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Hindawi Publishing Corporation EURASIP Journal on Image and Video Processing Volume 2007, Article ID 87929, 10 pages doi:10.1155/2007/87929 Research Article Telescopic Vector Composition and Polar Accumulated Motion Residuals for Feature Ex traction in Arabic Sign Language Recognition T. Shanableh 1 and K. Assaleh 2 1 Department of Computer Science, College of Engineering, American University of Sharjah, P.O. Box 26666, Sharjah, United Arab Emirates 2 Department of Electrical Engineering, College of Engineering, American University of Sharjah, P.O. Box 26666, Sharjah, United Arab Emirates Received 9 January 2007; Revised 1 May 2007; Accepted 2 August 2007 Recommended by Thierry Pun This work introduces two novel approaches for feature extraction applied to video-based Arabic sign language recognition, namely, motion representation through motion estimation and motion representation through motion residuals. In the former, motion estimation is used to compute the motion vectors of a video-based deaf sign or gesture. In the preprocessing stage for feature extraction, the horizontal and vertical components of such vectors are rearranged into intensity images and transformed into the frequency domain. In the second approach, motion is represented through motion residuals. The residuals are then thresholded and transformed into the frequency domain. Since in both approaches the temporal dimension of the video-based gesture needs to be preserved, hidden Markov models are used for classification tasks. Additionally, this paper proposes to project the motion information in the time domain through either telescopic motion vector composition or polar accumulated differences of motion residuals. The feature vectors are then extracted from the projected motion information. After that, model parameters can be evaluated by using simple classifiers such as Fisher’s linear discriminant. The paper reports on the classification accuracy of the proposed solutions. Comparisons with existing work reveal that up to 39% of the misclassifications have been corrected. Copyright © 2007 T. Shanableh and K. Assaleh. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. 1. INTRODUCTION Although used in over 21 countries covering a large geo- graphical and demographical portion of the world, Arabic sign language (ArSL) has received little attention in sign language recognition research. To date, only small num- ber of research papers has been published on ArSL. Signer- independent recognition of Arabic sign language alphabet using polynomial networks was reported in [1]. More re- cently, the authors introduced the recognition of Arabic iso- lated gestures by computing the prediction error between successive images using either forward prediction or bidirec- tional prediction. The Absolute differences are transformed into the frequency domain. Feature vectors are then extracted from the frequency coefficients [2]. Related work on recognition of non-Arabic using temporal-domain feature extraction mainly rely on compu- tationally expensive motion analysis approaches such as mo- tion estimation. Moreover, since the temporal characteris- tics are preserved, classification can be done using hidden Markov models (HMMs). For instance, in [3] the authors Motion Equations for Constant Acceleration in One Dimension Motion Equations for Constant Acceleration in One Dimension Bởi: OpenStaxCollege Kinematic equations can help us describe and predict the motion of moving objects such as these kayaks racing in Newbury, England (credit: Barry Skeates, Flickr) We might know that the greater the acceleration of, say, a car moving away from a stop sign, the greater the displacement in a given time But we have not developed a specific equation that relates acceleration and displacement In this section, we develop some convenient equations for kinematic relationships, starting from the definitions of displacement, velocity, and acceleration already covered Notation: t, x, v, a First, let us make some simplifications in notation Taking the initial time to be zero, as if time is measured with a stopwatch, is a great simplification Since elapsed time is Δt = tf − t0, taking t0 = means that Δt = tf, the final time on the stopwatch When initial time is taken to be zero, we use the subscript to denote initial values of position and velocity That is, x0 is the initial position and v0 is the initial velocity We put no subscripts on the final values That is, t is the final time, x is the final position, and v is the final velocity This gives a simpler expression for elapsed time—now, Δt = t It also 1/21 Motion Equations for Constant Acceleration in One Dimension simplifies the expression for displacement, which is now Δx = x − x0 Also, it simplifies the expression for change in velocity, which is now Δv = v − v0 To summarize, using the simplified notation, with the initial time taken to be zero, Δt = t Δx = x − x0 Δv = v − v0 } where the subscript denotes an initial value and the absence of a subscript denotes a final value in whatever motion is under consideration We now make the important assumption that acceleration is constant This assumption allows us to avoid using calculus to find instantaneous acceleration Since acceleration is constant, the average and instantaneous accelerations are equal That is, − a = a = constant, so we use the symbol a for acceleration at all times Assuming acceleration to be constant does not seriously limit the situations we can study nor degrade the accuracy of our treatment For one thing, acceleration is constant in a great number of situations Furthermore, in many other situations we can accurately describe motion by assuming a constant acceleration equal to the average acceleration for that motion Finally, in motions where acceleration changes drastically, such as a car accelerating to top speed and then braking to a stop, the motion can be considered in separate parts, each of which has its own constant acceleration Solving for Displacement (Δx) and Final Position (x) from Average Velocity when Acceleration (a) is Constant To get our first two new equations, we start with the definition of average velocity: − v = Δx Δt Substituting the simplified notation for Δx and Δt yields − v = x − x0 t Solving for x yields − x = x0 + v t, 2/21 Motion Equations for Constant Acceleration in One Dimension where the average velocity is − v = v0 + v (constant a) − v +v The equation v = 02 reflects the fact that, when acceleration is constant, v is just the simple average of the initial and final velocities For example, if you steadily increase your velocity (that is, with constant acceleration) from 30 to 60 km/h, then your average − v +v velocity during this steady increase is 45 km/h Using the equation v = 02 to check this, we see that − v = v0 + v = 30 km/h+60 km/h = 45 km/h, which seems logical Calculating Displacement: How Far does the Jogger Run? A jogger runs down a straight stretch of road with an average velocity of 4.00 m/s for 2.00 What is his final position, taking his initial position to be zero? Strategy Draw a sketch The final position x is given by the equation − x = x0 + v t − To find x, we identify the values of x0, v , and t from the statement of the problem and substitute them into the equation Solution − Identify the knowns v = 4.00 m/s, Δt = 2.00 min, and x0 = m 3/21 Motion Equations for Constant Acceleration in One Dimension Enter the known values into the equation − x = x0 + v t = + (4.00 m/s)(120 s) = 480 m Discussion Velocity and final displacement are both positive, which means they are in the same direction − The equation x = x0 + v t gives insight into the relationship between displacement, average velocity, and time It shows, for example, that displacement is a linear function − of average velocity (By linear function, we mean that displacement depends on v − −2 rather than on v raised to some other power, such as v When graphed, linear functions look like straight lines with a constant slope.) On a car trip, for example, we will get twice as far in a given time if we average 90 km/h than if we average 45 km/h There is a linear relationship between displacement and average velocity For a given time t, an object moving twice ...Proc Natl Conf Theor Phys 37 (2012), pp 107-114 STUDYING BLOCKING EFFECT FOR MANY PARTICLES DIFFUSION IN ONE-DIMENSIONAL DISORDERED LATTICE M.T LAN, P.T BINH, N.V HONG, P.K HUNG Hanoi University of Science and Technology No 1, Dai Co Viet, Hanoi, Vietnam Abstract The diffusion of many particles in one-dimensional disordered lattice has been studied using Monte-Carlo method with periodic boundary conditions We focus on the influence of energetic disorder and number of particle on diffusivity The site and transition energies are adopted in accordance to Gaussian distribution We consider two type lattices: the site disordered lattice (SD); transition disordered lattice (TD) In particular, the blocking effect concerning existence of many particles has been clarified under different temperature and energetic conditions The simulation results reveal F-effect and τ -effect which affect the diffusivity As increasing number of particles, the diffusion coefficient DM decreases for both lattices due to F-effect is stronger than τ -effect The blocking effect is strongly expression as increasing number of particles For both lattices the blocking effect is almost independent on the temperature I INTRODUCTION The diffusion of particles (atom, molecular and ion) in disordered systems (thin-film, amorphous materials, polymers and glasses) has been widely studied for recent decades and received wide attention by many research centres which relates to the field of fuel cells, membrane technology, nano devices [1-10] Experimental investigations have shown that diffusion in disordered systems has a lot of specific properties such as a strong reduction of the asymptotic diffusion coefficients, anomalous frequency dependence of the conductivity, dispersive transport, etc The explanation of the diffusion processes in disordered materials has been a challenge to theory In this work, we probe the diffusion of particles in one-dimensional lattice with site and transition disorders using Monte-Carlo (MC) simulation and analytical method The particle-particle interaction plays its own role which is interesting and intensively investigated [11-14], but they have no essential relation to the role of energetic disorder and event shadows its influence Hence, the lattices with non-interacting particles are employed here, and both aspects: energetic disorder and blocking effect, have been studied in two separate systems: the lattice SD where the transition energies are constant but site energies are adopted in accordance to Gaussian distribution [15], and lattice TD that conversely, the transition energies are adopted in accordance to Gaussian distribution and site energies are kept constant II CALCULATION METHOD Let us consider the hoping of particles between sites in one-dimensional disordered lattice Each site is characterized by its energy Ei Hoping of particle to neighboring sites i-1 and i+1 is described by transition energy Ei,i−1 and Ei,i+1 The transition and site 108 M.T LAN, P.T BINH, N.V HONG, P.K HUNG energies are assigned to each site in a random way from a given distribution Gaussian distribution: −(Ex − µ)2 p(E) = √ exp( ) (1) 2σ σ 2π To simply the energy is adopted in accordance to the standard Gaussian distribution with the parameter is given by: −(Ex )2 p(E) = √ exp( ); 2π with p(E) = (2) −5 Here the letter x may be s or t corresponding to the site or transition energy, respectively Once the particle presents at site i, its probability to hop into neighboring site i+1 is given by −(Ei,i+1 β) (3) pi,i+1 = (Ei,j+1 β) + Ei,j−1 β The jump which carries the particle out of site i, is a Poisson process with averaged delay time 2τ0 exp(−Ei β) τi = (4) exp(−Ei,i+1 β) + exp(−Ei,i−1 β) where τ0 is frequency period; β = 1/kB T;kB is Boltzmann constant, and T temperature The time τi in fact is the mean residence time of particle on site i The Monte-Carlo (MC) method is developed mostly for the stationary state and simple form, it does not involve the ... by accelerating for a longer time 6/21 Motion Equations for Constant Acceleration in One Dimension Solving for Final Position When Velocity is Not Constant (a ≠ 0) We can combine the equations. .. manipulating the definition of acceleration a= Δv Δt Substituting the simplified notation for Δv and Δt gives us a= v − v0 t (constant a) 4/21 Motion Equations for Constant Acceleration in One Dimension. .. (Such information might be useful to a traffic engineer.) Strategy Draw a sketch 13/21 Motion Equations for Constant Acceleration in One Dimension We are asked to solve for the time t As before,