre is computed: ; i=1,2 (12) Where: are time derivatives for angular rate and (13) The following sum of squared errors is calculated: ; (14) A search function is used to find which satisfy the following constrain: (15) The knee flexion/extension angle based on the gyroscope information is calculated with the following equation: (16) The measured accelerations are shifted onto the joint axes by applying the following: (17) (18) Where, represent the same quantity in the two different local coordinate systems, which rotate with respect to each other around the flexion axis. The flexion/extension angle calculated according to acceleration data can be defined as the angle between the projections of . (19) Where, and are pairs of joint plane axes, defined by: ; The knee flexion/extension angle defined by fusing the accelerometer and gyro data is defined by: (20) Where: knee flexion extension angle calculated according to accelerometer data at time t; knee flexion extension angle calculated according to gyroscope data at time t; the weight of the accelerometer data. By using the most effective methods presented in the literature review, the current study will attempt to validate the inertial sensor protocol proposed by Seel et. al 2014 against a OSSCA method and to compare laboratory and non-laboratory based inertial motion capture.

Path Builder Essay

During my experience with the path builder I organized and planed my time by taking two days to complete each subject giving myself enough time to take breaks in-between modules so I won’t get to overwhelmed. My impressions of the tools and the process were that the tools were very use full and helped a lot during the process of the learning path. I learned that my weaknesses are Whole numbers, decimals, linear equations and inequalities; absolute value, I also learned that my strengths are usage and style, the craft of writing, and research. The learning path topics that I completed were Whole numbers, decimals, linear equations and inequalities; absolute value, reading fundamentals, reading introductory, reading intermediate, usage and style, the craft of writing, and research. If I had to complete the suggested Learning Path topics in the future No I do not think I am self-motivated at a level to complete the suggested Learning Path topics in the future because it was a lot to complete in so little time. I believe that AIU resources a counselor and or a mentor can assist with self-motivation, I also believe that I will use College Algebra in my academic journey. In the work place of law enforcement you might use Measuring when measuring the weight of an illegal substance confiscated during a search and seizure. Or In determining the sequence of events that occurred at an accident scene, officers are called upon to take measurements and discern angles in order to compile the necessary evidence to reconstruct the event.

Piero Della Francesca and the Use of Geometry in His Art Essay

Piero della Francesca and the use of geometry in his art This paper takes a look at the art work of Piero della Francesca and, in particular, the clever use of geometry in his work; there will be a diagram illustrating this feature of his work at the end of this essay. To begin, the paper will explore one of the geometric proofs worked out in art by Piero and, in the process of doing so, will capture his exquisite command of geometry as geometry is expressed – or can be expressed – in art. By looking at some of Piero’s most noteworthy works, we also can see the skilful geometry behind them. For instance, the Flagellation of Christ is characterized by the fact that the frame is a root-two rectangle; significantly, Piero manages to ensure that Christ’s head is at the center of the original square, which requires a considerable amount of geometric know-how, as we shall see. In another great work, Piero uses the central vertical and horizontal zones to symboli cally reference the resurrection of Christ and also his masterful place in the hierarchy that distinguishes God from Man. Finally, Bussagli presents a sophisticated analysis of Piero’s, Baptism of Christ that reveals the extent to which the man employed different axes in order to create works that reinforced the Trinitarian message of the scriptures. Overall, his work is a compelling display of how the best painting inevitably requires more than a little mathematics. Piero is noteworthy for us today because he was keen to use perspective painting in his artwork. He offered the world his treatise on perspective painting entitled, De Prospectiva Pingendi (On the perspective for painting). The series of perspective problems posed and solved builds from the simple to the complex: in Book I, Piero introduces the idea that the apparent size of the object is its angle subtended at the eye; he refers to Euclid’s Elements Books I and VI (and to Euclid’s Optics) and, in Proposition 13, he explores the representation of a square lying flat on the ground before the viewer. To put a complex matter simply, a horizontal square with side BC is to be viewed from point A, which is above the ground plane and in front of the square, over point D. The square is supposed to be horizontal, but it is shown as if it had been raised up and standing vertically; the construction lines AC and AG cut the vertical side BF in points E and H, respectively. BE, subtending the same angle at A as the horizontal side BC, represents the height occupied by the square in the drawing. EH, subtending the same angle at A as the far side of the square (CG) constitutes the length of that side of the square drawn. According to Piero, the artist can then draw parallels to BC through A and E and locate a point A on the first of these to represent the viewer’s position with respect to the edge of the square designated BC. Finally, the aspiring artist reading Piero’s treatise can draw A’B and A’C, cutting the parallel through E at D’ and E’. Piero gives the following proof in illustrating his work: Theorem: E’D’ = EH. This simple theorem is described as the first new European theorem in geometry since Fibonacci (Petersen, para.8-12). It is not for nothing that some scholars have described Piero as being an early champion of, and innovator in, primary geometry (Evans, 385). The Flagellation of Christ is a classic instance of Piero’s wonderful command of geometry at work. Those who have looked at this scrupulously detailed and planned work note that the dimensions of the painting are as follows: 58.4 cm by 81.5 cm; this means that the ratio of the sides stands at 1.40 ~ 21/2. If one were to swing arc EB from A, one ends up with a square (this will all be illustrated at the very end of this paper in the appendices). Thus, to cut to the core of the matter, the width of the painting equals the diagonal of the square, thereby verifying that the frame is a root-two rectangle. Scholars further note that the diagonal, AE, of the square mentioned above passes through the V, which happens to be the vanishing point of perspective. Additionally, in square ATVK we find that the arc KT from A cuts the diagonal at Christ’s head, F, halfway up the painting; this essentially means that Christ’s head is at the center of the original square, (Calter, slide 14.2). A visual depiction of the geometry of the Flagellation of Christ is located in the appendices of this paper. Paul Calter has provided us with some of the best descriptions of how Piero cleverly uses geometry to create works of enduring beauty, symmetry and subtlety. He takes a great deal of time elaborating upon Piero’s Resurrection of Christ (created between 1460-1463) in which Piero employs the square format to great effect. Chiefly stated, the painting is constructed as a square and the square format gives a mood of overall stillness to the finished product. Christies located exactly on center and this, too, gives the final good a sense of overall stillness. The central vertical divides the scene with winter on left and summer on the right; clearly, the demarcation is intended to correlate the rebirth of nature with the rebirth of Christ. Finally, Calter notes that horizontal zones are manifest in the work: the painting is actually divided into three horizontal bands and Christ occupies the middle band, with his head and shoulders reaching into the upper band of sky. The guards are in the zone below the line marked by Christ’s foot (Calter, slide 14.3). In the appendix of this paper one can bear witness to the quiet geometry at play in the work by looking at the finished product. One other work of Piero’s that calls attention to his use of geometry is the Baptism of Christ. In a sophisticated analysis, Bussagli writes that there are two ideal axes that shape the entire composition: the first axis is central, paradigmatic and vertical; the second axis is horizontal and perspective oriented. The first one, according to Bussagli coordinates the characters related to the Gospel episode and thus to the Trinitarian epiphany; the second axis indicates the human dimension – where the story takes place – and intersects with the divine, as represented by the figure of Christ. To elaborate on the specifics of the complex first axis, Bussagli writes that Piero placed the angels that represent the trinity, the catechumen about to receive the sacrament, and the Pharisees on the perspective directed horizontal axis (Bussagli, 12). The end result is that the Trinitarian message is reinforced in a way that never distracts or detracts from the majesty of t he actual composition. To end, this paper has looked at some of Piero Della Francesca’s most impressive works and at the astounding way in which Piero uses geometry to impress his religious vision and sensibilities upon those fortunate enough to gaze upon his works. Piero had a subtle understanding of geometry and geometry, in his hands, becomes a means of telling a story that might otherwise escape the notice of the casual observer. In this gentleman’s work, the aesthetic beauty of great art, the penetrating logic of exact mathematics, and the devotion of the truly committed all come together as one. Source: Calter, Paul. â€Å"Polyhedra and plagiarism in the Renaissance.† 1998. 25 Oct. 2011 http://www.dartmouth.edu/~matc/math5.geometry/unit13/unit13.html#Francesca Appendix B: visual illustration of the Resurrection of Christ [pic] Source: Source: Calter, Paul. â€Å"Polyhedra and plagiarism in the Renaissance.† 1998. 25 Oct. 2011 http://www.dartmouth.edu/~matc/math5.geometry/unit13/unit13.html#Francesca Works Cited: Bussagli, Marco. Piero Della Francesca. Italy: Giunti Editore, 1998. Calter, Paul. â€Å"Polyhedra and plagiarism in the Renaissance.† 1998. 25 Oct. 2011 http://www.dartmouth.edu/~matc/math5.geometry/unit13/unit13.html#Francesca Evans, Robin. The Projective Cast: Architecture and its three geometries. USA: MIT Press, 1995. Petersen, Mark. â€Å"The Geometry of Piero Della Francesca.† Math across the Curriculum. 1999. 25 Oct. 2011 http://www.mtholyoke.edu/courses/rschwart/mac/Italian/geometry.shtml

Adolescent Athletes Can Struggle With Nutrition Based...

BACKGROUND/INTRODUCTION Adolescent athletes can struggle with nutrition-based knowledge. Lack of healthy food options, lack of time, convenience, media mis-representation and dietary fads makes making the â€Å"right† food choices over complicated and expensive Professional athletes generally turn to their parents and coaches, teachers and sports clubs for advice. It’s safe to suggest that a large number of these are unable to provide specific recommendations for individuals, meaning we can all be easily sucked in by peer and media influence. The minefield of misinformation that exists in the sports nutrition world online makes it easier to readily accept the social norms and trending ideas - but who s to say these are going to†¦show more content†¦While these considerations focus on maximizing the response to the stimulus of training, competitive adolescents have additional protein requirements to support general growth and development (Aernhouts et al.,2007; Meyer er al.,2007). It has been suggested that elite adolescent athletes should aim to intake between 1.3-1.8g per body weight (Kg) consumed in meals spread across the day with higher intakes (up to 2.5g/kg/d) after periods of intensified training (Phillips Van Loon, 2011). These do not differ largely with the recommendation for adults. In addition, there is evidence that the timing of intake of protein rather than the daily intake is important for maximizing the skeletal muscle response to resistance training. The consumption of modest amounts (around 20g) of high quality protein immediately after training enhances the acute protein synthetic response to exercise stimulus (Hawley et al., 2011). Total energy intake is also important to consider when addressing protein intake as insufficient energy will cause protein to be used as a substrate for energy by the body (Campbell et al., 2007; Petrie et al., 2004) This is why we need to also address carbohydrate intake. 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