on the estimation of an average rigid body motion this paper investigates the definition and the estimation of the frechet mean of a random rigid body motion in super p the sample space se p contains objects me r t where r is a p p rotation matrix and t is a p 1 translation vector this work is motivated by applications in biomechanics where the posture of a joint at a given time is expressed as mise 3 the rigid body displacement needed to map a system of axes on one segment of the joint to a similar system on the other segment this posture can also be reported as m super 1e r super t r super tt by interchanging the role of the two segments several definitions of a frechet mean for a random motion are proposed using weighted least squares distances a special emphasis is given to a frechet mean that is equivariant with respect to the inverse transform this means that if p is the frechet mean for m then p super 1 is the frechet mean for m super 1 where m is a random se p object the sampling properties of moment estimators of the frechet means are studied in a large concentration setting where the scatter of the random ms around their mean value p is small and as the sample size goes to some simple exponential family models for se p data that generalize downs 1972 fisher von mises matrix distribution for rotation matrices are introduced and the least squares mean values for these distributions are calculated asymptotic comparisons between the estimators presented in this work are carried out for a particular model when pe2 a numerical example involving the motion of the ankle is presented to illustrate the methodology copyright 2012 oxford university press

variable frame rate fixed bit rate vocoding method a method of operating a vocoder so that a variable frame rate results while maintaining a constant bit rate is disclosed a base frame rate remains constant however spectral change is measured to determine an appropriate subframe rate within the base frame only one of a plurality of separate vector quantization processes is selected in response to spectral change for performance of a vector quantization operation on lpc spectrum coefficients each of the plurality of vector quantization operations utilizes its own codebook that contains a different quantity of reference patterns from that contained in the other codebooks each vector quantization operation produces a reference pattern descriptor code that contains a different number of bits from that produced by the other vector quantization processes vector quantization operations producing smaller less spectrally accurate outputs are selected when more subframes are included with a base frame and vector quantization operations producing larger more spectrally accurate outputs are selected when fewer subframes are included within a base frame

instantaneous helical axis estimation from 3 d video data in neck kinematics for whiplash diagnostics to date the diagnosis of whiplash injuries has been very difficult and largely based on subjective clinical assessment the work by winters and peles multiple muscle systems biomechanics and movement organization springer new york 1990 suggests that the use of finite helical axes fhas in the neck may provide an objective assessment tool for neck mobility thus the position of the fha describing head trunk motion may allow discrimination between normal and pathological cases such as decreased mobility in particular cervical joints for noisy unsmoothed data the fhas must be taken over rather large angular intervals if the fhas are to be reconstructed with sufficient accuracy in the winters and peles study these intervals were approximately 10 in order to study the movements microstructure the present investigation uses instantaneous helical axes ihas estimated from low pass smoothed video data here the small step noise sensitivity of the fha no longer applies and proper low pass filtering allows estimation of the iha even for small rotation velocity of the moving neck for marker clusters mounted on the head and trunk technical system validation showed that the ihas direction dispersions were on the order of one degree while their position dispersions were on the order of 1 mm for low pass cut off frequencies of a few hz the dispersions were calculated from weighted errors in order to account for the adverse effects of vanishing various simple planar models relating the instantaneous 2 d centre of rotation with the geometry and kinematics of a multi joint neck model are derived in order to gauge the utility of the fha and iha approaches some preliminary results on asymptomatic and pathological subjects are provided in terms of the ruled surface formed by sampled ihas and of their piercing points through the mid sagittal plane during a prescribed flexion extension movement of the neck

method of and device for speech signal coding and decoding by subband analysis and vector quantization with dynamic bit allocation according to the coding method the digital speech signal is split into subbands each subband is coded independently of the others the first two subbands undergo an adaptive linear prediction operation yielding a residual normalized with respect to a quantized r m s value the residual samples are quantized and coded by a variable bit number as to the third subband the samples normalized with respect to a quantized gain term are directly quantized and coded by a variable bit number while splitting the subband signals into sample blocks for the first two subbands the coefficient vectors of subband linear prediction filters relevant to each block are also determined by vector quantization and linear prediction inverse filtering operations quantized r m s values are also determined to calculate the numbers of bits permitting subband signals coding the coded signal consists of subband signal quantization level indices of r m s value quantization level indices and of linear prediction filter coefficient vector indices

the achievable region approach to the optimal control of stochastic systems summary the achievable region approach seeks solutions to stochastic optimization problems by characterizing the space of all possible performances the achievable region of the system of interest and optimizing the overall system wide performance objective over this space this is radically different from conventional formulations based on dynamic programming the approach is explained with reference to a simple two class queuing system powerful new methodologies due to the authors and co workers are deployed to analyse a general multiclass queuing system with parallel servers and then to develop an approach to optimal load distribution across a network of interconnected stations finally the approach is used for the first time to analyse a class of intensity control problems

comparison of different calculations of three dimensional joint kinematics from video based system data when skin fixed marker trajectories are used to calculate 3d joint kinematics the measurement errors i e the difference between the trajectories of the external markers and those of the skeleton influence to some extent the accuracy of the results depending both on the calculation method and on the axes about which the rotations are expressed the purpose of this paper is to compare several expressions of joint angular variations two kinematic concepts are used to calculate the changes in the orientation of the distal segment versus the proximal one the first method consists of computing the components of the spatial attitude vector the second one deals with the determination of elementary rotations about successive axes for each of these methods two sets of three axes are tested to express the results the axes forming the reference frame affixed to the body segment adjacent to the joint named fixed axes and a set consisting of a first axis belonging to the proximal segment a third axis belonging to the distal segment and a second floating axis defined as the cross product between the two other ones named mobile axes to compare these four distinct expressions on the knee joint numerical simulations of perturbed skin marker trajectories are performed based on experimental data recorded by a motion analysis system during a normal gait cycle a significant difference is pointed out only for the internal external rotation angle for which the best expression from the viewpoint of sensitivity to experimental errors is obtained using the components of the attitude vector in a segment embedded reference frame

3 d attitude representation of human joints a standardization proposal abstract in view of the singularities asymmetries and other adverse properties of existing three dimensional definitions for joint and segment angles the present paper proposes a new convention for unambiguous and easily interpretable 3 d joint angles based on the concept of the attitude vector as derived from euler s theorem the suggested standard can be easily explained to non mathematically trained clinicians is readily implemented in software and can be simply related to classical cardanic eulerian angles for planar rotations about a coordinate system s axes the proposed convention coincides with the cardanic convention the attitude vector dispenses with the gimbal lock and non orthogonality disadvantages of cardanic eulerian conventions therefore its components have better metrical properties and they are less sensitive to measurement errors and to coordinate system uncertainties than cardanic eulerian angles a sensitivity analysis and a physical interpretation of the proposed standard are given and some experimental results that demonstrate its advantages

constant data rate speech encoder for limited bandwidth path a speech signal has its characteristics extracted and encoded 16 transmitted over a limited data rate path 18 and is decoded 20 and synthesized 22 at the receiving end the characteristics include line spectral frequencies lsf pitch and jitter the lsf are extracted by autoregression and split vector quantized svq in a single frame and in parallel in blocks of two three and four frames the svq codes have equal length and are evaluated for distortion in conjunction with a threshold the threshold is varied in such a manner as tend to select for transmission those codewords which maintain a constant data rate into a transmit buffer a single bit jitter bit and encoded pitch value are product coded with the selected lsf codeword and all are transmitted over the data path 18 to the receiver the receiver decodes the characteristics and controls a pitch generated 1226 in response to the pitch value and a random pitch jitter in response to the jitter bit two sets of line spectrum filters receive random noise and the pitch signal respectively the filtered signals are modulated by multipliers 1222 1230 controlled by the lsf codes and the filtered signals are summed and applied to a final lsf controlled filter

orientation statistics without parametric assumptions summary maximum likelihood estimation using the matrix von mises fisher distribution in orientation statistics leads to unacceptably complicated likelihood equations essentially because of the inconvenient form of the normalizing constant in the probability distribution for the case of 3 x 2 or 3 x 3 orientations the main cases of practical importance an alternative approach is developed here by transforming the data into unsigned four dimensional directions and using known results on the sampling properties of the spectral decomposition of the resulting sample moment of inertia matrix it is demonstrated that the necessary computations are relatively simple by applying some of the techniques to a set of vectorcardiogram data

bounds and policies for dynamic routing in loss networks we consider the problem of maximizing a weighted sum of expected rewards in steady state in multiclass loss networks under dynamic routing and admission control with poisson arrivals and exponentially distributed holding times by aggregating the underlying markov decision process we derive linear programming relaxations that contain the achievable performance region under all admissible policies and lead to a series of progressively tighter upper bounds these relaxations allow stronger bounds at the expense of higher computational times we further propose a series of routing and admission control policies from the relaxations that outperform in computational experiments other heuristic policies such as the dynamic alternative routing with trunk reservation and the least busy alternative routing variations of which are used in practice the suboptimality guarantees defined as best bound best policy range from 0 to 2 5 under symmetry conditions symmetric network topology arrival rates link capacities rewards and from 4 to 10 under asymmetry conditions we discuss the qualitative behavior of these policies and obtain insights about their performance

a directional model for the statistical analysis of movement in three dimensions summary movement of an object in three dimensions involves rotation and translation the data for analysis are the coordinates of landmarks on the object recorded at several time points statistical models for describing the rotational component of the movement of an object are proposed in this work under the fixed axis model the object rotates around an axis that does not change in time the angular position of the object is then characterised by its rotation axis and an angle giving the extent of the rotation of the object with respect to a reference point more complicated models occur when the rotation axis varies in time under the fixed angle model the quaternions for the time varying orientations of the object are shown to lie in a two dimensional great circle on the surface of the unit sphere in four dimensions simple estimators are given of the comnmon rotation axis and of the angles characterising the time varying orientation of the object a score statistic for testing the fit of the fixed axis model is constructed and methods for handling the autocorrelation of the errors at neighbouring data points are provided the analysis of data collected by an optotrack camera system on a rotating forearm illustrates the methodology presented in this paper

digital speech coder having improved vector excitation source an improved excitation vector generation and search technique fig 1 is described for a code excited linear prediction celp speech coder 100 using a codebook of excitation code vectors a set of m basis vectors vm n are used along with the excitation signal codewords i to generate the codebook of excitation vectors ui n according to a vector sum technique 120 of converting the selector codewords into a plurality of interim data signals multiplying the set of m basis vectors by the interim data signals and summing the resultant vectors to produce the set of 2m codebook vectors the entire codebook of 2m possible excitation vectors is efficiently searched by using the vector sum generation technique with the m basis vectors without ever having to generate and evaluate each of the 2m code vectors themselves furthermore only m basis vectors need to be stored in memory 114 as opposed to all 2m code vectors

a model of the soft tissue artefact rigid component when using stereophotogrammetry and skin markers the reconstruction of skeletal movement is affected by soft tissue artefact sta this may be described by considering a marker cluster as a deformable shape undergoing a geometric transformation formed by a non rigid change in size and shape and a rigid component translation and rotation displacements a modal decomposition of the sta relative to an appropriately identified basis allows the separation of these components this study proposes a mathematical model of the sta that embeds only its rigid component and estimates the relevant six mode amplitudes as linear functions of selected proximal and distal joint rotations during the analysed task this model was successfully calibrated for thigh and shank using simultaneously recorded pin and skin marker data of running volunteers the root mean square difference between measured and model estimated sta rigid component was 1 1 0 8 mm median inter quartile range over 3 subjects 5 trials 33 markers coordinates and it was mostly due to the wobbling not included in the model knee joint kinematics was estimated using reference pin marker data and skin marker data both raw and compensated with the model estimated sta sta compensation decreased inaccuracy on average from 6 to 1 for flexion extension from 43 to 18 for the other two rotations and from 69 to 25 for the linear displacements thus the proposed mathematical model provides an sta estimate which can be effectively used within optimal bone pose and joint kinematics estimators for artefact compensation and for simulations aimed at their comparative assessments

predictive split matrix quantization of spectral parameters for efficient coding of speech the present invention concerns efficient quantization of more than one lpc spectral models per frame in order to enhance the accuracy of the time varying spectrum representation without compromising on the coding rate such efficient representation of lpc spectral models is advantageous to a number of techniques used for digital encoding of speech and or audio signals

asymptotically optimal loss network control we consider a loss network which employs alternative routing and derive the asymptotically optimal call acceptance and routing policy the limit being as the number of links becomes large we show that a well known control policy least busy alternative routing with trunk reservation is asymptotically optimal the approach of the paper is not specific to the loss network control problem that we consider but is applicable more generally the results are obtained by combining weak convergence with linear programming techniques

new least squares solutions for estimating the average centre of rotation and the axis of rotation a new method is proposed for estimating the parameters of ball joints also known as spherical or revolute joints and hinge joints with a fixed axis of rotation the method does not require manual adjustment of any optimisation parameters and produces closed form solutions it is a least squares solution using the whole 3d motion data set we do not assume strict rigidity but only that the markers maintain a constant distance from the centre or axis of rotation this method is compared with other methods that use similar assumptions in the cases of random measurement errors systematic skin movements and skin movements with random measurement noise simulation results indicate that the new method is superior in terms of the algorithm used the closure of the solution consistency and minimal manual parameter adjustment the method can also be adapted to joints with translational movements

two dimensional rigid body kinematics using image contour registration a method for calculating two dimensional rigid body kinematic parameters using shape features is presented proposed applications include the noninvasive quantification of planar joint motion in vivo by using digitized images computed tomographs radiographs etc of a bone contour at two positions the contour curvatures can be best fit to obtain a one to one mapping or registration of the bone images this produces a dense field of displacement vectors from which planar rigid body kinematic parameters can be estimated accuracy was studied using radiographic images of cadaveric femoral bone the two motions of pure rotation with a fixed center of rotation and of pure translation were simulated for pure rotation error in rotation was independent of the rotation magnitude with an average n 10 error of 0 3 0 8 degrees the translation error averaged 0 9 0 5 mm for pure translation the error in rotation was 0 01 0 69 degrees and the error in translation was 0 62 0 98 mm n 10 this novel method has broad applications in the field of planar kinematics especially in cases for which marker fixation is neither possible nor practical

soft tissue artifact compensation by linear 3d interpolation and approximation methods several compensation methods estimate bone pose from a cluster of skin mounted makers each influenced by soft tissue artifact sta in this study linear 3d interpolation and approximation methods affine mapping kriging and radial basis function rbf and the conventional singular value decomposition svd method were examined to determine their suitability for sta compensation the ability of these four methods to estimate knee angles and displacements was compared using simulated gait data with and without added sta the knee angle and the displacement estimates of all four methods were similar with root mean square errors rmses near 1 5 degrees and 4mm respectively the 3d interpolation and approximation methods were more complicated to implement than the conventional svd method however these non standard methods provided additional geometric homothety stretch and time functions that model the deformation of the cluster of markers this additional information may be useful to model and compensate the sta

saddlepoint approximations for the normalizing constant of fisher bingham distributions on products of spheres and stiefel manifolds in an earlier paper kume wood 2005 showed how the normalizing constant of the fisher bingham distribution on a sphere can be approximated with high accuracy using a univariate saddlepoint density approximation in this sequel we extend the approach to a more general setting and derive saddlepoint approximations for the normalizing constants of multicomponent fisher bingham distributions on cartesian products of spheres and fisher bingham distributions on stiefel manifolds in each case the approximation for the normalizing constant is essentially a multivariate saddlepoint density approximation for the joint distribution of a set of quadratic forms in normal variables both first order and second order saddlepoint approximations are considered computational algorithms numerical results and theoretical properties of the approximations are presented in the challenging high dimensional settings considered in this paper the saddlepoint approximations perform very well in all examples considered some key words directional data fisher matrix distribution kent distribution orientation statistics

evaluation of knee functional calibration with and without the effect of soft tissue artefact functional calibration methods were devised to improve repeatability and accuracy of the knee flexion extension axis which is used to define the medio lateral axis of the femur coordinate system in gait analysis repeatability of functional calibration methods has been studied extensively in healthy individuals but not accuracy in the absence of a benchmark knee axis we captured bi plane fluoroscopy data of the knee joint in 17 subjects with unilateral total knee arthroplasty during treadmill walking the prosthesis provided a benchmark knee axis to evaluate the functional calibration methods stereo photogrammetry data of thigh and shank marker clusters were captured simultaneously to investigate the effect of soft tissue artefact sta three methods were tested the axis transformation technique att finds the best single fixed axis of rotation 2dofknee finds the axis that minimises knee varus valgus and trajajc finds the axis perpendicular to the trajectory in the transverse plane of the femur of a point located on the longitudinal axis of the tibia using fluoroscopy data functional axes formed an angle of less than 2 in the transverse plane with the benchmark axis true internal external range of movement was correlated with decreased accuracy for att while varus valgus range of movement was correlated with decreased accuracy for 2dofknee and trajajc sta had negative impact on accuracy and variability using stereo photogrammetry data the accuracy of 2dofknee was 1 7 sd 5 1 smaller than att 2 9 sd 5 1 but not to trajajc 1 7 sd 5 2 our results confirm that of previous studies which utilised the femur condylar axis as reference

system for embedded coding of speech signals the set of possible excitation signals is subdivided into a plurality of subsets the first of which provides the contribution to the coded signal necessary to set up a transmission at a minimum rate guaranteed by the network whilst the others supply a contribution which when added to that of the first subset causes a rate increase by successive steps at the receiving side a decoded signal is generated by using the excitation contribution of the first subset alone if the coded signals are received at the minimum rate whilst for rates higher than the minimum rate the contributions of the subsets which have allowed such rate increase are also used

efficient codebook structure for code excited linear prediction coding a speech communication system using a code excited linear prediction speech decoder the decoder using a first codebook containing a first digital value sequence selected from the set of binary values 0 1 the decoder also using a second codebook containing a second digital value sequence having values selected from the set of binary values 1 0 the first digital value sequence and the second digital value sequence are combined to become a third digital value sequence having a set of ternary values from the set of 1 0 1

bounds on the performance of dynamic routing schemes for highly connected networks we describe a procedure for bounding the performance of dynamic routing schemes for loss or queueing networks the bound is developed from a network flow synthesis of a collection of markov decision processes one for each resource of the network the bound emerges as a solution to a dual pair of convex programming problems where the primal problem describes mean flows through the network and the dual problem describes implied costs and surplus values at resources of the network the bound is particularly appropriate for large highly connected networks where it may be approached by simple trunk reservation or threshold routing schemes

analysis of simple algorithms for dynamic load balancing the principle of load balancing is examined for dynamic resource allocation subject to certain constraints the emphasis is on the performance of simple allocation strategies which can be implemented on line either finite capacity constraints on resources or migration of load can be incorporated into the setup the load balancing problem is formulated as a stochastic optimal control problem variants of a least load routing policy are shown to lead to a fluid type limit and to be asymptotically optimal

objective bayesian meta analysis for sparse discrete data this paper presents a bayesian model for meta analysis of sparse discrete binomial data which are out of the scope of the usual hierarchical normal random effect models treatment effectiveness data are often of this type the crucial linking distribution between the effectiveness conditional on the healthcare center and the unconditional effectiveness is constructed from specific bivariate classes of distributions with given marginals this assures coherency between the marginal and conditional prior distributions utilized in the analysis further we impose a bivariate class of priors that is able to accommodate a wide range of heterogeneity degrees between the multicenter clinical trials involved applications to real multicenter data are given and compared with previous meta analysis copyright 2014 john wiley sons ltd

finite centroid and helical axis estimation from noisy landmark measurements in the study of human joint kinematics abstract recent work on joint kinematics indicates that the finite centroid centre of rotation and the finite helical axis axis of rotation screw axis twist axis are highly susceptible to measurement errors when they are experimentally determined from landmark position data this paper presents an analytical model to describe these effects under isotropic conditions for the measurement errors and for the spatial landmark distribution it appears that the position and direction errors are inversely proportional to the rotation magnitude and that they are much more error prone than the relatively well determined rotation and translation magnitudes furthermore the direction and rotation magnitude errors are inversely proportional to the landmark distribution radius and the position and translation magnitude errors are minimal if the mean position of the landmarks coincides with the centroid or helical axis for the planar centroid the use of rigid body constraints results in considerable precision improvement relative to the classical finite reuleaux method for centroid reconstruction these analytical results can be used to define suitable measurement configurations and they are used in this paper to explain experimental results on rontgenphotogrammetrically acquired in vitro wrist joint movement

accuracy of a ct based bone contour registration method to measure relative bone motions in the hindfoot abstract for measuring the in vivo range of motion of the hindfoot a ct based bone contour registration method ct bcm was developed to determine the three dimensional position and orientation of bones to validate this technique we hypothesized that the range of motion in the hindfoot is equally accurately measured by roentgen stereophotogrammetric analysis rsa as by the ct bcm technique tantalum bone markers were placed in the distal tibia talus and calcaneus of one cadaver specimen with a fixed lower leg the cadaveric foot was held in neutral and subsequently loaded in eight extreme positions immediately after acquiring a ct scan with the foot in a position rsa radiographs were made bone contour registration and rsa was performed helical axis parameters were calculated for talocrural and subtalar joint motion from neutral to extreme positions and between opposite extreme positions differences between ct bcm and rsa were calculated compared with rsa the ct bcm data registered an overall root mean square difference rmsd of 0 21 for rotation about the helical axis and 0 20 mm translation along the helical axis for the talocrural and subtalar joint and for all motions combined the rmsd of the position and direction of the helical axes was 3 3 mm and 2 4 respectively the latter errors were larger with smaller helical rotations the differences are similar to those reported for validated rsa and thus are not clinically relevant concluding ct bcm is an accurate and accessible alternative for studying joint motion as it does not have the risk of infection and overlapping bone markers

using directional statistics to test hypotheses regarding rigid body attitude comparison to univariate and multivariate cardan angle tests abstract rigid body attitude and single joint kinematics are typically expressed using three cardan angles which represent rotations in anatomical planes it was recently shown in the biomechanics literature that cardan angles inaccurately estimate true mean attitude due to an important mathematical inadequacy attitude under representation at least four quantities are needed to unambiguously specify attitude directional statistics which is the multivariate generalization of univariate circular statistics solves this problem using four dimensional unit vectors and the mathematics of hyperspherical geometry the purpose of this study was to compare the results of directional analysis to the results of uni and multi variate cardan analysis for representative joint kinematic data during gait we analyzed hip knee and pelvis data from three open datasets and report exemplary results for knee kinematics in v cut vs side shuffle tasks we also conducted monte carlo simulations using synthetic data with precisely controlled true angular effects to systematically compare directional and cardan analyses results show that directional analysis yielded considerably smaller p values p 0 03 than cardan analysis p 0 055 for the exemplary dataset simulation results confirmed that directional analysis is considerably more powerful i e much more able to detect true angular effects than both uni and multi variate cardan analysis these results suggest that directional statistics should be used to analyse attitude including 3d joint kinematics to avoid false negatives

calculating the 2d motion of lumbar vertebrae using splines in this study we investigate the use of splines and the icp method besl p mckay n 1992 a method for registration of 3d shapes ieee transactions on pattern analysis and machine intelligence 14 239 256 for calculating the transformation parameters for a rigid body undergoing planar motion parallel to the image plane we demonstrate the efficacy of the method by estimating the finite centre of rotation and angle of rotation from lateral flexion extension radiographs of the lumbar spine in an in vitro error study the method displayed an average error of rotation of 0 44 0 45 degrees and an average error in fcr calculation of 7 6 8 5 mm the method was shown to be superior to that of crisco et al two dimensional rigid body kinematics using image contour registration journal of biomechanics 28 1 119 124 and brinckmann et al quantification of overload injuries of the thoracolumbar spine in persons exposed to heavy physical exertions or vibration at the workplace part i the shape of vertebrae and intervertebral discs study of a yound healthy population and a middle aged control group clinical biomechanics supplement 1 s5 s83 for the tests performed here in general we believe the use of splines to represent planar shapes to be superior to using digitised curves or landmarks for several reasons first with appropriate software splines require less effort to define and are a compact representation with most vertebra outlines using less than 30 control points second splines are inherently sub pixel representations of curves even if the control points are limited to pixel resolutions third there is a well defined method the icp algorithm for registering shapes represented as splines finally like digitised curves splines are able to represent a large class of shapes with little effort but reduce potential segmentation errors from two dimensions parallel and perpendicular to the image gradient to just one parallel to the image gradient we have developed an application for performing all the necessary computations which can be downloaded from http www claritysmart com

vector quantizing apparatus and speech analysis synthesis system using the apparatus a vector quantizing apparatus having a general vector quantization circuit and a storage means for storing at least one frame of data as the result of comparison by a matching circuit is provided further provided are a speech analysis synthesis system having a spectral envelope generator for generating a spectral envelope which is so smooth that excessive beating is avoided a spectral envelope vector converter for sampling the spectral envelope at equal intervals on mel scale a vector quantizer for quantizing vectors and a spectral envelope reconstructor for reconstructing the spectral envelope by interpolation on the basis of combined parabolas

a directional model for the estimation of the rotation axes of the ankle joint this article is motivated by the estimation of the directions of the two rotation axes of the ankle these axes carry information on individual ankles they are useful in the construction of biomechanical models and the treatment of orthopedic problems in biomechanics the rotation axes of the ankle often are estimated using optimization techniques this work investigates a statistical model for carrying out the estimation the data set for analysis is a time ordered sequence of 3 3 rotation matrixes giving the ankle s orientations as the foot moves with respect to the lower leg these rotation matrixes are assumed to follow fisher von mises distributions the predicted values for the observed rotations feature four angles for the orientation of two rotation axes and two series of time varying rotation angles about the two axes maximum likelihood estimators of the parameters are derived approximations to their sampling distributions are obtained when the errors are clustered around the identity matrix

in vivo determination of the anatomical axes of the ankle joint complex an optimization approach this study investigates the feasibility of a subject specific three dimensional model of the ankle joint complex for kinematic and dynamic analysis of movement the ankle joint complex was modelled as a three segment system connected by two ideal highe joints the talocrural and the subtalar joint a mathematical formulation was developed to express the three dimensional translation and rotation between the foot and shank segments as a function of the two joint angles and 12 model parameters describing the locations of the joint axes an optimization method was used to fit the model parameters to three dimensional kinematic data of foot and shank markers obtained during test movements throughout the entire physiological range of motion of the ankle joint the movement of the talus segment which cannot be measured non invasively is not necessary for the analysis this optimization method was used to determine the position and orientation of the joint axes in 14 normal subjects after optimization the discrepancy between the best fitting model and actual marker kinematics was between 1 and 3 mm for all subjects the predicted inclination of the subtalar joint axis from the horizontal plane was 37 4 2 7 and the medial deviation was 18 0 16 2 the lateral side of the talucrural axis was directed slightly posteriorly 6 8 8 1 and inclined downward by 7 0 5 4 these results are similar to previously reported typical results from anatomical in vitro studies reproducibility was evaluated by repeated testing of one subject which resulted in variations of about one fifth of the standard deviation within the group the inclination of the subtalar joint axis was significantly correlated to the arch height and a radiographic tarsal index it is concluded that this optimization method provides the opportunity to incorporate inter individual anatomical differences into kinematic and dynamic analysis of the ankle joint complex this allows a more functional interpretation of kinematic data and more realistic estimates of internal forces

modeling and inference for measured crystal orientations and a tractable class of symmetric distributions for rotations in three dimensions electron backscatter diffraction ebsd is a technique used in materials science to study the microtexture of metals producing data that measure the orientations of crystals in a specimen we examine the precision of such data based on a useful class of distributions on orientations in three dimensions as represented by 3 3 orthogonal matrices with positive determinants although such modeling has received attention in the statistical literature the approach taken typically has been based on general special manifold considerations and the resulting methodology may not be easily accessible to nonspecialists we take a more direct modeling approach beginning from a simple intuitively appealing mechanism for generating random orientations specifically in three dimensional space the resulting class of distributions has many desirable properties including directly interpretable parameters and relatively simple theory we investigate the basic properties of the entire class and one sample quasi likel

low data rate speech encoder with mixed excitation a speech signal has its characteristics extracted and encoded 16 transmitted over a limited data rate path 18 and is decoded 20 and synthesized 22 at the receiving end the characteristics include line spectral frequencies lsf pitch and jitter the lsf are extracted by autoregression and splitvector quantized svq in a single frame and in parallel in blocks of two three and four frames the svq codes have equal length and are evaluated for distortion in conjunction with a threshold the threshold is varied in such a manner as tend to select for transmission those codewords which maintain a constant data rate into a transmit buffer a single bit jitter bit and encoded pitch value are product coded with the selected lsf codeword and all are transmitted over the data path 18 to the receiver the receiver decodes the characteristics and controls a pitch generated 1226 in response to the pitch value and a random pitch jitter in response to the jitter bit two sets of line spectrum filters receive random noise and the pitch signal respectively the filtered signals are modulated by multipliers 1222 1230 controlled by the lsf codes and the filtered signals are summed and applied to a final lsf controlled filter

the score residual a quality index to assess the accuracy of joint estimations abstract the determination of an accurate centre of rotation cor from skin markers is essential for the assessment of abnormal gait patterns in clinical gait analysis despite the many functional approaches to estimate cors no non invasive analytical determination of the error in the reconstructed joint location is currently available the purpose of this study was therefore to verify the residual of the symmetrical centre of rotation estimation score as a reliable indirect measure of the error of the computed joint centre to evaluate the score residual numerical simulations were performed to evaluate cor estimations at different ranges of joint motion a statistical model was developed and used to determine the theoretical relationships among the score residual the magnitude of the skin marker artefact the corrections to the marker positions and the error of the cor estimations to the known centre of rotation we found that the equation err 0 5rs provides a reliable relationship among the cor error err and the scaled score residual rs providing that any skin marker artefact is first minimised using the optimal common shape technique ocst measurements on six healthy volunteers showed a reduction of score residual from 11 to below 6 mm and therefore demonstrated consistency of the theoretical considerations and numerical simulations with the in vivo data this study also demonstrates the significant benefit of the ocst for reducing skin marker artefact and thus for predicting the accuracy of determining joint centre positions in functional gait analysis for the first time this understanding of the score residual allows a measure of error in the non invasive assessment of joint centres this measure now enables a rapid assessment of the accuracy of the cor as well as an estimation of the reproducibility and repeatability of skeletal motion patterns

ground reaction intrinsic and extrinsic variability assessment and related method for artefact treatment ground reaction gr components measured by a dynamometric platform represent the dynamic interaction of the moving human body with the ground and depend on the subject platform relative position and orientation the observed variability among the gr measurements of the walking trials of an individual is either due to variability in the motor performance intrinsic variability or due to changes in the direction of walking and in the position and orientation of the striking foot relative to the platform extrinsic variability a method based on the median operator is presented here which lets us quantify the two components of variability the application of the method to a large data set of normal subjects evidenced changes in progression direction foot orientation 95th percentile value is 6 9 degrees which can dramatically change the patterns of gr components this result warns about improper analysis of ground reaction measurement an algorithm for restoring gr measurements affected by artefact was derived from the above method this tool can be of valuable aid in clinical practice where patients conditions suggest to not insist on repetition of trials even if the required number of correct foot placements has not been achieved the artefact correction algorithm has been applied to a large data set artificially corrupted to evaluate its robustness

bone orientation and position estimation errors using cosserat point elements and least squares methods application to gait the aim of this study was to analyze the accuracy of bone pose estimation based on sub clusters of three skin markers characterized by triangular cosserat point elements tcpes and to evaluate the capability of four instantaneous physical parameters which can be measured non invasively in vivo to identify the most accurate tcpes moreover tcpe pose estimations were compared with the estimations of two least squares minimization methods applied to the cluster of all markers using rigid body rbls and homogeneous deformation hdls assumptions analysis was performed on previously collected in vivo treadmill gait data composed of simultaneous measurements of the gold standard bone pose by bi plane fluoroscopy tracking the subjects knee prosthesis and a stereophotogrammetric system tracking skin markers affected by soft tissue artifact femur orientation and position errors estimated from skin marker clusters were computed for 18 subjects using clusters of up to 35 markers results based on gold standard data revealed that instantaneous subsets of tcpes exist which estimate the femur pose with reasonable accuracy median root mean square error during stance swing 1 4 2 8deg for orientation 1 5 4 2mm for position a non invasive and instantaneous criteria to select accurate tcpes for pose estimation 4 8 7 3deg 5 8 12 3mm was compared with rbls 4 3 6 6deg 6 9 16 6mm and hdls 4 6 7 6deg 6 7 12 5mm accounting for homogeneous deformation using hdls or selected tcpes yielded more accurate position estimations than rbls method which conversely yielded more accurate orientation estimations further investigation is required to devise effective criteria for cluster selection that could represent a significant improvement in bone pose estimation accuracy

a solidification procedure to facilitate kinematic analyses based on video system data abstract when video based motion analysis systems are used to measure segmental kinematics the major source of error is the displacement of skin fixed markers relative to the underlying skeletal structure such displacements cause the marker representation of the segment to deform thereby decreasing the accuracy of subsequent three dimensional kinematic calculations we have developed a two step solidification procedure to address this problem first the mean rigid shape is computed which best represents the time varying marker configuration of each segment second a least squares minimization is used to replace the measured marker coordinates with those corresponding to the best fit mean rigid shape rigid body theory can then be applied unambiguously to perform kinematic analyses to evaluate this approach we defined an unperturbed three dimensional reference movement using kinematic data from the swing phase of gait after perturbing the marker coordinates with artificial noise the rotation matrix and translation vector absolute and relative movement between each pair of successive images were computed using 1 reference frames fixed directly to the perturbed marker coordinates 2 a least squares minimization procedure found in the literature and 3 the proposed solidification procedure the least squares and solidification procedures produced extremely similar results which relative to the direct calculation reduced kinematic errors on average by 20 25 when the maximum distance between markers was small e g

a correction for axis misalignment in the joint angle curves representing knee movement in gait analysis this paper derives a simple mathematical model relating changes in the orientations of the two cartesian coordinate systems involved in recording knee movement and the varus valgus and the internal external rotation angles for describing the knee s motion rotation matrices are given for changing the orientations of the two cartesian coordinate systems in such a way that the quadratic variations in the varus valgus and in the external internal angles are minimal these estimated rotation matrices are used to correct for axis misalignment the correction is calibrated by considering the impact of the new orientation of the thigh cartesian coordinate system on the hip joint angles the procedure is applied to kinematic data collected on normal subjects the uncertainty about the specification of the thigh cartesian coordinate system is shown to explain some of the between subject variability in the varus valgus and in the internal external rotation angles curves

influence of geometrical distribution of common points on the accuracy of coordinate transformation geometrical distribution of common points is of significance for coordinate transformation as the transformation parameters are computed through common points whose coordinates are known common points can be divided into a calculating set and a testing set whose geometrical distribution can be described by internal and external distribution parameters the former contains the number of points the reference coordinate and the coordinate difference the latter is defined as the overlapping degree between both sets both a rotation matrix and a translation vector are involved in the transformation parameters and could be evaluated by 3 approaches i e the coordinate error method the rms error method and the error method of relative euclidean distance an invalidation of the third method has been proven that evaluating indexes will remain invariant for a fixed testing set regardless of variation in the calculating set according to the classification of geometrical distribution of common points the influences of internal and external distribution parameters on the accuracy of coordinate transformation are related to the number of points symmetrical distribution and the overlapping degree which will be formulated and summarized in detail finally the above conclusions can be verified and proven by computer simulation and practical experiment respectively

a least squares algorithm for the equiform transformation from spatial marker co ordinates the present paper describes an algorithm for estimating the translation vector and the rotation matrix of a moving body from noisy measurements on the spatial co ordinates of at least three non collinear markers a sensitivity analysis of the estimated parameters and of the helical axis is presented in terms of characteristics of the marker distribution the implementation of the proposed algorithm in a fortran subroutine is appended

method of and device for speech signal coding and decoding by parameter extraction and vector quantization techniques this method provides a filtering of blocks of digital samples of speech signal by a linear prediction inverse filter followed by a shaping filter whose coefficients are chosen out of a codebook of quantized filter coefficient vectors obtaining a residual signal subdivided into vectors each vector is classified by an index q depending on the zero crossing frequency and r m s value it is then normalized on the basis of the quantized r m s value and then of a vector of quantized short term mean values the mean square error made in quantizing said vectors with vectors contained in a codebook and forming excitation waveforms in computed in this codebook the search is limited to a subset of vectors determined by index q and p of short term mean vector the coding signal consists of the index of the filter coefficient vector of indices q p of quantization index m of the r m s value and of the index of the vector of the excitation waveform which has generated minimum weighted mean square error fig 1

method of and device for coding speech signals with analysis by synthesis techniques the set of possible excitation signals is subdivided into a plurality of subsets the first of which provides the contribution to the coded signal necessary to set up a transmission at a minimum rate guaranteed by the network while the others supply a contribution which when added to that of the first subset causes a rate increase by successive steps at the receiving side a decoded signal is generated by using the excitation contribution of the first subset alone if the coded signals are received at the minimum rate while for rates higher than the minimum rate the contributions of the subsets which have allowed such rate increase are also used

optimal marker placement for calculating the instantaneous center of rotation abstract a computer simulation with error propagation was performed to determine the optimal placement of marker points for calculating the instantaneous center of rotation cri the authors assume that planar rigid body motion occurs between two positions each defined by marker points noisy marker points were generated by perturbing their coordinates with random values from a normal population of errors the effects of these errors on the range of errors in calculating cri location were investigated parametric analysis determined that marker point placement had important effects on cri error marker placement was optimal when the estimated cri was located at the midpoint between the marker points while increasing the distance between marker points increased accuracy there is a critical distance above which no additional increase in accuracy was noted when using this placement the farther the marker midpoint was from the cri the greater was the error at these placements increasing the distance between the marker points continually decreased cri error the methodologies presented here help to improve the accuracy with which the location of the cri can be calculated however it is emphasized that the cri remains sensitive to noise and investigators should apply this kinematic parameter knowingly

bias compensated least squares estimate of the center of rotation abstract it is shown that a recently published least squares method for the estimation of the average center of rotation is biased consequently a correction term is proposed and an iterative algorithm is derived for finding a bias compensated solution to the least squares problem the accuracy of the proposed bias compensated least squares method is compared to the previously proposed least squares method by monte carlo simulations the tests show that the new method gives a substantial improvement in accuracy

rigid and non rigid geometrical transformations of a marker cluster and their impact on bone pose estimation when stereophotogrammetry and skin markers are used bone pose estimation is jeopardised by the soft tissue artefact sta at marker cluster level this can be represented using a modal series of rigid rt translation and rotation and non rigid nrt homothety and scaling geometrical transformations the nrt has been found to be smaller than the rt and claimed to have a limited impact on bone pose estimation this study aims to investigate this matter and comparatively assessing the propagation of both sta components to bone pose estimate using different numbers of markers twelve skin markers distributed over the anterior aspect of a thigh were considered and sta time functions were generated for each of them as plausibly occurs during walking using an ad hoc model and represented through the geometrical transformations using marker clusters made of four to 12 markers affected by these stas and a procrustes superimposition approach bone pose and the relevant accuracy were estimated this was done also for a selected four marker cluster affected by stas randomly simulated by modifying the original sta nrt component so that its energy fell in the range 30 90 of total sta energy the pose error which slightly decreased while increasing the number of markers in the marker cluster was independent from the nrt amplitude and was always null when the rt component was removed it was thus demonstrated that only the rt component impacts pose estimation accuracy and should thus be accounted for when designing algorithms aimed at compensating for sta