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 (r²)
	Lowest r²	Highest r²
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 (r²)
	Lowest r²	Highest r²
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 (α_m)	165 º	176 º
Knee (β_m)	157 º	170 º
Ankle (γ_m)	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 (φ_l)

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

Contents

Abstract

Introduction

Methods

Subjects

Protocol

Sagittal view

Frontal view

Transversal view

Data analysis and statistics

Time-Lapse video

Results

Kinematic parameters

Sagittal view

Frontal view