A PCA based bio-motion generator to synthesize new patterns of human running

Synthesizing human movement is useful for most applications where the use of avatars is required. These movements should be as realistic as possible and thus must take into account anthropometric characteristics (weight, height, etc.), gender, and the performance of the activity being developed. The aim of this study is to develop a new methodology based on the combination of principal component analysis and partial least squares regression model that can generate realistic motion from a set of data (gender, anthropometry and performance). 18 volunteer runners have participated in the study. The joint angles of the main body joints were recorded in an experimental study using 3D motion tracking technology. A five-step methodology has been employed to develop a model capable of generating a realistic running motion. The described model has been validated for running motion, showing a highly realistic motion which fits properly with the real movements measured. The described methodology could be applied to synthesize any type of motion: walking, going up and down stairs, etc. As future work, we want to integrate the motion in realistic body shapes, generated with a similar methodology and from the same simple original dat. Abstract 14 Synthesizing human movement is useful for most applications where the use of avatars is 15 required. These movements should be as realistic as possible and thus must take into account 16 anthropometric characteristics (weight, height, etc.), gender, and the performance of the activity 17 being developed. The aim of this study is to develop a new methodology based on the combination 18 of principal component analysis and partial least squares regression model that can generate 19 realistic motion from a set of data (gender, anthropometry and performance). 18 volunteer runners 20 have participated in the study. The joint angles of the main body joints were recorded in an 21 experimental study using 3D motion tracking technology. A five-step methodology has been 22 employed to develop a model capable of generating a realistic running motion. The described 23 model has been validated for running motion, showing a highly realistic motion which fits properly 24 with the real movements measured. The described methodology could be applied to synthesize 25 any type of motion: walking, going up and down stairs, etc. As future work, we want to integrate 26 the motion in realistic body shapes, generated with a similar methodology and from the same 27 simple original data.

Introduction 75 a bio-motion generator which will solve the opposite problem of synthesizing new realistic 76 movements.

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In addition, existing literature focused on synthesizing motion does not correlate the generated 78 movement to age, gender, performance parameters such as velocity or anthropometrical features.
79 In this sense our research has three goals. The first one is to generate a database of running

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This procedure allowed us to obtain six observations representing the whole range of speeds 147 that each subject could execute.

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Mathematical procedure 149 The methodology used in our study comprised 5 steps:

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PLS methodology is explained in Wold (2006) and Geladi (1986). . This type of regression 222 model is suitable for the kind of data involved in the bio-motion generator since the input data of 223 the model is strongly correlated (anthropometrical information).

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The PLS regression model takes the 1D data -age, height, weight and velocity-as input 225 information and produces a set of PCA scores as output. The LRM model was applied to these 226 output PCA scores to reflect the influence of gender in the PCA scores.

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In the first step, we estimated a PLS model considering anthropometrical data and velocity of 228 the movement as independent variables and the PCA scores as dependent variables. The general 229 formula of a PLS model is: where is the matrix of dependent variables, is the matrix of independent variables, and

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Where is the matrix of mean anthropometrical data and velocity, and is the prediction  where is the matrix of mean anthropometrical data and velocity.

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Where σ c is the combined standard deviation of the true scores (T c ) and observed scores (E c ).
281 And S E is the combined standard deviation of the true scores and observed scores.

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We have obtained the SEM for each pair of true and predicted angles for the three spatial 283 directions in all the joints that form the human model. For that reason, we have represented the 284 SEM by its descriptive statistics (mean, std., 5-percentile and 95-percentile).

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Parallel analysis 287 The results of the PA (Fig. 2)

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Regression model 298 As it has been explained in the methodology, the regression model consists of two parts, the 299 first including the anthropometrical data (PLS) and the second the gender (LRM). The dependent 300 variables of the PLS are the scores of the first 12 principal components (PC) of the kinematical 301 running motion. Therefore, they are uncorrelated and the optimal number of PLS components are 302 separately determined for each PC score (PC 1... PC 12) according to its adjusted R 2 plot (Fig. 3).
303 PLS components are retained until their R 2 curve exhibits a decrease or a non-significant increase.
304 Thus, for instance, two PLS components are retained for PC 1, whereas no components are 305 considered for PC 7 and PC 9. Notice that for those PC with 0 retained components, the PLS model 306 provides their mean value as output. This way, the motion information associated to those PC 307 which is provided by the PLS model is the average motion.  Validation of the bio-motion generator 319 The results of the reliability study, computed from the 90 observations and the same calculated 320 by means of the leave-one-out technique, showed that the mean and standard deviation of ICC, 321 was 0.91(0.04) with a 5 percentile of 0.829 and 95 percentile of 0.971. Only one subject exhibit 322 an ICC lower than 0.8 in 2 observations (Fig. 4).

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In this paper we have demonstrated that the five-step methodology on which the bio-motion 332 generator is based provides running motion models closely resembling the measurements obtained 333 with real subjects. However, while the SEM study shows that the vast majority of errors detected 334 between actual and predicted data of the bio-motion generator are less than 10°, there are a 335 percentage of observations (8%) in which greater errors are observed. This can be explained 336 because the model has been obtained from a small number of subjects --only 18--and therefore 337 the bio-motion generator is not able to adjust the running specific characteristics of each corridor.

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The fifth step of the methodology consists of a two-step linear regression which correlates a 354 given list of 1D measurements with the PCA scores of movement. A linear regression technique 355 has been used before to approximate motion models from a reduced marker set and estimate the 356 remaining markers (Liu et al. 2005) or to model the motion-style and the spatio-temporal 357 movement (Torresani, Hackney, and Bregler 2006). However, it has not been used before to 358 synthesize new human motion directly from a set of anthropometrical and performance data. In 359 this sense, it can be considered a real breakthrough in the field of synthesis of human motion.

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The major contribution of this paper is a novel statiscal methodology for modelling human 362 movements. The method described in this article has been developed and validated for running 363 motion, but this same methodology could be used to synthesize other types of motion: walking, 364 going up and down stairs, or even for sport movements such as: jumping, pedalling, golf swing 365 and putting, etc.

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Our work aims to provide a realistic motion to body shapes that can be developed with the 367 methodology described in the work of Ballester et al. (2014). Those body shapes could include an 368 adjusted skeleton formed by a hierarchical set of interconnected joints and can be used to move 369 the body shape with the required or desired motion provided by our methodology (Fig. 6). The 370 integration of both methods will allow generating realistic avatars supplied with realistic motion 371 from a set of adjustable and simple anthropometrical and performance data and without the need 372 of the realization of new measurements.

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A limitation of this study is the sample size. Further work needs to be done in order to validate 374 with a broader sample of people. Notwithstanding this limitations, the findings suggest that the 375 model is valid. Fig. 6: Reconstructed virtual biomechanical model (skeleton+motion).