Comparative Analysis on the Filtering Methods of Human

Kinematics Data

Hongbing Ba

, Jihe Zhou

IAba Teachers University,Shuimo Town, Aba Prefecture , China

Chengdu Sport Institute,Chengdu City,Sichuan , China

Keywords: Kinematics data，Filtering Method，Comparison analysis.

Abstract: In this paper, the infinite pulse filter was analyzed in the comparative experiment method. Through the

experimental analysis: In particular, the need to deal with extreme values of human motion data, to give

priority to low-pass filter, the data changes are relatively smooth to consider using infinite pulse filtering.

Due to the continuity of human motion and given that the data end distortion rate is higher than the initial

one, it is necessary to take some extra frames after the action keyframes to reduce the error caused by end-

of-sequencedistortion.

1 INTRODUCTION

Human kinematics data obtained by sports

biomechanics needs to be smoothed by low-pass

filter generally. In this paper, the infinite pulse filter

was analyzed in the comparative experiment

method, in order to understand the effect of the two

methods in obtaining the human kinematics data.

2. RESEARCH METHODS

2.1 Research Object

The research object of this paper is the FIR filter,

including low pass filter (fourth-order butter worth

filter) and IIR filter (the standard filter function is

butter worth filter).

Usually, data collected from human kinematics

can be classified into three basic motion forms:

linear motion, quadratic function type motion and

trigonometric function type motion. In this

study[1],the horizontal (X) motion data in oblique

motion was used as linear signal data , the vertical

(Y) motion data was used as two quadratic function

type (parabolic type) signal data and the horizontal

(X) motion data in the swing was used as triangular

function type data.

2.2 Experimental Analysis Method

2.2.1 Experimental Data Acquisition

Two BASLER A6 high-speed cameras were used to

shoot balls (tennis) respectively for oblique motion

and simple pendulum motion with shooting

frequency of 200 Hz, and the trajectories of balls

should be closely and parallel to the vertical and flat

wall with potable paper.

2.2.2 Experimental Data Processing

The high- titanium 3D V1.0C video analysis system

produced by Beijing Senmiaoxin Company was used

to analyze and process the image data, and dot with

vibration amplitude (i.e. output frequency of

100Hz), and two kinds of filtering methods were

used to smooth respectively. The differences

between the results were compared after the

processing of two filtering methods. The data after

processing were processed with Excel 2003 and

SPSS17.0.

2.2.3 Reference Standard

The image with sampling frequency of 200Hz was

processed by the Adobe Photoshop CS2 9.0 software

frame by frame, dotted amplitude by amplitude after

image magnification. The coordinates (pixels) of the

center of the ball were recorded accurately, and then

converted to the actual coordinates.

Then the EXCL was used to trace point and

connect lines, and then the Adobe Photoshop CS2

9.0 software was used again to obtain the coordinate

of the center of the balls, which was the reference

standard.

Table 1: the average deviation of data processed by different smoothing methods (units: centimeters).

The reasons for choosing it as the reference were

that:

(1) It was easy to mark the center of the ball by

magnifying the ball, and it is of high accuracy to

identify the coordinates by the pixel coordinates.

(2) The image with acquisition frequency of

200Hz is more accurate than that of 100Hz in actual

processing.

2.2.4 Error Evaluation Method

The average deviation was used to evaluate the

error, that is, the average displacement difference

between the position and the corresponding

reference standard position in each frame was the

average deviation. That is:

(1)

( was the distance between the displacement and the

reference standard displacement after the

smooth treatment at )

3 RESULTS AND ANALYSIS

3.1 Comparative Analysis on the

Smoothing Errors of the Two

Filtering Methods

The three types of data were processed by two kinds

of filtering methods with the cut-off frequency of

6Hz. Considering the distortion rate of the end of

filtering, the data at the end part was truncated, with

5 frames and 10 frames in the slanting motion (90

frames left), 10 frames and 40 frames in the

oscillating motion, (390 frames left), and then the

error of the result was compared to determine the

effect of various filtering methods.

From table 1, it can be concluded that, in general,

two kinds of filtering methods were different in

dealing with the error of three kinds of signal data

types, and the low-pass filtering method was better

in effect. For the three kinds of signal types, the

error of oblique horizontal motion (X direction) was

the largest, that of the oblique vertical motion (Y

motion) was the second, and that of the swing

horizontal motion (X motion)was the smallest.

In the linear data signal type, the filtering effects

had significant difference. In the case of the same

cut frequency, the effect is that the low pass filter is

better than the infinite pulse filter.

In the processing of the quadratic function type

data, the effect of the low pass filter is better in the

two filtering methods.

3.2 Phase Analysis

The high efficiency of IIR filter is at the expense of

nonlinearity. The IIR filter with better selecting

performance will be worse in phase characteristic,

but the FIR filter can get a strict linear phase. So the

IIR filter is used for data processing with low phase

requirement. If the phase request is strict, FIR filter

is better than IIR filter in performance and economy.

IIR filter is used in speech processing with low

phase requirements, while FIR filter is used in the

processing of relative sensitive image data signals

[2] .

The horizontal displacement (X direction

motion) in the projectile motion, oblique vertical

∑

displacement (Y direction motion) and swing

horizontal displacement (X direction) data were

taken as the research objects respectively, and

filtered by two different filtering methods (cut

frequency of 8Hz).

In order to quantify the difference, the 90 frame

data of the oblique projectile X direction motion

were selected for linear programming. The

programming model is as follows:

（2）

Table 2 :Linear programming after data processing of

oblique projectile X direction motion .

(The P value is 0.000, indicating that only the

first three decimal digits are displayed after

computer computing)

It can be seen from Table 2 that the correlation

coefficient R2 was greater than 0.98, and the

probability was less than 0.001, so the fitting of data

after the processing of various methods was very

significant. The comparison of slope k showed that

low pass filtering was closer to the slope of

reference standard and the slope of infinite pulse is

less than standard. The comparison of phase

difference showed that infinite pulse filtering had

obvious phase retardation.

Therefore, in the case of the overall rising trend,

the slope of infinite pulse filter is the least, and it can

delay the change of data in the data processing.

The first 90 frame data of the oblique projectile

X direction motion was selected for quadratic

programming. The programming model was as

follows:

（3）

It can be seen from table 3 that the correlation

coefficient R2 was greater than 0.99, and the

probability P was less than 0.001, so the fitting of

data after the processing of various methods was

very significant. According to the law of the

parabolic function image, it can be known that the

value of the coefficient a was negatively correlated

with the size of the opening. It can be concluded that

the low pass filter was equivalent to the reference

standard, and the opening of the infinite pulse was

slightly larger than the standard.

Table 3 :Quadratic programming after data processing of

oblique projectile X direction motion.

(The P value is 0.000, indicating that only the

first three decimal digits are displayed after

computer computing)

Therefore, in the case of the overall downward

trend, the opening of the image was downward while

the opening of the infinite pulse filter was the

smallest. As a result, the downward trend was

slower and the phase was delayed, so the change of

data was delayed too.

The first 400 frames data of the oblique

projectile X direction motion was selected for

nonlinear programming. The programming model

was as follows:

（4）

Table 4: Nonlinear programming after data processing of

wobble X direction motion.

(The P value is 0.000, indicating that only the

first three decimal digits are displayed after

computer computing)

It can be seen from table 4 that the correlation

coefficient R2 was greater than 0.998, and the

probability P was less than 0.001, so the fitting of

data after the processing of various methods was

kt C=+

Yat btC=++

sin( )XA btcd=++

very significant. The value of the parameter B in the

table showed the frequency of the signal data after

various processing, and it can be seen that the

difference between the low pass filter and the

infinite pulse was small. The comparison of phase

difference showed there is little difference in the

whole, and the infinite pulse was slightly backward

than the low pass filter phase.

3.3 Endpoint Distortion Analysis

The data after the processing of filtering and

smoothing was distorted[3], and the related research

has confirmed that the distortion rate at the end of

the data sequence was larger than that at the

beginning of the data sequence [4]. We are

discussing the degree of the distortion at the end

now. The degree of distortion was measured by an

average deviation of D in this experiment. The

original data of oblique horizontal motion (X

motion), oblique vertical motion (Y motion) and

swing horizontal motion (X motion) was filtered by

various filtering methods (cut frequency of 8Hz),

and then compared with reference standard data. The

average deviation between the first 10 frames and

the last 10 frames was selected to compare.

Table 5 :Comparison of beginning and end distortion after

filtering processing (unit: cm).

It can be seen from table 5 that the degree of

distortion of the beginning and the end was ranked

according to size as infinite pulse filter and low pass

filter. In the case that the filtered data was distorted

at the beginning of the original data sequence larger

than the end of the sequence, the distortion of the

end of the two filtered data was greater than the

beginning, and the distortion of low pass filter was

the smallest.

3.4The Influence on the Extremum

Generally, smoothing the data will have an effect on

the maximum and minimum[5]. Over smoothing

will weaken the extreme value, that is, the minimum

value will increase and the maximum value will

decrease. The higher the truncation frequency is, the

more extreme the value is weakened. Different

processing methods have different effects on the

extremum. In this study, these two filtering methods

(cut frequency of 8Hz) were used to compare the

extreme values obtained by smoothing the oblique Y

motion and the swing X motion data with extreme

values and the reference extreme values.

Table 6 The influence of different filtering methods on the

extremum (unit: meter).

(Due to only the Oblique Y motion had a

maximal value, and the swing X motion had

maximum and minimum in the data collected, so

only the three extremums were discussed)

It can be seen from the data in Table 6 that the

data of oblique Y motion reduced after the

processing of low-pass filter and infinite impulse

filter, and reduced a lot after the smoothing of

infinite impulse; as for thedata of swing X emotion,

the maximum and minimum was equal to the

standard after the processing of low pass filter, the

maximum after the processing of infinite impulse

filter became small and the minimum became large.

In the two filtering methods, the extremum-

keeping of the low pass filter was stronger and the

infinite impulse filter weakened the extremum

greatly.

4 CONCLUSIONS AND

SUGGESTIONS

Through the above analysis, the following

conclusions and suggestions are obtained:

4.1 Conclusions

In general, no matter what data is processed, the

performance of low-pass filtering is better; when

dealing with trigonometric data, there is basically no

difference between low-pass filtering and infinite

pulse filtering.

Low-pass filter can maintain a good phase,

infinite pulse filter phase delay more obvious

changes more slowly, the mutation of the data has a

stabilizing effect.

There are data distortion problems in both filters.

Generally, the distortion rate of the filter results at

the end of the sequence is slightly larger than the

distortion rate at the beginning.

Under the same cut-off frequency, the low-pass

filter has the ability to maintain the extreme value,

and the infinite pulse filter to the extreme weaken.

4.2 Suggestions

In particular, the need to deal with extreme

values of human motion data, to give priority to low-

pass filter, the data changes are relatively smooth to

consider using infinite pulse filtering.

Due to the continuity of human motion and given

that the data end distortion rate is higher than the

initial one, it is necessary to take some extra frames

after the action keyframes to reduce the error caused

by end-of-sequence distortion.

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and Telecommunications Press, 2005, 9

4. Cleve B.Moler.Numerical computing with

MATCAB[M].society for Industrial Applved

Mathematics . 2004.

5. Liu Weimin and others.Effect of Data Smoothing on

the Extremum in Kinematic Data--taking the digital

low pass filtering method as an example[J]. Shandong

Sports Science & Technology, 2000, 12 (4)