Gait parameters for identification purposes

Vrije Universiteit

Faculty of Human Movement Science

Specialization: Human Movement System

Research project

Author: Menno Merlijn

Supervisor: Gert de Groot

Jurien Bijhold

Zeno Gerardts

June 2000

Contents

	Page
Abstract	3
Introduction	4
Methods	7
Results	12
Discussion	22
Conclusions	27
Appendix	28
References	34

Abstract

The gait parameters of eleven subjects were evaluated to provide data for identification purposes of subjects. The subjects were filmed (video, 50Hz) in frontal, transversal and sagittal view. The subjects walked by at their favorite walking speed. The measured parameters were hip, knee and ankle joint angle and their time averaged values, thigh, foot and trunk angle, step length and width, cycle time and walking speed. Correlation coefficients within and between subjects for the hip, knee and ankle rotation pattern in the sagittal aspect and for the trunk rotation pattern in the transversal aspect were almost similar. This implies that the intra and inter individual variance were equal. There for these gait parameters could not distinguish between subjects. In order to detect significant differences for the mean hip, knee and ankle joint angle, thigh angle, the step length, step width, walking speed, cycle time and foot angle a simple ANOVA with a follow-up test was used. The number of significant difference between subjects defined the usefulness of the gait parameter. The best parameter with most significant differences between subjects was the foot angle (64 % - 73 % of the maximal attainable significant differences), followed by the time average hip joint angle (58 %) and the step length (45 %). The other parameters score less than 25 %, which is poor for identification purposes.

To investigate the possibility of time-lapse video, time average hip joint angle (α_m) is also analyzed in time-lapse video (12.5 Hz). A small, but negligible decrease in the number of significant differences between subjects was found (from 58 % to 56 %). This means that for α_m time-lapse video is useable for identification purposes.

Introduction

Nowadays bank robberies and other crimes are often filmed with video cameras, placed at stores, banks and squares. These videotapes are offered to the ‘Nederlands Forensisch Instituut’ (N.F.I.) with the question to identify one or more persons. If a robber has covered his face the identification is more difficult. Then the question is asked if it is possible to compare the gait of the robber with the gait of the suspect. For this purpose it is necessary that some of the gait parameters have subject characteristic features.

Human gait contains numerous parameters. These parameters could be categorized into spatial-temporal and kinematic parameters. Because it is impossible to investigate all gait parameters in this study a selection has been made on the criteria that the gait parameters could probably also be obtained in non-laboratorial settings and could be characteristic for a person. Spatial-temporal parameters that will be investigated are step length, step width, walking speed and cycle time. There is a high correlation between step length and height of a person (Murray et al. 1964)(Grieve & Gear 1966), what indicates that step length could be differs between subjects if there are differences in height. Step width could contain information about the coordination of the person. An increased step width could be related with stabilization problems (Gary 1990). Walking speed and cycle time are measured for practical usage in obtaining some of the kinematic parameters. Kinematic parameters that will be investigated are joint rotations of the hip, knee and ankle, mean joint angles of the hip, knee and ankle and thigh, trunk and foot angles. Because of the frequent use of joint rotations of the hip, knee and ankle joint in literature these parameters are used in this study (Murray et al. 1964)(Gary 1990)(Hills & Parker 1991)(Frigo & Tesio 1986)(Eng & Winter 1995). The mean joint angle is not investigated in literature, but could contain some additional information about the joint angle of a person. In the thigh angle there could be a difference in valgus or varus position of the legs between subjects. The trunk and foot angle are used, because they are necessary for stabilization purposes (Hills et al. 1991).

To obtain the spatial-temporal and kinematic parameters the subject has to be filmed in three different views. For the kinematic parameters a sagittal or transversal view is necessary. For the kinematic parameters hip, knee and angle rotation and the mean hip, knee and ankle joint angle have to be filmed in the sagittal view. The thigh rotation has to be filmed in a transversal view, and the trunk and foot angle have to be filmed in the transversal view.

In practice most of the times one camera is placed. This means that the subject is captured in 2D. In laboratorial settings it is possible to film in 3D. Other options are 2x2D or 3x2D, which use respectively 2 or 3 unsynchronised cameras. In gait studies all kind of analyse methods are used. But the 2D or 2x2D are most common in research to gait parameter, like step length, step width, joint rotations, etc. (Murray et al. 1964)(Hills & Parker 1991)(Yamasaki et al. 1991). When 3x2D is used all aspects of the walker could be filmed and analysed separately. In this study gait parameters that appear in all three dimensions are filmed. This implies that a 3x2D or 3D film technique would be necessary.

To investigate the possibility of gait recognition for identification purposes gait parameters have to be obtained that differ between people. This could be realised by investigating peoples gait in a laboratorial setting. The advantage of a laboratorial setting is that it is more controllable, like camera position and a good light condition. The disadvantage of the laboratorial setting is that it is not directly comparable with the in practice settings. Parameters that could be used for recognition in laboratorial settings could be hardly useful in practice settings.

The best way to obtain these characteristic parameters is under circumstances that exact body points could be acquired. Placement markers at the requested positions could do this. When markers are attached to clothing the marker could shift by movement of the clothing. This will result in a wrong position of the marker what would influence the results. To avoid that problem, markers should be attached to the skin. Then only skin movement with respect to the bones disturb the position data. This indicates that the best way to obtain body positions clothing need to be absent.

Subjects have to walk at their favourite walking speed to detect the gait characteristics like step length (Rose & Gamble 1994). Walking velocity appeared to be a parameter that affects the movement pattern. If a person walks a favourite walking speed and is forced to walk faster to the rhythm of a metronome, that tells the subject to walk with a higher frequency, stride length will be decreased. The decreased stride length could be explained by the fact that the subject has to accommodate to the new step frequency (Gary 1990).

Movement characteristics could contain person specific properties. This study investigates the possibility to identify a person on gait parameters. Under the following conditions: a 2D camera set-up in the sagittal, frontal and transversal views with no extra light exposure films the subject, with the absents of clothing excepted shoes, and supplied with markers on the shoulder, hip, knee, ankle, metatarsophangealis and on the toecap. The subject walked with a favourite walking velocity. The result might be a list of parameters with a high inter individual and a low intra individual difference.

Frequently in practice there is a low sample frequency (time-lapse video) to save space on the tapes. If it is possible to recognise people by their gait specific parameters, then the question could be asked if it is also possible with time-lapse video. This study will also look if it is possible to identify a person on gait parameters in time-lapse video by reducing the analysed sample frequency from 50 to 12.5 Hz.

Methods

Subjects

Eleven healthy college students, with a mean age of 23.2 years, mean height of 182 m, and mean body mass of 73.5 kg, participated in this study (see table 1). They had no known lesions of lower extremity.

	Mean (sd)
Age	23.2 (± 2.6) years
Height	182.4 (± 6.9) cm
Weight	73.5 (± 2.6) kg

Table 1. Subject characteristics.

Protocol

The subjects were provided with little bulb markers with the size of 3 cm, positioned at the left and right shoulder joint (M_2, M₁) (tuberculum majus of the humerus), left and right hip joint (M_4, M₃) (trochantor major), left and right knee joint (M₆, M₅) (epicondylus lateralis of the femur), right ankle joint (M₇)(malleolus lateralis), left and right toe joint (M₉, M₈)(articulatio metatarsophangeales) and the left and right toecap (M₁₁, M₁₀). The marker positions are presented in figure 1. The subjects wore their underwear and shoes. The subjects were asked to walk with their favourite walking speed along the cameras. For each subject seven trials were for data analysis. The subjects were asked to look at a piece of paper, which hang at 1.5 m height in front of them. This makes the subjects walk straight up and distract them of thinking of the walking. The subject walked about 7 meters straight, after 2.5 meters the subject was filmed till about 6 meters. After the 7 meters the subject turned to the right and walked back for the next trial.

Camera and camera positions

The data for this study were obtained in two different camera set-ups. By the first run the subjects are filmed by two camera’s at right angles to the transversal and frontal view. A digital video camera (Sony: DCR-TRV-9E) for the transversal and a S-VHS camera for the frontal aspect were used; both of them had a frame rate of 50 Hz. The cameras were not synchronised (2x2D). In the second run the subjects were filmed at right angles to the sagittal view using a digital camera (Sony: DCR-TRV-9E). At least one step cycle time is filmed.

To calibrate the system a calibration frame was used: horizontal and vertical was 1 meter. No additional lighting was used.

The filmed data were captured into a computer and then analyzed with the software package WINalyze. This program detects the position of the visible markers in all of the captured frames. The image positions of the markers were transported to Matlab and Excel. In these programs spatial-temporal en kinematic parameters of the gait were calculated.

Figure 1. Presents the positions of the markers and the calculated angles. M₁ and M₂ are the right and left tuberculum majus of the humerus, M₃ and M₄ are the right and left trochantor major, M₅ and M₆ are the right and left epicondylus lateralis of the femur, M₇ is the malleolus lateralis, M₈ and M₉ are the right and left articulatio metatarsophangeales, M₁₀ and M₁₁ are the left and the right toecap.

Sagittal view

The used kinematic parameters are hip, knee and ankle joint angles (figure 1). The hip joint (a) is defined by the angle between the trunk and the thigh. The knee joint (b) is defined by the angle between the thigh and lower leg. The ankle joint (g) is defined by the angle between the lower leg and the foot. These parameters were determined during one step cycle. The step cycle started at the moment the largest hip rotation angle was reached. That is approximately at the moment that the foot leaves the ground.

Other parameters could be obtained out of the joint angles, like highest, lowest and time averaged joint angles. Only the time averaged joint angles are calculated because in literature only small differences were found between subjects for the highest and lowest hip joint angle (Rebecca & Oatis 1995).

For the hip, knee and ankle joint angles the time average angle is calculated by

(1)

T is the cycle time. For the time average knee and ankle joint angles is a replaced by respectively b and g in (1).

Frontal view

The kinematic parameter was the thigh angle (j) (figure 1). This angle is defined by the angle between the line of the position of the marker on the hip and the marker on the knee with the vertical. This angle is measured for the stand leg at the moment that the foot of the leg in the swing phase passes the stand leg.

Transversal view

The kinematic parameters are the foot (d) and trunk (y) angle. The foot angle is defined by the angle between the line of the marker on the toecap and the marker on the toe joint with the movement direction in which the movement direction is determined by the x-axis of the transversal camera view (figure 1). The foot angle is calculated at the instant the foot is positioned visually at the ground, just before the foot is out of sight through the body of the subject, which moves over it. The trunk angle is defined by the angle between the markers on the shoulders with the movement direction (figure 1).

For the trunk angles the time average angle is calculated in the same way as the time average hip, knee and ankle joint were calculated.

The spatial-temporal parameters are step length, step width, cycle duration and walking speed. The step length and step width are defined by the difference in position of the marker on the metatarsophangeales of the right foot (M₈) and the marker on the metatarsophangeales of the left foot (M₉). The values for a left and right step are averaged. The cycle duration is defined by the time used to complete a left and right step. The cycle time is obtained by the difference in time between the third and the first step. The walking speed is defined by two times the step length divided by the cycle duration.

Marker coordinates

After the subject was filmed the videotape was digitalised (only for S-VHS) and captured (DVmaster) into the computer (P350, Windows 98). The movie files were imported in WINanalyse in which the positions of the markers were tracked in time. The output of WINanalyse is a list of coordinates for each marker, which was inserted into Matlab for the calculation of the kinematic and spatial-temporal parameters.

Data analysis and statistics

For the spatial-temporal parameters the individual mean of the different trials and standard deviation are calculated. This is also done for the time average hip, knee and ankle joint angle, the thigh angle, the foot angle and the time average trunk angle.

To determine inter individual differences in the mean values of these parameters a simple ANOVA is used. A Scheffé follow-up test is used to determine which subjects differ from each other. There is a significant different when p<0.05.

The correlation coefficient (r) between the time series of the intra individual trials quantifies the intra individual variance (r²). The correlation coefficient between the time series of inter individual trials quantifies the inter individual variance for the kinematic parameters. The mean correlation coefficient of all intra and inter individual correlation coefficients are calculated with Z-transformation *.

If the inter individual coefficient of determination is high and the intra individual coefficient of determination is low for a gait parameter, than this parameter could discriminate between subjects.

Time-Lapse video

To indicate if it is possibility to use time lapse-video for identification purposes, the best discriminating time average joint angle between subjects is analysed with a sample frequency of 12.5 Hz instead of 50 Hz. The lower sample frequency is obtained by skipping frames.

Results

Kinematic parameters

Sagittal view

The hip (α), knee (β) and ankle (γ) joint angles were calculated. To compare the joint angles of each trial and each subject the joint angles were synchronized by the use of a data cut of at the highest hip angle. After this process some of the joint angles contain more data points then one step cycle. This data was cut of so that one step cycle remain. The cycle time was normalized to exclude the variation in cycle time between intra and inter individual trials. An example curve from subject 1 of the hip joint angle in percentage of the walking cycle is presented in figure 2.

Figure 2. Plot of the hip joint angle in percentage of the walking cycle of the 7 trials of subject 1.

All intra and inter individual correlation coefficients of the time series were calculated. The lowest and highest intra and inter individual mean coefficients of determination are presented in respectively table 2 and table 3. A list with the mean correlation coefficient for each subject and between subjects could be found in the appendix (Table A1-A4).

Intra individual
Mean coefficients of determination (r^2)
	Lowest r^2	Highest r^2
Hip (α)	0.98	0.99
Knee (β)	0.31	0.93
Ankle (γ)	0.17	0.92

Table 2. The highest and lowest mean correlation coefficients with their matching explained variance for the hip, knee and ankle rotation patterns between the 7 trials within a subject.

Inter individual
Mean coefficient of determination (r^2)
	Lowest r^2	Highest r^2
Hip (α)	0.92	0.98
Knee (β)	0.05	0.88
Ankle (γ)	0.04	0.83

Table 3. The highest and lowest mean correlation coefficients with their matching explained variance for the hip, knee and ankle rotation patterns between the trials of different subjects.

Table 2 and 3 show a high intra and inter individual coefficient of determination for the hip joint angle (α). This indicates that there is little variation in hip joint angles (α). In contrast to the hip rotation pattern, there is a wide variety in the knee and ankle rotation patterns.

The coefficient of determination variance varies from low till high for the knee (β) and ankle (γ) joint angles. The parameter could be discriminate between subjects if the intra individual coefficient of determination is high and inter individual coefficient of determination is low. Table 2 and 3 shows for hip, knee and ankle this is not the case. So these parameters could not be used to discriminate between subjects.

The lowest and highest calculated time average hip (α_m), knee (β_m) and ankle (γ_m) joint angles are presented in table 4. The time average joint angles for each subject could be found in the appendix (Table A5).

Time average joint angles
	Lowest	Highest
Hip (αm)	165 º	176 º
Knee (βm)	157 º	170 º
Ankle (γm)	115 º	128 º

Table 4. Lowest and highest time averaged hip, knee and ankle joint angle (degrees) for all subjects.

To detect if there are statistically significant inter individual differences simple ANOVA is used. At least some inter individual time average joint angles were significantly different. For the average hip joint angle, F(10,66) = 103.37, p< 0.001, for the average knee joint angle, F(10,66) = 2.73, p<0.01 and for the average ankle joint angle, F(10,66) = 12.84, p<0.001. To identify which subjects differ from each other the Scheffé follow-up test is done. The results are presented in table 5. Subjects are ordered by the magnitude of the time average joint angles. This is presented in the first row of table 5a, 5b and 5c. On each following row two groups are presented (grey and white) that differ significant from each other. The ideal table in which all subjects are significant different from each other would present ten following rows. So the more rows, the better is the parameter for identification purposes. For example, in table 5a could be seen that the time average hip joint angle of subject 9 differ significant from all the other subjects. Subjects 10, 3 differ form 9,1, 4, 7, 6. Subjects 11, 5, 8, 2 form 9,4, 7, 6. And subject 1 from 9, 10, 3, 6, 7.

From table 5 it can be concluded that to distinguish between subjects the best parameter is the time average hip joint angle, which contain 4 rows of two groups that differ significant from each other. For the time average ankle joint angle only 2 rows are presented, which means that there are less inter individual significant differences than for the time average hip joint angle. The poorest parameter for detecting individual differences was the mean knee joint angle with just one significant difference between the subjects 4 and 5.

Subjects	9	10	3	11	5	8	2	1	4	7	6
	9	10	3	11	5	8	2	1	4	7	6
		10	3					1	4	7	6
				11	5	8	2		4	7	6
								1		7	6

Table 5a. Time averaged hip joint angle (α_m).

Subjects	5	1	3	2	7	9	11	10	8	6	4
	5										4

Table 5b. Time averaged knee joint angle (β_m).

Subjects	2	3	5	7	1	6	9	4	11	8	10
	2				1	6	9	4	11	8	10
		3	5						11	8	10

Table 5c. Time averaged ankle joint angle (γ_m).

The time average joint angles α_m, β_m and γ_m. The first row presents the subjects sorted by the size of the mean ankle joint angle. The following rows present two groups (grey and white column), which differ significantly from each other. More following rows indicate that more subjects differ significant form each other.

Frontal view

The thigh angle (φ) of the stand leg is measured at the moment when leg in the swing phase passes the stand leg. The subject with the lowest and highest thigh angles for the left (φ_l) and the right (φ_r) thigh are presented in table 6. A table with the thigh angles for each subject is presented in the appendix (Table A8).

Thigh angles (φ)
	Lowest	Highest
Left thigh (φl)	-11.0 º	-5.1 º
Right thigh (φr)	7.4 º	11.0 º

Table 6. Lowest and highest left and the right thigh angle in degrees.

To detect if there are inter individual differences in the thigh angle (φ) a simple ANOVA is used. For the left thigh angle, F(10,66) = 16.57, p< 0.001 and for the right thigh angle F(10,66) = 9.40, p<0.001. This indicates that at least some subjects differ significant from each other on both parameters. Table 7a and 7b presents the result from the Scheffé follow-up test in the same way described in the results from the sagittal view. From table 7 could be concluded that the best parameter to discriminate between subjects is the left thigh angle (φ_l), which contain 3 rows of two groups that differ significant from each other. For the right thigh angle (φ_r) only 2 rows are presented with groups that differ significant from each other. So less inter individual significant differences are presented for the right thigh angle. This makes the left thigh angle better for identification of subjects then the right thigh angle.

Subjects	4	6	10	11	7	9	3	1	5	2	8
	4								5	2	8
		6	10	11							8

Table 7a. Right thigh angle (φ_r).

Subject	8	3	9	6	5	10	2	11	1	4	7
	8		9	6	5	10	2	11	1	4	7
		3						11	1	4	7
			9								7

Table 7b. Left thigh angle.(φ_l).

For explanation of these tables see text and table 5 of the sagittal results.

Transversal view

For the transversal view two kinematic movement parameters are calculated. The first one is the foot angle (δ) of the left and the right foot. The foot angle is measured at the moment the foot is positioned at the ground, just before the foot is out of sight through the body of the subject, which moves over it. The second kinematic parameter is the trunk angle (ψ).

The subjects with the lowest and highest left and right foot angles are presented in table 10. A table with the foot angles for each subject is presented in the appendix (Table A10). The left foot angle (δ_l) is presented like a negative rotation for easier comparison between the left (δ_l) and the right (δ_r) foot angel.

Foot angle (δ)
	Lowest	Highest
Left (δl)	-41.1 º	-16.9 º
Right (δr)	13.7 º	31.5 º

Table 10. Lowest and highest values for the left and right foot angle (in degrees).

To detect inter individual differences in feet angle a simple ANOVA is used. For the left feet angle, F(10,106) = 106.73, p< 0.001 and for the right feet angle F(10,103) = 56.24, p<0.001. Table 11a and 11b presents the result from the Scheffé follow-up test. For an explanation about these tables see results of the sagittal view. From table 11 could be concluded that to distinguish between subjects the best parameter is the left foot angle, which contain 5 rows of two groups that differ significant from each other. The right foot angle contains 4 rows. The number of rows of both foot angles indicates that there are a numerous inter individual significant differences.

Subjects	8	11	2	6	9	7	3	5	10	4	1
	8		2	6	9	7	3	5	10	4	1
		11		6	9	7	3	5	10	4	1
			2	6	9			5	10	4	1
						7	3		10	4	1

Table 11a. The right foot angle (δ_r).

Subjects	1	5	4	10	7	6	3	9	2	11	8
	1	5	4	10	7	6	3	9	2	11	8
		5				6	3	9	2	11	8
			4	10	7		3	9	2	11	8
						6			2	11	8
							3	9	2	11	8

Table 11b. The left foot angle (δ_l).

For explanation of these tables see text and table 5 of the sagittal results.

The time series of the trunk angle (ψ) is analyzed in the same way as the joint rotations of the sagittal view. Intra and inter individual correlation coefficients and coefficients of determination are calculated. The lowest and highest correlation coefficients with the explained variance are presented in table 12. A table with all correlation coefficients is presented in the appendix (Table A12 and A13). The intra and inter individual correlation coefficient of the trunk rotation pattern were approximately the same. This indicates that the trunk rotation pattern is not a good parameter to distinguish between subjects.

Mean trunk angle correlation coefficients and explained variance
	r^2	r^2
Intra individual	0.71	0.97
Inter individual	0.64	0.94

Table 12. The lowest and highest intra and inter individual correlation coefficients and the explained variance for the trunk angle (ψ).

Spatial-temporal parameters

The step length, step width, cycle duration and walking speed are obtained from the sagittal view. The lowest and the highest values are presented in table 8. More detailed information about the parameters for each subject could be found in the appendix (Table A14).

Spatial-temporal parameters
	Lowest	Highest
Step length	751 mm	924 mm
Step width	214 mm	286 mm
Cycle duration	0.93 s	1.07 s
Walking speed	1.42 m/s	1.98 m/s

Table 8. The lowest and highest values for the spatial temporal parameters.

To detect inter individual differences for step length, step width, cycle duration and walking speed a simple ANOVA is used. For the step length, F(10,66) = 67.40, p< 0.001, for the step width F(10,66) = 6.92, p<0.001, for the cycle duration F(10,60)=7.84, p<0.001 and for the walking speed F(10,66)=15.80,p<0.001. The results of the Scheffé follow-up test for the spatial-temporal parameters are presented in table 9a, 9b and 9c. From table 9 could be concluded that to discriminate between subjects the best parameter is the step length, which contain 4 rows of two groups that differ significant from each other. The poorest parameter was the step width, which contains only 1 row. The parameters walking speed and cycle time contain 2 rows. This means that there are more inter individual significant differences for the step length than for the other spatial-temporal parameters.

Subjects	11	5	9	2	10	1	7	4	8	6	3
	11	5					7	4	8	6	3
			9					4	8	6	3
				2	10	1	7			6	3
								4			3

Table 9a. Step length.

Subjects	1	4	10	5	11	8	2	6	9	7	3
	1							6	9	7	3

Table 9b. Step width.

Subjects	5	10	11	6	2	9	8	1	4	7	3
	5	10	11							7	3
				6	2	9	8	1	4		3

Table 9c. Walking speed.

Subjects	7	1	3	9	4	11	2	8	5	10	6
	7								5	10	6
		1									6

Table 9d. Cycle time.

For explanation of these tables see text and table 5 of the sagittal results.

Summary of the results

To compare the usefulness between the investegated gait parameters a measure for discriminant power is needed. The number of inter individual significant differences could be used as measure. Because more inter individual significant differences makes a gait parameter better for discrimination between subjects. Each subject could differ significant from 10 other subjects. When a sum is made of all significant differences of all subjects for a specific gait parameter a maximum of 110 could be obtained (for 11 subjects). In that case all subjects differ significant from each other. The results for each parameter are presented in table 13. The last row presents the percentage from the maximum score that could be obtained for each parameter.

For example the left foot angle (δ_l) of subject 6 was significant different from 5 other subjects.

Table 13 shows seen that the left foot angle is the best discriminating parameter between subjects. The left foot angle scored 73% of the possible attainable significant differences; followed by the right foot angle (64%), mean hip joint angle (58%) and the step length (45%). The remaining gait parameters score 25% or less of the possible attainable significant differences.

pp	δl	δr	αm	sl	φl	γm	ws	φr	ct	sw	βm
1	10	7	5	2	2	1	1	0	1	4	0
2	8	5	4	2	1	6	1	1	0	1	0
3	7	5	5	10	4	3	9	0	1	0	0
4	6	7	7	4	2	1	1	3	0	0	1
5	7	5	4	5	1	3	2	1	1	0	1
6	5	6	8	8	1	1	1	1	3	1	0
7	6	5	8	4	3	0	3	1	3	1	0
8	9	9	4	4	9	3	1	5	0	0	0
9	7	6	10	4	2	1	1	0	0	1	0
10	6	7	5	2	1	3	2	1	1	0	0
11	9	8	4	5	2	3	2	1	0	0	0
Sum	80	70	64	50	28	25	24	14	10	8	2
	73 %	64 %	58 %	45 %	25 %	23 %	22 %	13 %	9 %	7 %	2 %

Table 13. The number significant differences between subjects for the parameters, left foot angle (δ_l), right foot angle (δ_r), mean hip joint angle (α_m), step length (sl), left thigh angle (φ_l), mean ankle joint angle (γ_m), walking speed (ws), right thigh angle (φ_r), cycle time (ct), step width (sw) and mean knee joint angle (β_m). The last rows presents the sum of each parameter with the percentage from the maximum attainable score.

Time-lapse video

Time-lapse video results are obtained by deleting three of each four frames. This decreases the visual frame rate to 12.5 Hz. The best parameter for identification purposes in the sagittal aspect was the time average hip joint angle (α_m). The results of the time average hip joint angle with a sample frequency of 12.5 Hz (α_m^12.5) and the results of the 50 Hz sample frequency obtained out of table 4 (α_m⁵⁰) are presented in table 14. A detailed table for all subjects is presented in the appendix (Table A17).

Time averaged hip joint angles (αm^50 and αm^12.5)
	Lowest	Highest
αm^12.5	164.5 (±0.70) º	176.0 (±1.33) º
αm^50	164.8 (±0.55) º	175.7 (±0.94) º

Table 14. The lowest and highest mean hip joint angle in degrees with the standard deviation by a sample frequency of 12.5 and 50 Hz.

There is just a small difference in the lowest and highest mean hip joint angle if a lower sample frequency is used. Especially the standard deviation increased. This means that there is more variation within the different trials of the subject. The results of the simple ANOVA for the time average hip joint angle with a 12.5 Hz sample frequency was, F(10,66) = 67.91, p<0.001. The Scheffé follow-up test is presented in table 15. For an explanation about this table see results of the sagittal view. This table contains 4 rows with 2 groups that differ significant from each other. That is the same result as for the time average hip joint angle with a 50 Hz sample frequency. When the percentage of maximal the maximum significant difference scores is calculated (described in summery of results) 56% is found instead of 58% for a 50 Hz sample frequency. This indicates that the discrimination possibility is approximately the same for the 12.5 and 50 Hz sample frequencies.

Subjects	9	10	3	11	5	8	2	1	4	7	6
	9	10	3	11	5	8	2	1	4	7	6
		10	3					1	4	7	6
				11	5	8			4	7	6
							2	1		7	6

Table 15. Mean hip joint angle (α_m^12.5).

For an explanation of this table see see text and table 5 of the sagittal results.

Discussion

Sagittal

The results from the intra and inter individual correlation coefficients of the hip joint angle showed that there was little variation in the hip joint angle within and between individuals. This agrees with the findings of Murray et al. (1964).

The knee and angle joint angles showed a variance in rotation patterns within and between subjects. This was in contrast with the findings of Murray et al. (1964) who found almost identical curves for the knee and ankle rotation patterns within and between subjects. A possible explanation for the wide variance within and between subjects in knee and ankle rotation pattern could be the result of three different problems. The first problem is the measure procedure. There is a poor accuracy of obtaining the coordinates of the markers when the leg is in the swing phase, because the markers on the ankle and foot have a high velocity. This makes it difficult to obtain the proper position for the markers in the swing phase. Murray et al. (1964) used interrupted-light photography with light reflecting strips attached to each segment. This makes the whole thigh, lower leg and foot visible. More marker positions will make the gathering of the coordinates more accurate. A second problem is a data analyse problem. To obtain one step cycle the beginning of the step cycle is determined by the moment that the hip joint is maximal. That is approximately at the moment that the foot leaves the ground. It could be, that the rotation pattern is not exactly synchronized between the hip and the knee, and the hip and the ankle. There could be a little time delay in the knee and ankle joint angle compared with the hip joint angle in some cases. This could cause a shift in the pattern. In future research this could be avoided by analysing the hip, knee and ankle joint angle separately. The third problem that could be occurred was a methodological problem. The subjects were free in their choice of walking speed; this results in different walking speeds and different cycle frequencies within and between the different trials of a subjects. In the study of Murray et al. (1964) the cycle time was controlled by use of a metronome, which makes equal cycle times for all trial of each subject. Especially the knee rotation pattern could be affected by different walking speeds or cycle times (Frigo & Tesio 1986).

Rebecca & Oatis (1995) made a summary of studies, which have obtained hip, knee and ankle rotations. They looked at differences in the maximal and minimal attained joint angles in the walking cycle between studies. They found only small differences, what indicate that the joint angles in the different studies were almost similar.

The results form the follow-up tests for the time average hip, knee and ankle joint angles showed more significant differences between subjects for the time average hip joint angle than for the time average knee and ankle joint angles. This result makes the time average hip joint angle better for identification purposes than the time average knee and ankle joint angles.

Frontal

There are significant differences between subjects for the left and right thigh angle. For the left thigh angle more subjects differ significant from each other than for the right thigh angle (table 7 and 13). This indicates that the left thigh angle is rather better for identification purposes than the left thigh angle. A possible explanation for this finding will be discussed later in the transversal view.

Transversal

There are a lot of significant differences between subjects for the left and right foot angle. The left foot angle has showed more significant differences between subjects than the right foot angle (table 11 and 13). When all angles for the left and right foot are compared. The left angle is larger (28.6 º)(more in-toeing) than the right foot angle (23.8 º). Murray et al. (1964) also found differences in left and right foot. But there was not mentioned if the differences in foot angle were in both directions, the left foot angle larger than the right foot angle or vice-versa. In the study of Hills & Parker (1991) a comparison of the foot angle among obese and normal children was made. The obese children had more out-toeing than the normal subjects. Probably caused by stabilizing problems. An explanation for the difference in foot angle between the left and the right foot could be caused by the fact that the subject always turned to the right after the piece of strait walking. It could be that for turning to the right there is more out-toeing of the right foot and more in-toeing of the left foot for the needed stability. It could be that the piece of straight walking was to short and has to be longer to reduce the turning effect. Another explanation is that the attached markers on the left and right foot are not placed exactly symmetrical. This explanation is less probable, because in all cases the left foot angle is larger than the right foot angle. If there was some variety in the marker position on the left and the right foot, the right foot angle should have been larger in some trials than the left foot angle.

The same pattern could be seen in the thigh angle in the transversal view. The right thigh angle is larger than the left thigh angle. Turning to the right could also cause hanging over to the right.

The intra and inter individual correlation coefficients of the trunk rotation pattern were high. This indicates that there is little variation in the trunk rotation pattern. The trunk rotation is for stabilizing purposes and is out-phase with the pelvic rotation (Rose & Gamble 1994).

Spatial-temporal parameters

The step length is the best spatial-temporal parameter for recognition (table 9 and 13). In the study of Murray et al. (1964) differences in step length were only found by large age differences. The results of Murray et al. (1964) could be explained by the fact that the subjects in this study were restricted to walk with a constant cadence. A constant cadence could alter the step length (Gary 1990). Rose & Gamble (1994) stated that only step length could be used as gait parameter if walking speed is freely chosen.

For the other spatial-temporal parameters just a few significant differences between subjects were found. This indicates that only the extreme values significantly differ from each other. This makes the walking speed, cycle time and step width not suitable for identification purposes. This agrees with findings of Murray et al. (1964), who found no differences in step width between subjects.

Time-lapse video

When time-lapse video is used less images are available. If the best identification parameters (time average hip joint angle (α_m), foot angle (δ) and step length) are analysed in the time-lapse video, then images have to be available at a specific time. For example to obtain the foot angle, the foot has to stand motion less on the ground and for the step length one image with the left foot and one image with the right foot on the ground are necessary. The lower the sample frequency, the lower is the chance that an image is presented in which the foot stand motionless at the ground.

The time average hip joint angle asked for a sequence of images otherwise no average could be calculated. This study indicates that a sample frequency of 12.5 Hz is enough for identification on the time average hip joint angle. So these parameters could also be used in time-lapse video when the appropriate images are available.

Camera positions

From this study a recommendation for the best camera position could be made for gait recognition. The best position for the camera is to place it that way that the person in the transversal aspect could be filmed. With this camera view step length and foot angle could be filmed, which were two good recognition parameters. A sagittal camera view could also be used but this has only the time average hip joint angle as good recognition parameter.

Application of this study

In practice

The in practice situation is different from the laboratorial situation used in this study. It is impossible to use the same method of this study for the in practice situation. In this study each subjects perform seven trials from which the mean is calculated. In the in practice situation only one trial is available. This makes it impossible to look at intra individual differences. The subjects wore markers, but in case of bank robberies the robber would not. That would make it more complicated or even impossible to obtain joint positions. The subjects walked straightforward with their favourite walking speed. In practice situations walking people will make curves and speed-up or slowing-down their walking speed, what alters the gait pattern that should be used in straightforward walking with the favourite walking speed. The camera position in the in practice situation is most of the times not right angled at the movement direction, what makes it difficult to obtain body positions.

Further research has to focus if it is also possible to use foot angle, time average hip joint angle and step length in a less controlled setting. For example with clothing and without the use of markers.

Conclusions

The results of the present study have indicated that gait parameters could be used for identification purposes in laboratorial settings. Especially foot angle, step length and time average hip joint angle are good for identification purposes in laboratorial settings. To obtain these parameters a transversal and sagittal camera view is necessary. The time average hip joint angle obtained with a 12.5 Hz sample frequency could also be used for identification purposes.

To answer the question if these gait parameters could also be used in practice further research is necessary to the effect of wearing clothing and shoes, the absence of markers.

Appendix

Sagittal

subject	hip	knee	ankle
1	0.9880	0.9158	0.8687
2	0.9920	0.7689	0.8967
3	0.9878	0.9225	0.4860
4	0.9903	0.9099	0.9578
5	0.9879	0.6278	0.4181
6	0.9904	0.5526	0.7358
7	0.9934	0.9623	0.7819
8	0.9900	0.6788	0.5999
9	0.9875	0.9567	0.8394
10	0.9888	0.7474	0.5689
11	0.9900	0.7865	0.7006

A1. This table presents all mean correlation coefficients for the 7 trials within the subject for the hip, knee and ankle joint.

Subjects	1	2	3	4	5	6	7	8	9	10
1
2	0.9904
3	0.9876	0.9830
4	0.9790	0.9820	0.9757
5	0.9890	0.9876	0.9858	0.9871
6	0.9842	0.9832	0.9857	0.9757	0.9835
7	0.9758	0.9803	0.9792	0.9727	0.9768	0.9852
8	0.9798	0.9775	0.9847	0.9746	0.9802	0.9814	0.9870
9	0.9848	0.9834	0.9859	0.9828	0.9858	0.9782	0.9839	0.9892
10	0.9846	0.9771	0.9858	0.9785	0.9833	0.9814	0.9804	0.9889	0.9847
11	0.9684	0.9643	0.9771	0.9583	0.9688	0.9812	0.9855	0.9867	0.9767	0.9838

A2. This table presents all mean correlation coefficients between the subjects for the hip rotation pattern.

Subjects	1	2	3	4	5	6	7	8	9	10
1
2	0.8643
3	0.8761	0.8449
4	0.7379	0.7517	0.8608
5	0.8182	0.6380	0.6790	0.5213
6	0.6928	0.7196	0.6631	0.5916	0.6956
7	0.9048	0.8687	0.9149	0.9238	0.7119	0.6723
8	0.2345	0.4833	0.3427	0.4407	0.5697	0.6442	0.3759
9	0.5223	0.6112	0.6740	0.7963	0.5642	0.7107	0.7415	0.7486
10	0.6289	0.6995	0.7510	0.8135	0.5836	0.6756	0.7755	0.7472	0.9370
11	0.8409	0.7839	0.8837	0.8688	0.7032	0.6980	0.9073	0.6354	0.7378	0.7046

A3. This table presents all mean correlation coefficients between the subjects for the knee rotation pattern.

Subjects	1	2	3	4	5	6	7	8	9	10
1
2	0.7534
3	0.7227	0.5867
4	0.9101	0.7787	0.4774
5	0.5541	0.6418	0.4354	0.6025
6	0.8251	0.7415	0.5142	0.8832	0.6157
7	0.21	0.2088	0.5037	0.2311	0.2428	0.3493
8	0.6806	0.5738	0.4703	0.7963	0.5757	0.5803	0.5064
9	0.8897	0.7557	0.4888	0.9242	0.6907	0.7451	0.291	0.6295
10	0.4326	0.5596	0.4724	0.541	0.5677	0.395	0.3736	0.4827	0.4175
11	0.812	0.7934	0.4733	0.8721	0.6496	0.7127	0.3608	0.6164	0.7716	0.6926

A4. This table presents all mean correlation coefficients between the subjects for the ankle rotation pattern.

Subjects	Hip in degrees (SD)	Knee in degrees (SD)	Ankle in degrees (SD)
1	172.7 (±0.71) º	160.7 (±6.44) º	123.4 (±1.43) º
2	171.5 (±0.89) º	164.1 (±3.42) º	115.0 (±8.97) º
3	170.6 (±0.77) º	163.8 (±6.01) º	118.7 (±1.60) º
4	174.5 (±0.60) º	170.4 (±3.38) º	125.8 (±1.08) º
5	171.2 (±0.90) º	156.7 (±9.66) º	118.7 (±1.21) º
6	175.7 (±0.94) º	166.9 (±5.58) º	124.1 (±1.75) º
7	175.3 (±0.92) º	164.8 (±5.87) º	121.9 (±0.93) º
8	171.5 (±0.47) º	166.1 (±3.38) º	127.0 (±1.19) º
9	164.8 (±0.55) º	164.8 (±0.68) º	125.4 (±0.87) º
10	169.7 (±1.14) º	166.0 (±7.61) º	127.5 (±1.41) º
11	171.2 (±0.48) º	165.6 (±3.54) º	126.3 (±1.54) º

A5. This table presents the mean hip, knee and ankle joint angle and the standard deviation for the 7 trials.

Subjects	1	2	3	4	5	6	7	8	9	10	11
1		0.5148	0.0070	0.1298	0.2093	0.0000	0.0006	0.5005	0.0000	0.0000	0.1648
2	0.9993		0.8975	0.0000	1.0000	0.0000	0.0000	1.0000	0.0000	0.0582	1.0000
3	0.9997	1.0000		0.0000	0.9922	0.0000	0.0000	0.9049	0.0000	0.8978	0.9964
4	0.4196	0.9245	0.8951		0.0000	0.6052	0.9300	0.0000	0.0000	0.0000	0.0000
5	0.9971	0.7924	0.8378	0.0376		0.0000	0.0000	1.0000	0.0000	0.2113	1.0000
6	0.9283	0.9999	0.9997	0.9992	0.3312		1.0000	0.0000	0.0000	0.0000	0.0000
7	0.9966	1.0000	1.0000	0.9652	0.6866	1.0000		0.0000	0.0000	0.0000	0.0000
8	0.9731	1.0000	1.0000	0.9950	0.4680	1.0000	1.0000		0.0000	0.0617	1.0000
9	0.9965	1.0000	1.0000	0.9656	0.6851	1.0000	1.0000	1.0000		0.0000	0.0000
10	0.9770	1.0000	1.0000	0.9938	0.4881	1.0000	1.0000	1.0000	1.0000		0.2636
11	0.9868	1.0000	1.0000	0.9882	0.5544	1.0000	1.0000	1.0000	1.0000	1.0000

A6. The results of the Scheffé follow-up test of the mean hip and knee joint angle. The upper triangle presents the results of the mean hip joint angle and the lower triangle the results of the mean knee joint angle. The bold numbers indicate a significant difference (p<0.05) between subjects.

subjects	1	2	3	4	5	6	7	8	9	10
1
2	0.0067
3	0.5771	0.8564
4	0.9925	0.0001	0.0510
5	0.5780	0.8558	1.0000	0.0511
6	1.0000	0.0017	0.3368	0.9997	0.3376
7	0.9999	0.0673	0.9440	0.8085	0.9443	0.9958
8	0.8839	0.0000	0.0085	1.0000	0.0085	0.9756	0.4469
9	0.9981	0.0001	0.0842	1.0000	0.0845	1.0000	0.8904	0.9999
10	0.7468	0.0000	0.0031	0.9996	0.0032	0.9160	0.2801	1.0000	0.9976
11	0.9725	0.0000	0.0263	1.0000	0.0264	0.9975	0.6787	1.0000	1.0000	1.0000

A7. The results of the Scheffé follow-up test of the mean ankle joint angle. The bold numbers indicate a significant difference (p<0.05) between subjects.

Frontal

	Left	Right
Subject	Mean (SD) in degrees	Mean (SD) in degrees
1	-5.6 (± 1.4) º	9.3 (± 1.7) º
2	-6.5 (± 2.4) º	9.9 (± 0.8) º
3	-8.7 (± 0.7) º	9.2 (± 0.6) º
4	-5.6 (± 0.6) º	7.4 (± 0.7) º
5	-7.2 (± 1.1) º	9.9 (± 1.2) º
6	-7.3 (± 0.9) º	7.9 (± 0.6) º
7	-5.1 (± 0.6) º	8.5 (± 0.9) º
8	-11.0 (± 0.5) º	11.0 (± 0.7) º
9	-8.1(± 0.8) º	9.0 (± 0.9) º
10	-6.7 (± 0.7) º	8.3 (± 0.9) º
11	-5.9 (± 0.7) º	8.5 (± 0.5) º

A8. The mean left and right thigh angle and standard deviation in degrees.

Subject	1	2	3	4	5	6	7	8	9	10	11
1		0.9987	1.0000	0.1238	0.9988	0.4927	0.9793	0.2706	1.0000	0.9055	0.9757
2	0.9928		0.9891	0.0069	1.0000	0.0667	0.5623	0.8561	0.9380	0.3408	0.5415
3	0.0086	0.2315		0.2310	0.9902	0.6797	0.9966	0.1498	1.0000	0.9714	0.9958
4	1.0000	0.9900	0.0073		0.0073	0.9999	0.8689	0.0000	0.4243	0.9660	0.8812
5	0.7131	0.9992	0.7898	0.6817		0.0698	0.5736	0.8487	0.9421	0.3507	0.5529
6	0.6318	0.9975	0.8524	0.5984	1.0000		0.9968	0.0001	0.8656	0.9999	0.9975
7	1.0000	0.8499	0.0008	1.0000	0.2927	0.2289		0.0062	0.9999	1.0000	1.0000
8	0.0000	0.0000	0.1518	0.0000	0.0002	0.0004	0.0000		0.0629	0.0018	0.0056
9	0.0786	0.6777	0.9999	0.0688	0.9896	0.9956	0.0108	0.0207		0.9967	0.9998
10	0.9705	1.0000	0.3627	0.9623	1.0000	0.9998	0.7195	0.0000	0.8181		1.0000
11	1.0000	0.9996	0.0262	1.0000	0.8857	0.8310	0.9982	0.0000	0.1793	0.9964

A9. The results of the Scheffé follow-up test of the right and the left thigh angle. The upper triangle presents the results of the right thigh angle and the lower triangle the results of the left thigh angle. The bold numbers indicate a significant difference (p<0.05) between subjects.

Transversal

Subject	Feet angle (left)	Feet angle (right)
1	-41.1 (±2.65) º	31.5 (±2.57) º
2	-23.6 (±1.66) º	21.5 (±1.50) º
3	-25.9 (±2.10) º	24.2 (±2.30) º
4	-33.8 (±1.91) º	29.5 (±3.14) º
5	-35.3 (±2.39) º	27.2 (±1.14) º
6	-29.8 (±1.89) º	21.9 (±1.93) º
7	-31.8 (±2.62) º	23.9 (±1.56) º
8	-16.9 (±2.61) º	13.7 (±1.82) º
9	-25.5 (±2.37) º	22.1 (±3.19) º
10	-32.2 (±2.92) º	29.2 (±2.65) º
11	-18.5 (±1.61) º	17.1 (±2.43) º

A10. The mean left and the right feet angle and the standard deviation.

Subject	1	2	3	4	5	6	7	8	9	10	11
1		0.0000	0.0000	0.9524	0.1212	0.0000	0.0000	0.0000	0.0000	0.8173	0.0000
2	0.0000		0.7562	0.0000	0.0066	1.0000	0.9004	0.0000	1.0000	0.0000	0.0558
3	0.0000	0.8433		0.0138	0.6888	0.8805	1.0000	0.0000	0.9169	0.0121	0.0000
4	0.0000	0.0000	0.0000		0.9494	0.0000	0.0081	0.0000	0.0000	1.0000	0.0000
5	0.0005	0.0000	0.0000	0.9903		0.0135	0.5637	0.0000	0.0168	0.9724	0.0000
6	0.0000	0.0002	0.1470	0.0842	0.0010		0.9649	0.0000	1.0000	0.0000	0.0158
7	0.0000	0.0000	0.0002	0.8872	0.1558	0.9393		0.0000	0.9797	0.0070	0.0001
8	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000		0.0000	0.0000	0.3725
9	0.0000	0.9655	1.0000	0.0000	0.0000	0.1023	0.0002	0.0000		0.0000	0.0070
10	0.0000	0.0000	0.0002	0.9876	0.4797	0.8621	1.0000	0.0000	0.0002		0.0000
11	0.0000	0.0067	0.0000	0.0000	0.0000	0.0000	0.0000	0.9850	0.0000	0.0000

A11. The results of the Scheffé follow-up test of the left and the right foot angle. The upper triangle presents the results of the right foot angle and the lower triangle the results of the left foot angle. The bold numbers indicate a significant difference (p<0.05) between subjects.

Subjects	correlation coefficient
1	0.9221
2	0.9599
3	0.8401
4	0.9654
5	0.9733
6	0.9106
7	0.9340
8	0.9429
9	0.9828
10	0.9852
11	0.9282

A12. This table presents all mean correlation coefficients within the subject for the trunk angle in the transversal aspect.

Subjects	1	2	3	4	5	6	7	8	9	10
1
2	0.934
3	0.9365	0.9145
4	0.9361	0.8682	0.8159
5	0.9419	0.9323	0.8527	0.9773
6	0.9265	0.9328	0.9051	0.9456	0.9527
7	0.9423	0.9471	0.8435	0.9547	0.9542	0.9484
8	0.9252	0.8762	0.8001	0.9552	0.9482	0.9412	0.9372
9	0.9398	0.9706	0.9105	0.8805	0.9012	0.9445	0.9549	0.8153
10	0.9723	0.9632	0.9109	0.9372	0.9499	0.9386	0.9567	0.8865	0.9678
11	0.9179	0.9358	0.9222	0.88	0.9075	0.9134	0.9158	0.8079	0.9463	0.9524

A13. This table presents all mean correlation coefficients between the subjects for the trunk angle.

Subject	Step length	Step width	Cycle duration	Walking speed
	Mean (sd) in mm	Mean (sd) in mm	Mean (sd) in s	Mean (sd) in m/s
1	766 (±13.7)	214 (±30.0)	0.93 (±0.03)	1.65 (±0.08)
2	755 (±17.7)	260 (±9.0)	0.98 (±0.08)	1.55 (±0.13)
3	924 (±16.0)	286 (±34.3)	0.94 (±0.07)	1.98 (±0.17)
4	793 (±16.1)	236 (±20.0)	0.96 (±0.05)	1.66 (±0.08)
5	735 (±13.9)	243 (±14.8)	1.03 (±0.05)	1.42 (±0.07)
6	827 (±21.6)	270 (±34.4)	1.07 (±0.06)	1.54 (±0.11)
7	784 (±13.9)	284 (±17.5)	0.88 (±0.04)	1.79 (±0.08)
8	795 (±15.1)	253 (±11.8)	0.98 (±0.07)	1.63 (±0.14)
9	751 (±26.8)	274 (±16.6)	0.95 (±0.04)	1.58 (±0.07)
10	765 (±14.7)	243 (±18.6)	1.06 (±0.04)	1.45 (±0.09)
11	734 (±17.3)	252 (±15.1)	0.97 (±0.05)	1.51 (±0.09)

A14. The spatial-temporal data.

Subjects	1	2	3	4	5	6	7	8	9	10	11
1		0.9989	0.0000	0.5630	0.3337	0.0002	0.9579	0.4763	0.9860	1.0000	0.3079
2	0.1391		0.0000	0.0935	0.8930	0.0000	0.4818	0.0665	1.0000	0.9995	0.8756
3	0.0004	0.8905		0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000
4	0.9661	0.9208	0.0669		0.0002	0.2815	0.9997	1.0000	0.0359	0.5123	0.0002
5	0.7902	0.9945	0.2253	1.0000		0.0000	0.0056	0.0001	0.9754	0.3786	1.0000
6	0.0245	1.0000	0.9957	0.5901	0.8773		0.0376	0.3542	0.0000	0.0001	0.0000
7	0.0008	0.9360	1.0000	0.0979	0.2981	0.9987		0.9988	0.2731	0.9416	0.0048
8	0.3677	1.0000	0.6287	0.9935	1.0000	0.9955	0.7210		0.0243	0.4271	0.0001
9	0.0104	0.9993	0.9996	0.4132	0.7448	1.0000	0.9999	0.9766		0.9912	0.9690
10	0.7997	0.9938	0.2172	1.0000	1.0000	0.8701	0.2885	0.9999	0.7343		0.3511
11	0.3992	1.0000	0.5946	0.9955	1.0000	0.9936	0.6893	1.0000	0.9696	1.0000

A15. The results of the Scheffé follow-up test of the step length and the step width. The upper triangle presents the results of the step length and the lower triangle the results of the step width. The bold numbers indicate a significant difference (p<0.05) between subjects.

Subjects	1	2	3	4	5	6	7	8	9	10	11
1		0.9839	1.0000	0.9998	0.2388	0.0128	0.9839	0.9839	0.9999	0.0534	0.9939
2	0.9758		0.9981	1.0000	0.9487	0.3652	0.3652	1.0000	1.0000	0.6700	1.0000
3	0.0014	0.0000		1.0000	0.4133	0.0340	0.9294	0.9981	1.0000	0.1202	0.9996
4	1.0000	0.9555	0.0023		0.7186	0.1202	0.7186	1.0000	1.0000	0.3198	1.0000
5	0.1040	0.8511	0.0000	0.0752		0.9965	0.0058	0.9487	0.6700	1.0000	0.9057
6	0.9512	1.0000	0.0000	0.9187	0.9082		0.0001	0.3652	0.0992	1.0000	0.2776
7	0.8440	0.1000	0.3236	0.8955	0.0002	0.0681		0.3652	0.7643	0.0006	0.4636
8	1.0000	0.9941	0.0006	1.0000	0.1796	0.9849	0.7184		1.0000	0.6700	1.0000
9	0.9965	1.0000	0.0000	0.9915	0.6834	1.0000	0.2027	0.9996		0.2776	1.0000
10	0.2518	0.9677	0.0000	0.1945	1.0000	0.9852	0.0009	0.3816	0.8884		0.5674
11	0.8002	1.0000	0.0000	0.7292	0.9865	1.0000	0.0204	0.9018	0.9995	0.9994
Subjects	1	2	3	4	5	6	7	8	9	10	11

A16. The results of the Scheffé follow-up test of the cycle time and the walking speed. The upper triangle presents the results of the cycle time and the lower triangle the results of the walking speed. The bold numbers indicate a significant difference (p<0.05) between subjects.

Time-lapse video

12.5 Hz	50 Hz
172.9 (±1.08) º	172.7 (±0.71) º
171.7 (±1.28) º	171.5 (±0.89) º
170.5 (±1.04) º	170.6 (±0.77) º
174.1 (±0.64) º	174.5 (±0.60) º
171.2 (±1.44) º	171.2 (±0.90) º
176.0 (±1.33) º	175.7 (±0.94) º
175.8 (±0.75) º	175.3 (±0.92) º
171.2 (±0.74) º	171.5 (±0.47) º
164.5 (±0.70) º	164.8 (±0.55) º
169.5 (±1.25) º	169.7 (±1.14) º
171.1 (±0.60) º	171.2 (±0.48) º

A17. The mean hip joint angle with a sample frequency of 12.5 and 50 Hz in degrees and the standard deviation.

References

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Yamasaki, M., T. Sasaki & M. Torii (1991). Sex difference in the pattern of lower limb movement during treadmill walking. European Journal of Applied Physiology and Occupational Physiology. Vol. 62, p. 99-103.

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* This method for calculating the mean correlation coefficient is used of practical consideration. Possibly more advanced techniques should be applied.